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! $Header: /home/cvsroot/LMDZ4/libf/dyn3d/ppm3d.F,v 1.1.1.1 2004/05/19 12:53:07 lmdzadmin Exp $ |
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cFrom lin@explorer.gsfc.nasa.gov Wed Apr 15 17:44:44 1998 |
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cDate: Wed, 15 Apr 1998 11:37:03 -0400 |
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cFrom: lin@explorer.gsfc.nasa.gov |
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cTo: Frederic.Hourdin@lmd.jussieu.fr |
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cSubject: 3D transport module of the GSFC CTM and GEOS GCM |
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|
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|
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cThis code is sent to you by S-J Lin, DAO, NASA-GSFC |
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|
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cNote: this version is intended for machines like CRAY |
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C-90. No multitasking directives implemented. |
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|
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|
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C ******************************************************************** |
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C |
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C TransPort Core for Goddard Chemistry Transport Model (G-CTM), Goddard |
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C Earth Observing System General Circulation Model (GEOS-GCM), and Data |
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C Assimilation System (GEOS-DAS). |
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C |
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C ******************************************************************** |
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C |
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C Purpose: given horizontal winds on a hybrid sigma-p surfaces, |
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C one call to tpcore updates the 3-D mixing ratio |
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C fields one time step (NDT). [vertical mass flux is computed |
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C internally consistent with the discretized hydrostatic mass |
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C continuity equation of the C-Grid GEOS-GCM (for IGD=1)]. |
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C |
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C Schemes: Multi-dimensional Flux Form Semi-Lagrangian (FFSL) scheme based |
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C on the van Leer or PPM. |
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C (see Lin and Rood 1996). |
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C Version 4.5 |
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C Last modified: Dec. 5, 1996 |
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C Major changes from version 4.0: a more general vertical hybrid sigma- |
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C pressure coordinate. |
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C Subroutines modified: xtp, ytp, fzppm, qckxyz |
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C Subroutines deleted: vanz |
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C |
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C Author: Shian-Jiann Lin |
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C mail address: |
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C Shian-Jiann Lin* |
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C Code 910.3, NASA/GSFC, Greenbelt, MD 20771 |
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C Phone: 301-286-9540 |
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C E-mail: lin@dao.gsfc.nasa.gov |
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C |
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C *affiliation: |
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C Joint Center for Earth Systems Technology |
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C The University of Maryland Baltimore County |
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C NASA - Goddard Space Flight Center |
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C References: |
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C |
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C 1. Lin, S.-J., and R. B. Rood, 1996: Multidimensional flux form semi- |
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C Lagrangian transport schemes. Mon. Wea. Rev., 124, 2046-2070. |
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C |
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C 2. Lin, S.-J., W. C. Chao, Y. C. Sud, and G. K. Walker, 1994: A class of |
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C the van Leer-type transport schemes and its applications to the moist- |
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C ure transport in a General Circulation Model. Mon. Wea. Rev., 122, |
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C 1575-1593. |
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C |
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C ****6***0*********0*********0*********0*********0*********0**********72 |
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C |
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subroutine ppm3d(IGD,Q,PS1,PS2,U,V,W,NDT,IORD,JORD,KORD,NC,IMR, |
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& JNP,j1,NLAY,AP,BP,PT,AE,fill,dum,Umax) |
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|
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c implicit none |
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|
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c rajout de déclarations |
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c integer Jmax,kmax,ndt0,nstep,k,j,i,ic,l,js,jn,imh,iad,jad,krd |
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c integer iu,iiu,j2,jmr,js0,jt |
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c real dtdy,dtdy5,rcap,iml,jn0,imjm,pi,dl,dp |
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c real dt,cr1,maxdt,ztc,d5,sum1,sum2,ru |
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C |
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C ******************************************************************** |
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C |
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C ============= |
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C INPUT: |
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C ============= |
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C |
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C Q(IMR,JNP,NLAY,NC): mixing ratios at current time (t) |
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C NC: total number of constituents |
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C IMR: first dimension (E-W); number of Grid intervals in E-W is IMR |
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C JNP: 2nd dimension (N-S); number of Grid intervals in N-S is JNP-1 |
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C NLAY: 3rd dimension (number of layers); vertical index increases from 1 at |
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C the model top to NLAY near the surface (see fig. below). |
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C It is assumed that 6 <= NLAY <= JNP (for dynamic memory allocation) |
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C |
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C PS1(IMR,JNP): surface pressure at current time (t) |
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C PS2(IMR,JNP): surface pressure at mid-time-level (t+NDT/2) |
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C PS2 is replaced by the predicted PS (at t+NDT) on output. |
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C Note: surface pressure can have any unit or can be multiplied by any |
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C const. |
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C |
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C The pressure at layer edges are defined as follows: |
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C |
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C p(i,j,k) = AP(k)*PT + BP(k)*PS(i,j) (1) |
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C |
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C Where PT is a constant having the same unit as PS. |
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C AP and BP are unitless constants given at layer edges |
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C defining the vertical coordinate. |
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C BP(1) = 0., BP(NLAY+1) = 1. |
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C The pressure at the model top is PTOP = AP(1)*PT |
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C |
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C For pure sigma system set AP(k) = 1 for all k, PT = PTOP, |
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C BP(k) = sige(k) (sigma at edges), PS = Psfc - PTOP. |
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C |
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C Note: the sigma-P coordinate is a subset of Eq. 1, which in turn |
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C is a subset of the following even more general sigma-P-thelta coord. |
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C currently under development. |
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C p(i,j,k) = (AP(k)*PT + BP(k)*PS(i,j))/(D(k)-C(k)*TE**(-1/kapa)) |
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C |
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C ///////////////////////////////// |
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C / \ ------------- PTOP -------------- AP(1), BP(1) |
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C | |
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C delp(1) | ........... Q(i,j,1) ............ |
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C | |
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C W(1) \ / --------------------------------- AP(2), BP(2) |
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C |
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C |
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C |
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C W(k-1) / \ --------------------------------- AP(k), BP(k) |
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C | |
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C delp(K) | ........... Q(i,j,k) ............ |
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C | |
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C W(k) \ / --------------------------------- AP(k+1), BP(k+1) |
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C |
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C |
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C |
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C / \ --------------------------------- AP(NLAY), BP(NLAY) |
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C | |
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C delp(NLAY) | ........... Q(i,j,NLAY) ......... |
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C | |
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C W(NLAY)=0 \ / ------------- surface ----------- AP(NLAY+1), BP(NLAY+1) |
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C ////////////////////////////////// |
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C |
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C U(IMR,JNP,NLAY) & V(IMR,JNP,NLAY):winds (m/s) at mid-time-level (t+NDT/2) |
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C U and V may need to be polar filtered in advance in some cases. |
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C |
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C IGD: grid type on which winds are defined. |
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C IGD = 0: A-Grid [all variables defined at the same point from south |
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C pole (j=1) to north pole (j=JNP) ] |
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C |
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C IGD = 1 GEOS-GCM C-Grid |
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C [North] |
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C |
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C V(i,j) |
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C | |
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C | |
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C | |
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C U(i-1,j)---Q(i,j)---U(i,j) [EAST] |
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C | |
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C | |
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C | |
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C V(i,j-1) |
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C |
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C U(i, 1) is defined at South Pole. |
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C V(i, 1) is half grid north of the South Pole. |
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C V(i,JMR) is half grid south of the North Pole. |
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C |
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C V must be defined at j=1 and j=JMR if IGD=1 |
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C V at JNP need not be given. |
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C |
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C NDT: time step in seconds (need not be constant during the course of |
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C the integration). Suggested value: 30 min. for 4x5, 15 min. for 2x2.5 |
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C (Lat-Lon) resolution. Smaller values are recommanded if the model |
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C has a well-resolved stratosphere. |
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C |
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C J1 defines the size of the polar cap: |
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C South polar cap edge is located at -90 + (j1-1.5)*180/(JNP-1) deg. |
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C North polar cap edge is located at 90 - (j1-1.5)*180/(JNP-1) deg. |
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C There are currently only two choices (j1=2 or 3). |
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C IMR must be an even integer if j1 = 2. Recommended value: J1=3. |
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C |
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C IORD, JORD, and KORD are integers controlling various options in E-W, N-S, |
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C and vertical transport, respectively. Recommended values for positive |
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C definite scalars: IORD=JORD=3, KORD=5. Use KORD=3 for non- |
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C positive definite scalars or when linear correlation between constituents |
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C is to be maintained. |
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C |
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C _ORD= |
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C 1: 1st order upstream scheme (too diffusive, not a useful option; it |
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C can be used for debugging purposes; this is THE only known "linear" |
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C monotonic advection scheme.). |
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C 2: 2nd order van Leer (full monotonicity constraint; |
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C see Lin et al 1994, MWR) |
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C 3: monotonic PPM* (slightly improved PPM of Collela & Woodward 1984) |
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C 4: semi-monotonic PPM (same as 3, but overshoots are allowed) |
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C 5: positive-definite PPM (constraint on the subgrid distribution is |
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C only strong enough to prevent generation of negative values; |
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C both overshoots & undershoots are possible). |
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C 6: un-constrained PPM (nearly diffusion free; slightly faster but |
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C positivity not quaranteed. Use this option only when the fields |
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C and winds are very smooth). |
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C |
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C *PPM: Piece-wise Parabolic Method |
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C |
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C Note that KORD <=2 options are no longer supported. DO not use option 4 or 5. |
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C for non-positive definite scalars (such as Ertel Potential Vorticity). |
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C |
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C The implicit numerical diffusion decreases as _ORD increases. |
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C The last two options (ORDER=5, 6) should only be used when there is |
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C significant explicit diffusion (such as a turbulence parameterization). You |
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C might get dispersive results otherwise. |
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C No filter of any kind is applied to the constituent fields here. |
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C |
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C AE: Radius of the sphere (meters). |
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C Recommended value for the planet earth: 6.371E6 |
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C |
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C fill(logical): flag to do filling for negatives (see note below). |
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C |
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C Umax: Estimate (upper limit) of the maximum U-wind speed (m/s). |
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C (220 m/s is a good value for troposphere model; 280 m/s otherwise) |
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C |
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C ============= |
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C Output |
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C ============= |
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C |
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C Q: mixing ratios at future time (t+NDT) (original values are over-written) |
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C W(NLAY): large-scale vertical mass flux as diagnosed from the hydrostatic |
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C relationship. W will have the same unit as PS1 and PS2 (eg, mb). |
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C W must be divided by NDT to get the correct mass-flux unit. |
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C The vertical Courant number C = W/delp_UPWIND, where delp_UPWIND |
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C is the pressure thickness in the "upwind" direction. For example, |
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C C(k) = W(k)/delp(k) if W(k) > 0; |
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C C(k) = W(k)/delp(k+1) if W(k) < 0. |
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C ( W > 0 is downward, ie, toward surface) |
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C PS2: predicted PS at t+NDT (original values are over-written) |
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C |
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C ******************************************************************** |
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C NOTES: |
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C This forward-in-time upstream-biased transport scheme reduces to |
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C the 2nd order center-in-time center-in-space mass continuity eqn. |
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C if Q = 1 (constant fields will remain constant). This also ensures |
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C that the computed vertical velocity to be identical to GEOS-1 GCM |
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C for on-line transport. |
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C |
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C A larger polar cap is used if j1=3 (recommended for C-Grid winds or when |
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C winds are noisy near poles). |
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C |
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C Flux-Form Semi-Lagrangian transport in the East-West direction is used |
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C when and where Courant number is greater than one. |
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C |
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C The user needs to change the parameter Jmax or Kmax if the resolution |
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C is greater than 0.5 deg in N-S or 150 layers in the vertical direction. |
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C (this TransPort Core is otherwise resolution independent and can be used |
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C as a library routine). |
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C |
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C PPM is 4th order accurate when grid spacing is uniform (x & y); 3rd |
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C order accurate for non-uniform grid (vertical sigma coord.). |
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C |
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C Time step is limitted only by transport in the meridional direction. |
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C (the FFSL scheme is not implemented in the meridional direction). |
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C |
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C Since only 1-D limiters are applied, negative values could |
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C potentially be generated when large time step is used and when the |
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C initial fields contain discontinuities. |
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C This does not necessarily imply the integration is unstable. |
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C These negatives are typically very small. A filling algorithm is |
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C activated if the user set "fill" to be true. |
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C |
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C The van Leer scheme used here is nearly as accurate as the original PPM |
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C due to the use of a 4th order accurate reference slope. The PPM imple- |
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C mented here is an improvement over the original and is also based on |
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C the 4th order reference slope. |
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C |
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C ****6***0*********0*********0*********0*********0*********0**********72 |
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C |
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C User modifiable parameters |
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C |
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parameter (Jmax = 361, kmax = 150) |
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C |
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C ****6***0*********0*********0*********0*********0*********0**********72 |
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C |
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C Input-Output arrays |
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C |
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|
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real Q(IMR,JNP,NLAY,NC),PS1(IMR,JNP),PS2(IMR,JNP), |
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& U(IMR,JNP,NLAY),V(IMR,JNP,NLAY),AP(NLAY+1), |
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& BP(NLAY+1),W(IMR,JNP,NLAY),NDT,val(NLAY),Umax |
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integer IGD,IORD,JORD,KORD,NC,IMR,JNP,j1,NLAY,AE |
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integer IMRD2 |
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real PT |
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logical cross, fill, dum |
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C |
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C Local dynamic arrays |
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C |
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real CRX(IMR,JNP),CRY(IMR,JNP),xmass(IMR,JNP),ymass(IMR,JNP), |
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& fx1(IMR+1),DPI(IMR,JNP,NLAY),delp1(IMR,JNP,NLAY), |
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& WK1(IMR,JNP,NLAY),PU(IMR,JNP),PV(IMR,JNP),DC2(IMR,JNP), |
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& delp2(IMR,JNP,NLAY),DQ(IMR,JNP,NLAY,NC),VA(IMR,JNP), |
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& UA(IMR,JNP),qtmp(-IMR:2*IMR) |
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C |
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C Local static arrays |
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C |
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real DTDX(Jmax), DTDX5(Jmax), acosp(Jmax), |
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& cosp(Jmax), cose(Jmax), DAP(kmax),DBK(Kmax) |
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data NDT0, NSTEP /0, 0/ |
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data cross /.true./ |
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SAVE DTDY, DTDY5, RCAP, JS0, JN0, IML, |
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& DTDX, DTDX5, ACOSP, COSP, COSE, DAP,DBK |
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C |
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|
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JMR = JNP -1 |
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IMJM = IMR*JNP |
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j2 = JNP - j1 + 1 |
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NSTEP = NSTEP + 1 |
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C |
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C *********** Initialization ********************** |
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if(NSTEP.eq.1) then |
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c |
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write(6,*) '------------------------------------ ' |
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write(6,*) 'NASA/GSFC Transport Core Version 4.5' |
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write(6,*) '------------------------------------ ' |
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c |
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WRITE(6,*) 'IMR=',IMR,' JNP=',JNP,' NLAY=',NLAY,' j1=',j1 |
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WRITE(6,*) 'NC=',NC,IORD,JORD,KORD,NDT |
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C |
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C controles sur les parametres |
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if(NLAY.LT.6) then |
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write(6,*) 'NLAY must be >= 6' |
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stop |
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endif |
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if (JNP.LT.NLAY) then |
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write(6,*) 'JNP must be >= NLAY' |
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stop |
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endif |
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IMRD2=mod(IMR,2) |
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if (j1.eq.2.and.IMRD2.NE.0) then |
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write(6,*) 'if j1=2 IMR must be an even integer' |
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stop |
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endif |
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|
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C |
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if(Jmax.lt.JNP .or. Kmax.lt.NLAY) then |
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write(6,*) 'Jmax or Kmax is too small' |
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stop |
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endif |
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C |
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DO k=1,NLAY |
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DAP(k) = (AP(k+1) - AP(k))*PT |
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DBK(k) = BP(k+1) - BP(k) |
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ENDDO |
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C |
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PI = 4. * ATAN(1.) |
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DL = 2.*PI / float(IMR) |
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DP = PI / float(JMR) |
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C |
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if(IGD.eq.0) then |
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C Compute analytic cosine at cell edges |
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call cosa(cosp,cose,JNP,PI,DP) |
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else |
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C Define cosine consistent with GEOS-GCM (using dycore2.0 or later) |
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call cosc(cosp,cose,JNP,PI,DP) |
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endif |
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C |
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do 15 J=2,JMR |
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15 acosp(j) = 1. / cosp(j) |
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C |
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C Inverse of the Scaled polar cap area. |
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C |
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RCAP = DP / (IMR*(1.-COS((j1-1.5)*DP))) |
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acosp(1) = RCAP |
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acosp(JNP) = RCAP |
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endif |
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C |
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if(NDT0 .ne. NDT) then |
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DT = NDT |
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NDT0 = NDT |
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|
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if(Umax .lt. 180.) then |
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write(6,*) 'Umax may be too small!' |
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endif |
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CR1 = abs(Umax*DT)/(DL*AE) |
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MaxDT = DP*AE / abs(Umax) + 0.5 |
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write(6,*)'Largest time step for max(V)=',Umax,' is ',MaxDT |
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if(MaxDT .lt. abs(NDT)) then |
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write(6,*) 'Warning!!! NDT maybe too large!' |
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endif |
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C |
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if(CR1.ge.0.95) then |
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JS0 = 0 |
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JN0 = 0 |
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IML = IMR-2 |
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ZTC = 0. |
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else |
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ZTC = acos(CR1) * (180./PI) |
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C |
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JS0 = float(JMR)*(90.-ZTC)/180. + 2 |
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JS0 = max(JS0, J1+1) |
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IML = min(6*JS0/(J1-1)+2, 4*IMR/5) |
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JN0 = JNP-JS0+1 |
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endif |
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C |
| 396 |
C |
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do J=2,JMR |
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DTDX(j) = DT / ( DL*AE*COSP(J) ) |
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|
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DTDX5(j) = 0.5*DTDX(j) |
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enddo |
| 402 |
C |
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|
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DTDY = DT /(AE*DP) |
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DTDY5 = 0.5*DTDY |
| 406 |
C |
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endif |
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C |
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C *********** End Initialization ********************** |
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C |
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C delp = pressure thickness: the psudo-density in a hydrostatic system. |
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do k=1,NLAY |
| 413 |
do j=1,JNP |
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do i=1,IMR |
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delp1(i,j,k)=DAP(k)+DBK(k)*PS1(i,j) |
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delp2(i,j,k)=DAP(k)+DBK(k)*PS2(i,j) |
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enddo |
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enddo |
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enddo |
| 420 |
|
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C |
| 422 |
if(j1.ne.2) then |
| 423 |
DO 40 IC=1,NC |
| 424 |
DO 40 L=1,NLAY |
| 425 |
DO 40 I=1,IMR |
| 426 |
Q(I, 2,L,IC) = Q(I, 1,L,IC) |
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40 Q(I,JMR,L,IC) = Q(I,JNP,L,IC) |
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endif |
| 429 |
C |
| 430 |
C Compute "tracer density" |
| 431 |
DO 550 IC=1,NC |
| 432 |
DO 44 k=1,NLAY |
| 433 |
DO 44 j=1,JNP |
| 434 |
DO 44 i=1,IMR |
| 435 |
44 DQ(i,j,k,IC) = Q(i,j,k,IC)*delp1(i,j,k) |
| 436 |
550 continue |
| 437 |
C |
| 438 |
do 1500 k=1,NLAY |
| 439 |
C |
| 440 |
if(IGD.eq.0) then |
| 441 |
C Convert winds on A-Grid to Courant number on C-Grid. |
| 442 |
call A2C(U(1,1,k),V(1,1,k),IMR,JMR,j1,j2,CRX,CRY,dtdx5,DTDY5) |
| 443 |
else |
| 444 |
C Convert winds on C-grid to Courant number |
| 445 |
do 45 j=j1,j2 |
| 446 |
do 45 i=2,IMR |
| 447 |
45 CRX(i,J) = dtdx(j)*U(i-1,j,k) |
| 448 |
|
| 449 |
C |
| 450 |
do 50 j=j1,j2 |
| 451 |
50 CRX(1,J) = dtdx(j)*U(IMR,j,k) |
| 452 |
C |
| 453 |
do 55 i=1,IMR*JMR |
| 454 |
55 CRY(i,2) = DTDY*V(i,1,k) |
| 455 |
endif |
| 456 |
C |
| 457 |
C Determine JS and JN |
| 458 |
JS = j1 |
| 459 |
JN = j2 |
| 460 |
C |
| 461 |
do j=JS0,j1+1,-1 |
| 462 |
do i=1,IMR |
| 463 |
if(abs(CRX(i,j)).GT.1.) then |
| 464 |
JS = j |
| 465 |
go to 2222 |
| 466 |
endif |
| 467 |
enddo |
| 468 |
enddo |
| 469 |
C |
| 470 |
2222 continue |
| 471 |
do j=JN0,j2-1 |
| 472 |
do i=1,IMR |
| 473 |
if(abs(CRX(i,j)).GT.1.) then |
| 474 |
JN = j |
| 475 |
go to 2233 |
| 476 |
endif |
| 477 |
enddo |
| 478 |
enddo |
| 479 |
2233 continue |
| 480 |
C |
| 481 |
if(j1.ne.2) then ! Enlarged polar cap. |
| 482 |
do i=1,IMR |
| 483 |
DPI(i, 2,k) = 0. |
| 484 |
DPI(i,JMR,k) = 0. |
| 485 |
enddo |
| 486 |
endif |
| 487 |
C |
| 488 |
C ******* Compute horizontal mass fluxes ************ |
| 489 |
C |
| 490 |
C N-S component |
| 491 |
do j=j1,j2+1 |
| 492 |
D5 = 0.5 * COSE(j) |
| 493 |
do i=1,IMR |
| 494 |
ymass(i,j) = CRY(i,j)*D5*(delp2(i,j,k) + delp2(i,j-1,k)) |
| 495 |
enddo |
| 496 |
enddo |
| 497 |
C |
| 498 |
do 95 j=j1,j2 |
| 499 |
DO 95 i=1,IMR |
| 500 |
95 DPI(i,j,k) = (ymass(i,j) - ymass(i,j+1)) * acosp(j) |
| 501 |
C |
| 502 |
C Poles |
| 503 |
sum1 = ymass(IMR,j1 ) |
| 504 |
sum2 = ymass(IMR,J2+1) |
| 505 |
do i=1,IMR-1 |
| 506 |
sum1 = sum1 + ymass(i,j1 ) |
| 507 |
sum2 = sum2 + ymass(i,J2+1) |
| 508 |
enddo |
| 509 |
C |
| 510 |
sum1 = - sum1 * RCAP |
| 511 |
sum2 = sum2 * RCAP |
| 512 |
do i=1,IMR |
| 513 |
DPI(i, 1,k) = sum1 |
| 514 |
DPI(i,JNP,k) = sum2 |
| 515 |
enddo |
| 516 |
C |
| 517 |
C E-W component |
| 518 |
C |
| 519 |
do j=j1,j2 |
| 520 |
do i=2,IMR |
| 521 |
PU(i,j) = 0.5 * (delp2(i,j,k) + delp2(i-1,j,k)) |
| 522 |
enddo |
| 523 |
enddo |
| 524 |
C |
| 525 |
do j=j1,j2 |
| 526 |
PU(1,j) = 0.5 * (delp2(1,j,k) + delp2(IMR,j,k)) |
| 527 |
enddo |
| 528 |
C |
| 529 |
do 110 j=j1,j2 |
| 530 |
DO 110 i=1,IMR |
| 531 |
110 xmass(i,j) = PU(i,j)*CRX(i,j) |
| 532 |
C |
| 533 |
DO 120 j=j1,j2 |
| 534 |
DO 120 i=1,IMR-1 |
| 535 |
120 DPI(i,j,k) = DPI(i,j,k) + xmass(i,j) - xmass(i+1,j) |
| 536 |
C |
| 537 |
DO 130 j=j1,j2 |
| 538 |
130 DPI(IMR,j,k) = DPI(IMR,j,k) + xmass(IMR,j) - xmass(1,j) |
| 539 |
C |
| 540 |
DO j=j1,j2 |
| 541 |
do i=1,IMR-1 |
| 542 |
UA(i,j) = 0.5 * (CRX(i,j)+CRX(i+1,j)) |
| 543 |
enddo |
| 544 |
enddo |
| 545 |
C |
| 546 |
DO j=j1,j2 |
| 547 |
UA(imr,j) = 0.5 * (CRX(imr,j)+CRX(1,j)) |
| 548 |
enddo |
| 549 |
ccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
| 550 |
c Rajouts pour LMDZ.3.3 |
| 551 |
ccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
| 552 |
do i=1,IMR |
| 553 |
do j=1,JNP |
| 554 |
VA(i,j)=0. |
| 555 |
enddo |
| 556 |
enddo |
| 557 |
|
| 558 |
do i=1,imr*(JMR-1) |
| 559 |
VA(i,2) = 0.5*(CRY(i,2)+CRY(i,3)) |
| 560 |
enddo |
| 561 |
C |
| 562 |
if(j1.eq.2) then |
| 563 |
IMH = IMR/2 |
| 564 |
do i=1,IMH |
| 565 |
VA(i, 1) = 0.5*(CRY(i,2)-CRY(i+IMH,2)) |
| 566 |
VA(i+IMH, 1) = -VA(i,1) |
| 567 |
VA(i, JNP) = 0.5*(CRY(i,JNP)-CRY(i+IMH,JMR)) |
| 568 |
VA(i+IMH,JNP) = -VA(i,JNP) |
| 569 |
enddo |
| 570 |
VA(IMR,1)=VA(1,1) |
| 571 |
VA(IMR,JNP)=VA(1,JNP) |
| 572 |
endif |
| 573 |
C |
| 574 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
| 575 |
do 1000 IC=1,NC |
| 576 |
C |
| 577 |
do i=1,IMJM |
| 578 |
wk1(i,1,1) = 0. |
| 579 |
wk1(i,1,2) = 0. |
| 580 |
enddo |
| 581 |
C |
| 582 |
C E-W advective cross term |
| 583 |
do 250 j=J1,J2 |
| 584 |
if(J.GT.JS .and. J.LT.JN) GO TO 250 |
| 585 |
C |
| 586 |
do i=1,IMR |
| 587 |
qtmp(i) = q(i,j,k,IC) |
| 588 |
enddo |
| 589 |
C |
| 590 |
do i=-IML,0 |
| 591 |
qtmp(i) = q(IMR+i,j,k,IC) |
| 592 |
qtmp(IMR+1-i) = q(1-i,j,k,IC) |
| 593 |
enddo |
| 594 |
C |
| 595 |
DO 230 i=1,IMR |
| 596 |
iu = UA(i,j) |
| 597 |
ru = UA(i,j) - iu |
| 598 |
iiu = i-iu |
| 599 |
if(UA(i,j).GE.0.) then |
| 600 |
wk1(i,j,1) = qtmp(iiu)+ru*(qtmp(iiu-1)-qtmp(iiu)) |
| 601 |
else |
| 602 |
wk1(i,j,1) = qtmp(iiu)+ru*(qtmp(iiu)-qtmp(iiu+1)) |
| 603 |
endif |
| 604 |
wk1(i,j,1) = wk1(i,j,1) - qtmp(i) |
| 605 |
230 continue |
| 606 |
250 continue |
| 607 |
C |
| 608 |
if(JN.ne.0) then |
| 609 |
do j=JS+1,JN-1 |
| 610 |
C |
| 611 |
do i=1,IMR |
| 612 |
qtmp(i) = q(i,j,k,IC) |
| 613 |
enddo |
| 614 |
C |
| 615 |
qtmp(0) = q(IMR,J,k,IC) |
| 616 |
qtmp(IMR+1) = q( 1,J,k,IC) |
| 617 |
C |
| 618 |
do i=1,imr |
| 619 |
iu = i - UA(i,j) |
| 620 |
wk1(i,j,1) = UA(i,j)*(qtmp(iu) - qtmp(iu+1)) |
| 621 |
enddo |
| 622 |
enddo |
| 623 |
endif |
| 624 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
| 625 |
C Contribution from the N-S advection |
| 626 |
do i=1,imr*(j2-j1+1) |
| 627 |
JT = float(J1) - VA(i,j1) |
| 628 |
wk1(i,j1,2) = VA(i,j1) * (q(i,jt,k,IC) - q(i,jt+1,k,IC)) |
| 629 |
enddo |
| 630 |
C |
| 631 |
do i=1,IMJM |
| 632 |
wk1(i,1,1) = q(i,1,k,IC) + 0.5*wk1(i,1,1) |
| 633 |
wk1(i,1,2) = q(i,1,k,IC) + 0.5*wk1(i,1,2) |
| 634 |
enddo |
| 635 |
C |
| 636 |
if(cross) then |
| 637 |
C Add cross terms in the vertical direction. |
| 638 |
if(IORD .GE. 2) then |
| 639 |
iad = 2 |
| 640 |
else |
| 641 |
iad = 1 |
| 642 |
endif |
| 643 |
C |
| 644 |
if(JORD .GE. 2) then |
| 645 |
jad = 2 |
| 646 |
else |
| 647 |
jad = 1 |
| 648 |
endif |
| 649 |
call xadv(IMR,JNP,j1,j2,wk1(1,1,2),UA,JS,JN,IML,DC2,iad) |
| 650 |
call yadv(IMR,JNP,j1,j2,wk1(1,1,1),VA,PV,W,jad) |
| 651 |
do j=1,JNP |
| 652 |
do i=1,IMR |
| 653 |
q(i,j,k,IC) = q(i,j,k,IC) + DC2(i,j) + PV(i,j) |
| 654 |
enddo |
| 655 |
enddo |
| 656 |
endif |
| 657 |
C |
| 658 |
call xtp(IMR,JNP,IML,j1,j2,JN,JS,PU,DQ(1,1,k,IC),wk1(1,1,2) |
| 659 |
& ,CRX,fx1,xmass,IORD) |
| 660 |
|
| 661 |
call ytp(IMR,JNP,j1,j2,acosp,RCAP,DQ(1,1,k,IC),wk1(1,1,1),CRY, |
| 662 |
& DC2,ymass,WK1(1,1,3),wk1(1,1,4),WK1(1,1,5),WK1(1,1,6),JORD) |
| 663 |
C |
| 664 |
1000 continue |
| 665 |
1500 continue |
| 666 |
C |
| 667 |
C ******* Compute vertical mass flux (same unit as PS) *********** |
| 668 |
C |
| 669 |
C 1st step: compute total column mass CONVERGENCE. |
| 670 |
C |
| 671 |
do 320 j=1,JNP |
| 672 |
do 320 i=1,IMR |
| 673 |
320 CRY(i,j) = DPI(i,j,1) |
| 674 |
C |
| 675 |
do 330 k=2,NLAY |
| 676 |
do 330 j=1,JNP |
| 677 |
do 330 i=1,IMR |
| 678 |
CRY(i,j) = CRY(i,j) + DPI(i,j,k) |
| 679 |
330 continue |
| 680 |
C |
| 681 |
do 360 j=1,JNP |
| 682 |
do 360 i=1,IMR |
| 683 |
C |
| 684 |
C 2nd step: compute PS2 (PS at n+1) using the hydrostatic assumption. |
| 685 |
C Changes (increases) to surface pressure = total column mass convergence |
| 686 |
C |
| 687 |
PS2(i,j) = PS1(i,j) + CRY(i,j) |
| 688 |
C |
| 689 |
C 3rd step: compute vertical mass flux from mass conservation principle. |
| 690 |
C |
| 691 |
W(i,j,1) = DPI(i,j,1) - DBK(1)*CRY(i,j) |
| 692 |
W(i,j,NLAY) = 0. |
| 693 |
360 continue |
| 694 |
C |
| 695 |
do 370 k=2,NLAY-1 |
| 696 |
do 370 j=1,JNP |
| 697 |
do 370 i=1,IMR |
| 698 |
W(i,j,k) = W(i,j,k-1) + DPI(i,j,k) - DBK(k)*CRY(i,j) |
| 699 |
370 continue |
| 700 |
C |
| 701 |
DO 380 k=1,NLAY |
| 702 |
DO 380 j=1,JNP |
| 703 |
DO 380 i=1,IMR |
| 704 |
delp2(i,j,k) = DAP(k) + DBK(k)*PS2(i,j) |
| 705 |
380 continue |
| 706 |
C |
| 707 |
KRD = max(3, KORD) |
| 708 |
do 4000 IC=1,NC |
| 709 |
C |
| 710 |
C****6***0*********0*********0*********0*********0*********0**********72 |
| 711 |
|
| 712 |
call FZPPM(IMR,JNP,NLAY,j1,DQ(1,1,1,IC),W,Q(1,1,1,IC),WK1,DPI, |
| 713 |
& DC2,CRX,CRY,PU,PV,xmass,ymass,delp1,KRD) |
| 714 |
C |
| 715 |
|
| 716 |
if(fill) call qckxyz(DQ(1,1,1,IC),DC2,IMR,JNP,NLAY,j1,j2, |
| 717 |
& cosp,acosp,.false.,IC,NSTEP) |
| 718 |
C |
| 719 |
C Recover tracer mixing ratio from "density" using predicted |
| 720 |
C "air density" (pressure thickness) at time-level n+1 |
| 721 |
C |
| 722 |
DO k=1,NLAY |
| 723 |
DO j=1,JNP |
| 724 |
DO i=1,IMR |
| 725 |
Q(i,j,k,IC) = DQ(i,j,k,IC) / delp2(i,j,k) |
| 726 |
enddo |
| 727 |
enddo |
| 728 |
enddo |
| 729 |
C |
| 730 |
if(j1.ne.2) then |
| 731 |
DO 400 k=1,NLAY |
| 732 |
DO 400 I=1,IMR |
| 733 |
c j=1 c'est le pôle Sud, j=JNP c'est le pôle Nord |
| 734 |
Q(I, 2,k,IC) = Q(I, 1,k,IC) |
| 735 |
Q(I,JMR,k,IC) = Q(I,JMP,k,IC) |
| 736 |
400 CONTINUE |
| 737 |
endif |
| 738 |
4000 continue |
| 739 |
C |
| 740 |
if(j1.ne.2) then |
| 741 |
DO 5000 k=1,NLAY |
| 742 |
DO 5000 i=1,IMR |
| 743 |
W(i, 2,k) = W(i, 1,k) |
| 744 |
W(i,JMR,k) = W(i,JNP,k) |
| 745 |
5000 continue |
| 746 |
endif |
| 747 |
C |
| 748 |
RETURN |
| 749 |
END |
| 750 |
C |
| 751 |
C****6***0*********0*********0*********0*********0*********0**********72 |
| 752 |
subroutine FZPPM(IMR,JNP,NLAY,j1,DQ,WZ,P,DC,DQDT,AR,AL,A6, |
| 753 |
& flux,wk1,wk2,wz2,delp,KORD) |
| 754 |
parameter ( kmax = 150 ) |
| 755 |
parameter ( R23 = 2./3., R3 = 1./3.) |
| 756 |
real WZ(IMR,JNP,NLAY),P(IMR,JNP,NLAY),DC(IMR,JNP,NLAY), |
| 757 |
& wk1(IMR,*),delp(IMR,JNP,NLAY),DQ(IMR,JNP,NLAY), |
| 758 |
& DQDT(IMR,JNP,NLAY) |
| 759 |
C Assuming JNP >= NLAY |
| 760 |
real AR(IMR,*),AL(IMR,*),A6(IMR,*),flux(IMR,*),wk2(IMR,*), |
| 761 |
& wz2(IMR,*) |
| 762 |
C |
| 763 |
JMR = JNP - 1 |
| 764 |
IMJM = IMR*JNP |
| 765 |
NLAYM1 = NLAY - 1 |
| 766 |
C |
| 767 |
LMT = KORD - 3 |
| 768 |
C |
| 769 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
| 770 |
C Compute DC for PPM |
| 771 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
| 772 |
C |
| 773 |
do 1000 k=1,NLAYM1 |
| 774 |
do 1000 i=1,IMJM |
| 775 |
DQDT(i,1,k) = P(i,1,k+1) - P(i,1,k) |
| 776 |
1000 continue |
| 777 |
C |
| 778 |
DO 1220 k=2,NLAYM1 |
| 779 |
DO 1220 I=1,IMJM |
| 780 |
c0 = delp(i,1,k) / (delp(i,1,k-1)+delp(i,1,k)+delp(i,1,k+1)) |
| 781 |
c1 = (delp(i,1,k-1)+0.5*delp(i,1,k))/(delp(i,1,k+1)+delp(i,1,k)) |
| 782 |
c2 = (delp(i,1,k+1)+0.5*delp(i,1,k))/(delp(i,1,k-1)+delp(i,1,k)) |
| 783 |
tmp = c0*(c1*DQDT(i,1,k) + c2*DQDT(i,1,k-1)) |
| 784 |
Qmax = max(P(i,1,k-1),P(i,1,k),P(i,1,k+1)) - P(i,1,k) |
| 785 |
Qmin = P(i,1,k) - min(P(i,1,k-1),P(i,1,k),P(i,1,k+1)) |
| 786 |
DC(i,1,k) = sign(min(abs(tmp),Qmax,Qmin), tmp) |
| 787 |
1220 CONTINUE |
| 788 |
|
| 789 |
C |
| 790 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
| 791 |
C Loop over latitudes (to save memory) |
| 792 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
| 793 |
C |
| 794 |
DO 2000 j=1,JNP |
| 795 |
if((j.eq.2 .or. j.eq.JMR) .and. j1.ne.2) goto 2000 |
| 796 |
C |
| 797 |
DO k=1,NLAY |
| 798 |
DO i=1,IMR |
| 799 |
wz2(i,k) = WZ(i,j,k) |
| 800 |
wk1(i,k) = P(i,j,k) |
| 801 |
wk2(i,k) = delp(i,j,k) |
| 802 |
flux(i,k) = DC(i,j,k) !this flux is actually the monotone slope |
| 803 |
enddo |
| 804 |
enddo |
| 805 |
C |
| 806 |
C****6***0*********0*********0*********0*********0*********0**********72 |
| 807 |
C Compute first guesses at cell interfaces |
| 808 |
C First guesses are required to be continuous. |
| 809 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
| 810 |
C |
| 811 |
C three-cell parabolic subgrid distribution at model top |
| 812 |
C two-cell parabolic with zero gradient subgrid distribution |
| 813 |
C at the surface. |
| 814 |
C |
| 815 |
C First guess top edge value |
| 816 |
DO 10 i=1,IMR |
| 817 |
C three-cell PPM |
| 818 |
C Compute a,b, and c of q = aP**2 + bP + c using cell averages and delp |
| 819 |
a = 3.*( DQDT(i,j,2) - DQDT(i,j,1)*(wk2(i,2)+wk2(i,3))/ |
| 820 |
& (wk2(i,1)+wk2(i,2)) ) / |
| 821 |
& ( (wk2(i,2)+wk2(i,3))*(wk2(i,1)+wk2(i,2)+wk2(i,3)) ) |
| 822 |
b = 2.*DQDT(i,j,1)/(wk2(i,1)+wk2(i,2)) - |
| 823 |
& R23*a*(2.*wk2(i,1)+wk2(i,2)) |
| 824 |
AL(i,1) = wk1(i,1) - wk2(i,1)*(R3*a*wk2(i,1) + 0.5*b) |
| 825 |
AL(i,2) = wk2(i,1)*(a*wk2(i,1) + b) + AL(i,1) |
| 826 |
C |
| 827 |
C Check if change sign |
| 828 |
if(wk1(i,1)*AL(i,1).le.0.) then |
| 829 |
AL(i,1) = 0. |
| 830 |
flux(i,1) = 0. |
| 831 |
else |
| 832 |
flux(i,1) = wk1(i,1) - AL(i,1) |
| 833 |
endif |
| 834 |
10 continue |
| 835 |
C |
| 836 |
C Bottom |
| 837 |
DO 15 i=1,IMR |
| 838 |
C 2-cell PPM with zero gradient right at the surface |
| 839 |
C |
| 840 |
fct = DQDT(i,j,NLAYM1)*wk2(i,NLAY)**2 / |
| 841 |
& ( (wk2(i,NLAY)+wk2(i,NLAYM1))*(2.*wk2(i,NLAY)+wk2(i,NLAYM1))) |
| 842 |
AR(i,NLAY) = wk1(i,NLAY) + fct |
| 843 |
AL(i,NLAY) = wk1(i,NLAY) - (fct+fct) |
| 844 |
if(wk1(i,NLAY)*AR(i,NLAY).le.0.) AR(i,NLAY) = 0. |
| 845 |
flux(i,NLAY) = AR(i,NLAY) - wk1(i,NLAY) |
| 846 |
15 continue |
| 847 |
|
| 848 |
C |
| 849 |
C****6***0*********0*********0*********0*********0*********0**********72 |
| 850 |
C 4th order interpolation in the interior. |
| 851 |
C****6***0*********0*********0*********0*********0*********0**********72 |
| 852 |
C |
| 853 |
DO 14 k=3,NLAYM1 |
| 854 |
DO 12 i=1,IMR |
| 855 |
c1 = DQDT(i,j,k-1)*wk2(i,k-1) / (wk2(i,k-1)+wk2(i,k)) |
| 856 |
c2 = 2. / (wk2(i,k-2)+wk2(i,k-1)+wk2(i,k)+wk2(i,k+1)) |
| 857 |
A1 = (wk2(i,k-2)+wk2(i,k-1)) / (2.*wk2(i,k-1)+wk2(i,k)) |
| 858 |
A2 = (wk2(i,k )+wk2(i,k+1)) / (2.*wk2(i,k)+wk2(i,k-1)) |
| 859 |
AL(i,k) = wk1(i,k-1) + c1 + c2 * |
| 860 |
& ( wk2(i,k )*(c1*(A1 - A2)+A2*flux(i,k-1)) - |
| 861 |
& wk2(i,k-1)*A1*flux(i,k) ) |
| 862 |
12 CONTINUE |
| 863 |
14 continue |
| 864 |
C |
| 865 |
do 20 i=1,IMR*NLAYM1 |
| 866 |
AR(i,1) = AL(i,2) |
| 867 |
20 continue |
| 868 |
C |
| 869 |
do 30 i=1,IMR*NLAY |
| 870 |
A6(i,1) = 3.*(wk1(i,1)+wk1(i,1) - (AL(i,1)+AR(i,1))) |
| 871 |
30 continue |
| 872 |
C |
| 873 |
C****6***0*********0*********0*********0*********0*********0**********72 |
| 874 |
C Top & Bot always monotonic |
| 875 |
call lmtppm(flux(1,1),A6(1,1),AR(1,1),AL(1,1),wk1(1,1),IMR,0) |
| 876 |
call lmtppm(flux(1,NLAY),A6(1,NLAY),AR(1,NLAY),AL(1,NLAY), |
| 877 |
& wk1(1,NLAY),IMR,0) |
| 878 |
C |
| 879 |
C Interior depending on KORD |
| 880 |
if(LMT.LE.2) |
| 881 |
& call lmtppm(flux(1,2),A6(1,2),AR(1,2),AL(1,2),wk1(1,2), |
| 882 |
& IMR*(NLAY-2),LMT) |
| 883 |
C |
| 884 |
C****6***0*********0*********0*********0*********0*********0**********72 |
| 885 |
C |
| 886 |
DO 140 i=1,IMR*NLAYM1 |
| 887 |
IF(wz2(i,1).GT.0.) then |
| 888 |
CM = wz2(i,1) / wk2(i,1) |
| 889 |
flux(i,2) = AR(i,1)+0.5*CM*(AL(i,1)-AR(i,1)+A6(i,1)*(1.-R23*CM)) |
| 890 |
else |
| 891 |
CP= wz2(i,1) / wk2(i,2) |
| 892 |
flux(i,2) = AL(i,2)+0.5*CP*(AL(i,2)-AR(i,2)-A6(i,2)*(1.+R23*CP)) |
| 893 |
endif |
| 894 |
140 continue |
| 895 |
C |
| 896 |
DO 250 i=1,IMR*NLAYM1 |
| 897 |
flux(i,2) = wz2(i,1) * flux(i,2) |
| 898 |
250 continue |
| 899 |
C |
| 900 |
do 350 i=1,IMR |
| 901 |
DQ(i,j, 1) = DQ(i,j, 1) - flux(i, 2) |
| 902 |
DQ(i,j,NLAY) = DQ(i,j,NLAY) + flux(i,NLAY) |
| 903 |
350 continue |
| 904 |
C |
| 905 |
do 360 k=2,NLAYM1 |
| 906 |
do 360 i=1,IMR |
| 907 |
360 DQ(i,j,k) = DQ(i,j,k) + flux(i,k) - flux(i,k+1) |
| 908 |
2000 continue |
| 909 |
return |
| 910 |
end |
| 911 |
C |
| 912 |
subroutine xtp(IMR,JNP,IML,j1,j2,JN,JS,PU,DQ,Q,UC, |
| 913 |
& fx1,xmass,IORD) |
| 914 |
dimension UC(IMR,*),DC(-IML:IMR+IML+1),xmass(IMR,JNP) |
| 915 |
& ,fx1(IMR+1),DQ(IMR,JNP),qtmp(-IML:IMR+1+IML) |
| 916 |
dimension PU(IMR,JNP),Q(IMR,JNP),ISAVE(IMR) |
| 917 |
C |
| 918 |
IMP = IMR + 1 |
| 919 |
C |
| 920 |
C van Leer at high latitudes |
| 921 |
jvan = max(1,JNP/18) |
| 922 |
j1vl = j1+jvan |
| 923 |
j2vl = j2-jvan |
| 924 |
C |
| 925 |
do 1310 j=j1,j2 |
| 926 |
C |
| 927 |
do i=1,IMR |
| 928 |
qtmp(i) = q(i,j) |
| 929 |
enddo |
| 930 |
C |
| 931 |
if(j.ge.JN .or. j.le.JS) goto 2222 |
| 932 |
C ************* Eulerian ********** |
| 933 |
C |
| 934 |
qtmp(0) = q(IMR,J) |
| 935 |
qtmp(-1) = q(IMR-1,J) |
| 936 |
qtmp(IMP) = q(1,J) |
| 937 |
qtmp(IMP+1) = q(2,J) |
| 938 |
C |
| 939 |
IF(IORD.eq.1 .or. j.eq.j1. or. j.eq.j2) THEN |
| 940 |
DO 1406 i=1,IMR |
| 941 |
iu = float(i) - uc(i,j) |
| 942 |
1406 fx1(i) = qtmp(iu) |
| 943 |
ELSE |
| 944 |
call xmist(IMR,IML,Qtmp,DC) |
| 945 |
DC(0) = DC(IMR) |
| 946 |
C |
| 947 |
if(IORD.eq.2 .or. j.le.j1vl .or. j.ge.j2vl) then |
| 948 |
DO 1408 i=1,IMR |
| 949 |
iu = float(i) - uc(i,j) |
| 950 |
1408 fx1(i) = qtmp(iu) + DC(iu)*(sign(1.,uc(i,j))-uc(i,j)) |
| 951 |
else |
| 952 |
call fxppm(IMR,IML,UC(1,j),Qtmp,DC,fx1,IORD) |
| 953 |
endif |
| 954 |
C |
| 955 |
ENDIF |
| 956 |
C |
| 957 |
DO 1506 i=1,IMR |
| 958 |
1506 fx1(i) = fx1(i)*xmass(i,j) |
| 959 |
C |
| 960 |
goto 1309 |
| 961 |
C |
| 962 |
C ***** Conservative (flux-form) Semi-Lagrangian transport ***** |
| 963 |
C |
| 964 |
2222 continue |
| 965 |
C |
| 966 |
do i=-IML,0 |
| 967 |
qtmp(i) = q(IMR+i,j) |
| 968 |
qtmp(IMP-i) = q(1-i,j) |
| 969 |
enddo |
| 970 |
C |
| 971 |
IF(IORD.eq.1 .or. j.eq.j1. or. j.eq.j2) THEN |
| 972 |
DO 1306 i=1,IMR |
| 973 |
itmp = INT(uc(i,j)) |
| 974 |
ISAVE(i) = i - itmp |
| 975 |
iu = i - uc(i,j) |
| 976 |
1306 fx1(i) = (uc(i,j) - itmp)*qtmp(iu) |
| 977 |
ELSE |
| 978 |
call xmist(IMR,IML,Qtmp,DC) |
| 979 |
C |
| 980 |
do i=-IML,0 |
| 981 |
DC(i) = DC(IMR+i) |
| 982 |
DC(IMP-i) = DC(1-i) |
| 983 |
enddo |
| 984 |
C |
| 985 |
DO 1307 i=1,IMR |
| 986 |
itmp = INT(uc(i,j)) |
| 987 |
rut = uc(i,j) - itmp |
| 988 |
ISAVE(i) = i - itmp |
| 989 |
iu = i - uc(i,j) |
| 990 |
1307 fx1(i) = rut*(qtmp(iu) + DC(iu)*(sign(1.,rut) - rut)) |
| 991 |
ENDIF |
| 992 |
C |
| 993 |
do 1308 i=1,IMR |
| 994 |
IF(uc(i,j).GT.1.) then |
| 995 |
CDIR$ NOVECTOR |
| 996 |
do ist = ISAVE(i),i-1 |
| 997 |
fx1(i) = fx1(i) + qtmp(ist) |
| 998 |
enddo |
| 999 |
elseIF(uc(i,j).LT.-1.) then |
| 1000 |
do ist = i,ISAVE(i)-1 |
| 1001 |
fx1(i) = fx1(i) - qtmp(ist) |
| 1002 |
enddo |
| 1003 |
CDIR$ VECTOR |
| 1004 |
endif |
| 1005 |
1308 continue |
| 1006 |
do i=1,IMR |
| 1007 |
fx1(i) = PU(i,j)*fx1(i) |
| 1008 |
enddo |
| 1009 |
C |
| 1010 |
C *************************************** |
| 1011 |
C |
| 1012 |
1309 fx1(IMP) = fx1(1) |
| 1013 |
DO 1215 i=1,IMR |
| 1014 |
1215 DQ(i,j) = DQ(i,j) + fx1(i)-fx1(i+1) |
| 1015 |
C |
| 1016 |
C *************************************** |
| 1017 |
C |
| 1018 |
1310 continue |
| 1019 |
return |
| 1020 |
end |
| 1021 |
C |
| 1022 |
subroutine fxppm(IMR,IML,UT,P,DC,flux,IORD) |
| 1023 |
parameter ( R3 = 1./3., R23 = 2./3. ) |
| 1024 |
DIMENSION UT(*),flux(*),P(-IML:IMR+IML+1),DC(-IML:IMR+IML+1) |
| 1025 |
DIMENSION AR(0:IMR),AL(0:IMR),A6(0:IMR) |
| 1026 |
integer LMT |
| 1027 |
c logical first |
| 1028 |
c data first /.true./ |
| 1029 |
c SAVE LMT |
| 1030 |
c if(first) then |
| 1031 |
C |
| 1032 |
C correction calcul de LMT a chaque passage pour pouvoir choisir |
| 1033 |
c plusieurs schemas PPM pour differents traceurs |
| 1034 |
c IF (IORD.LE.0) then |
| 1035 |
c if(IMR.GE.144) then |
| 1036 |
c LMT = 0 |
| 1037 |
c elseif(IMR.GE.72) then |
| 1038 |
c LMT = 1 |
| 1039 |
c else |
| 1040 |
c LMT = 2 |
| 1041 |
c endif |
| 1042 |
c else |
| 1043 |
c LMT = IORD - 3 |
| 1044 |
c endif |
| 1045 |
C |
| 1046 |
LMT = IORD - 3 |
| 1047 |
|
| 1048 |
DO 10 i=1,IMR |
| 1049 |
10 AL(i) = 0.5*(p(i-1)+p(i)) + (DC(i-1) - DC(i))*R3 |
| 1050 |
C |
| 1051 |
do 20 i=1,IMR-1 |
| 1052 |
20 AR(i) = AL(i+1) |
| 1053 |
AR(IMR) = AL(1) |
| 1054 |
C |
| 1055 |
do 30 i=1,IMR |
| 1056 |
30 A6(i) = 3.*(p(i)+p(i) - (AL(i)+AR(i))) |
| 1057 |
C |
| 1058 |
if(LMT.LE.2) call lmtppm(DC(1),A6(1),AR(1),AL(1),P(1),IMR,LMT) |
| 1059 |
C |
| 1060 |
AL(0) = AL(IMR) |
| 1061 |
AR(0) = AR(IMR) |
| 1062 |
A6(0) = A6(IMR) |
| 1063 |
C |
| 1064 |
DO i=1,IMR |
| 1065 |
IF(UT(i).GT.0.) then |
| 1066 |
flux(i) = AR(i-1) + 0.5*UT(i)*(AL(i-1) - AR(i-1) + |
| 1067 |
& A6(i-1)*(1.-R23*UT(i)) ) |
| 1068 |
else |
| 1069 |
flux(i) = AL(i) - 0.5*UT(i)*(AR(i) - AL(i) + |
| 1070 |
& A6(i)*(1.+R23*UT(i))) |
| 1071 |
endif |
| 1072 |
enddo |
| 1073 |
return |
| 1074 |
end |
| 1075 |
C |
| 1076 |
subroutine xmist(IMR,IML,P,DC) |
| 1077 |
parameter( R24 = 1./24.) |
| 1078 |
dimension P(-IML:IMR+1+IML),DC(-IML:IMR+1+IML) |
| 1079 |
C |
| 1080 |
do 10 i=1,IMR |
| 1081 |
tmp = R24*(8.*(p(i+1) - p(i-1)) + p(i-2) - p(i+2)) |
| 1082 |
Pmax = max(P(i-1), p(i), p(i+1)) - p(i) |
| 1083 |
Pmin = p(i) - min(P(i-1), p(i), p(i+1)) |
| 1084 |
10 DC(i) = sign(min(abs(tmp),Pmax,Pmin), tmp) |
| 1085 |
return |
| 1086 |
end |
| 1087 |
C |
| 1088 |
subroutine ytp(IMR,JNP,j1,j2,acosp,RCAP,DQ,P,VC,DC2 |
| 1089 |
& ,ymass,fx,A6,AR,AL,JORD) |
| 1090 |
dimension P(IMR,JNP),VC(IMR,JNP),ymass(IMR,JNP) |
| 1091 |
& ,DC2(IMR,JNP),DQ(IMR,JNP),acosp(JNP) |
| 1092 |
C Work array |
| 1093 |
DIMENSION fx(IMR,JNP),AR(IMR,JNP),AL(IMR,JNP),A6(IMR,JNP) |
| 1094 |
C |
| 1095 |
JMR = JNP - 1 |
| 1096 |
len = IMR*(J2-J1+2) |
| 1097 |
C |
| 1098 |
if(JORD.eq.1) then |
| 1099 |
DO 1000 i=1,len |
| 1100 |
JT = float(J1) - VC(i,J1) |
| 1101 |
1000 fx(i,j1) = p(i,JT) |
| 1102 |
else |
| 1103 |
|
| 1104 |
call ymist(IMR,JNP,j1,P,DC2,4) |
| 1105 |
C |
| 1106 |
if(JORD.LE.0 .or. JORD.GE.3) then |
| 1107 |
|
| 1108 |
call fyppm(VC,P,DC2,fx,IMR,JNP,j1,j2,A6,AR,AL,JORD) |
| 1109 |
|
| 1110 |
else |
| 1111 |
DO 1200 i=1,len |
| 1112 |
JT = float(J1) - VC(i,J1) |
| 1113 |
1200 fx(i,j1) = p(i,JT) + (sign(1.,VC(i,j1))-VC(i,j1))*DC2(i,JT) |
| 1114 |
endif |
| 1115 |
endif |
| 1116 |
C |
| 1117 |
DO 1300 i=1,len |
| 1118 |
1300 fx(i,j1) = fx(i,j1)*ymass(i,j1) |
| 1119 |
C |
| 1120 |
DO 1400 j=j1,j2 |
| 1121 |
DO 1400 i=1,IMR |
| 1122 |
1400 DQ(i,j) = DQ(i,j) + (fx(i,j) - fx(i,j+1)) * acosp(j) |
| 1123 |
C |
| 1124 |
C Poles |
| 1125 |
sum1 = fx(IMR,j1 ) |
| 1126 |
sum2 = fx(IMR,J2+1) |
| 1127 |
do i=1,IMR-1 |
| 1128 |
sum1 = sum1 + fx(i,j1 ) |
| 1129 |
sum2 = sum2 + fx(i,J2+1) |
| 1130 |
enddo |
| 1131 |
C |
| 1132 |
sum1 = DQ(1, 1) - sum1 * RCAP |
| 1133 |
sum2 = DQ(1,JNP) + sum2 * RCAP |
| 1134 |
do i=1,IMR |
| 1135 |
DQ(i, 1) = sum1 |
| 1136 |
DQ(i,JNP) = sum2 |
| 1137 |
enddo |
| 1138 |
C |
| 1139 |
if(j1.ne.2) then |
| 1140 |
do i=1,IMR |
| 1141 |
DQ(i, 2) = sum1 |
| 1142 |
DQ(i,JMR) = sum2 |
| 1143 |
enddo |
| 1144 |
endif |
| 1145 |
C |
| 1146 |
return |
| 1147 |
end |
| 1148 |
C |
| 1149 |
subroutine ymist(IMR,JNP,j1,P,DC,ID) |
| 1150 |
parameter ( R24 = 1./24. ) |
| 1151 |
dimension P(IMR,JNP),DC(IMR,JNP) |
| 1152 |
C |
| 1153 |
IMH = IMR / 2 |
| 1154 |
JMR = JNP - 1 |
| 1155 |
IJM3 = IMR*(JMR-3) |
| 1156 |
C |
| 1157 |
IF(ID.EQ.2) THEN |
| 1158 |
do 10 i=1,IMR*(JMR-1) |
| 1159 |
tmp = 0.25*(p(i,3) - p(i,1)) |
| 1160 |
Pmax = max(p(i,1),p(i,2),p(i,3)) - p(i,2) |
| 1161 |
Pmin = p(i,2) - min(p(i,1),p(i,2),p(i,3)) |
| 1162 |
DC(i,2) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
| 1163 |
10 CONTINUE |
| 1164 |
ELSE |
| 1165 |
do 12 i=1,IMH |
| 1166 |
C J=2 |
| 1167 |
tmp = (8.*(p(i,3) - p(i,1)) + p(i+IMH,2) - p(i,4))*R24 |
| 1168 |
Pmax = max(p(i,1),p(i,2),p(i,3)) - p(i,2) |
| 1169 |
Pmin = p(i,2) - min(p(i,1),p(i,2),p(i,3)) |
| 1170 |
DC(i,2) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
| 1171 |
C J=JMR |
| 1172 |
tmp=(8.*(p(i,JNP)-p(i,JMR-1))+p(i,JMR-2)-p(i+IMH,JMR))*R24 |
| 1173 |
Pmax = max(p(i,JMR-1),p(i,JMR),p(i,JNP)) - p(i,JMR) |
| 1174 |
Pmin = p(i,JMR) - min(p(i,JMR-1),p(i,JMR),p(i,JNP)) |
| 1175 |
DC(i,JMR) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
| 1176 |
12 CONTINUE |
| 1177 |
do 14 i=IMH+1,IMR |
| 1178 |
C J=2 |
| 1179 |
tmp = (8.*(p(i,3) - p(i,1)) + p(i-IMH,2) - p(i,4))*R24 |
| 1180 |
Pmax = max(p(i,1),p(i,2),p(i,3)) - p(i,2) |
| 1181 |
Pmin = p(i,2) - min(p(i,1),p(i,2),p(i,3)) |
| 1182 |
DC(i,2) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
| 1183 |
C J=JMR |
| 1184 |
tmp=(8.*(p(i,JNP)-p(i,JMR-1))+p(i,JMR-2)-p(i-IMH,JMR))*R24 |
| 1185 |
Pmax = max(p(i,JMR-1),p(i,JMR),p(i,JNP)) - p(i,JMR) |
| 1186 |
Pmin = p(i,JMR) - min(p(i,JMR-1),p(i,JMR),p(i,JNP)) |
| 1187 |
DC(i,JMR) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
| 1188 |
14 CONTINUE |
| 1189 |
C |
| 1190 |
do 15 i=1,IJM3 |
| 1191 |
tmp = (8.*(p(i,4) - p(i,2)) + p(i,1) - p(i,5))*R24 |
| 1192 |
Pmax = max(p(i,2),p(i,3),p(i,4)) - p(i,3) |
| 1193 |
Pmin = p(i,3) - min(p(i,2),p(i,3),p(i,4)) |
| 1194 |
DC(i,3) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
| 1195 |
15 CONTINUE |
| 1196 |
ENDIF |
| 1197 |
C |
| 1198 |
if(j1.ne.2) then |
| 1199 |
do i=1,IMR |
| 1200 |
DC(i,1) = 0. |
| 1201 |
DC(i,JNP) = 0. |
| 1202 |
enddo |
| 1203 |
else |
| 1204 |
C Determine slopes in polar caps for scalars! |
| 1205 |
C |
| 1206 |
do 13 i=1,IMH |
| 1207 |
C South |
| 1208 |
tmp = 0.25*(p(i,2) - p(i+imh,2)) |
| 1209 |
Pmax = max(p(i,2),p(i,1), p(i+imh,2)) - p(i,1) |
| 1210 |
Pmin = p(i,1) - min(p(i,2),p(i,1), p(i+imh,2)) |
| 1211 |
DC(i,1)=sign(min(abs(tmp),Pmax,Pmin),tmp) |
| 1212 |
C North. |
| 1213 |
tmp = 0.25*(p(i+imh,JMR) - p(i,JMR)) |
| 1214 |
Pmax = max(p(i+imh,JMR),p(i,jnp), p(i,JMR)) - p(i,JNP) |
| 1215 |
Pmin = p(i,JNP) - min(p(i+imh,JMR),p(i,jnp), p(i,JMR)) |
| 1216 |
DC(i,JNP) = sign(min(abs(tmp),Pmax,pmin),tmp) |
| 1217 |
13 continue |
| 1218 |
C |
| 1219 |
do 25 i=imh+1,IMR |
| 1220 |
DC(i, 1) = - DC(i-imh, 1) |
| 1221 |
DC(i,JNP) = - DC(i-imh,JNP) |
| 1222 |
25 continue |
| 1223 |
endif |
| 1224 |
return |
| 1225 |
end |
| 1226 |
C |
| 1227 |
subroutine fyppm(VC,P,DC,flux,IMR,JNP,j1,j2,A6,AR,AL,JORD) |
| 1228 |
parameter ( R3 = 1./3., R23 = 2./3. ) |
| 1229 |
real VC(IMR,*),flux(IMR,*),P(IMR,*),DC(IMR,*) |
| 1230 |
C Local work arrays. |
| 1231 |
real AR(IMR,JNP),AL(IMR,JNP),A6(IMR,JNP) |
| 1232 |
integer LMT |
| 1233 |
c logical first |
| 1234 |
C data first /.true./ |
| 1235 |
C SAVE LMT |
| 1236 |
C |
| 1237 |
IMH = IMR / 2 |
| 1238 |
JMR = JNP - 1 |
| 1239 |
j11 = j1-1 |
| 1240 |
IMJM1 = IMR*(J2-J1+2) |
| 1241 |
len = IMR*(J2-J1+3) |
| 1242 |
C if(first) then |
| 1243 |
C IF(JORD.LE.0) then |
| 1244 |
C if(JMR.GE.90) then |
| 1245 |
C LMT = 0 |
| 1246 |
C elseif(JMR.GE.45) then |
| 1247 |
C LMT = 1 |
| 1248 |
C else |
| 1249 |
C LMT = 2 |
| 1250 |
C endif |
| 1251 |
C else |
| 1252 |
C LMT = JORD - 3 |
| 1253 |
C endif |
| 1254 |
C |
| 1255 |
C first = .false. |
| 1256 |
C endif |
| 1257 |
C |
| 1258 |
c modifs pour pouvoir choisir plusieurs schemas PPM |
| 1259 |
LMT = JORD - 3 |
| 1260 |
C |
| 1261 |
DO 10 i=1,IMR*JMR |
| 1262 |
AL(i,2) = 0.5*(p(i,1)+p(i,2)) + (DC(i,1) - DC(i,2))*R3 |
| 1263 |
AR(i,1) = AL(i,2) |
| 1264 |
10 CONTINUE |
| 1265 |
C |
| 1266 |
CPoles: |
| 1267 |
C |
| 1268 |
DO i=1,IMH |
| 1269 |
AL(i,1) = AL(i+IMH,2) |
| 1270 |
AL(i+IMH,1) = AL(i,2) |
| 1271 |
C |
| 1272 |
AR(i,JNP) = AR(i+IMH,JMR) |
| 1273 |
AR(i+IMH,JNP) = AR(i,JMR) |
| 1274 |
ENDDO |
| 1275 |
|
| 1276 |
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
| 1277 |
c Rajout pour LMDZ.3.3 |
| 1278 |
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
| 1279 |
AR(IMR,1)=AL(1,1) |
| 1280 |
AR(IMR,JNP)=AL(1,JNP) |
| 1281 |
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
| 1282 |
|
| 1283 |
|
| 1284 |
do 30 i=1,len |
| 1285 |
30 A6(i,j11) = 3.*(p(i,j11)+p(i,j11) - (AL(i,j11)+AR(i,j11))) |
| 1286 |
C |
| 1287 |
if(LMT.le.2) call lmtppm(DC(1,j11),A6(1,j11),AR(1,j11) |
| 1288 |
& ,AL(1,j11),P(1,j11),len,LMT) |
| 1289 |
C |
| 1290 |
|
| 1291 |
DO 140 i=1,IMJM1 |
| 1292 |
IF(VC(i,j1).GT.0.) then |
| 1293 |
flux(i,j1) = AR(i,j11) + 0.5*VC(i,j1)*(AL(i,j11) - AR(i,j11) + |
| 1294 |
& A6(i,j11)*(1.-R23*VC(i,j1)) ) |
| 1295 |
else |
| 1296 |
flux(i,j1) = AL(i,j1) - 0.5*VC(i,j1)*(AR(i,j1) - AL(i,j1) + |
| 1297 |
& A6(i,j1)*(1.+R23*VC(i,j1))) |
| 1298 |
endif |
| 1299 |
140 continue |
| 1300 |
return |
| 1301 |
end |
| 1302 |
C |
| 1303 |
subroutine yadv(IMR,JNP,j1,j2,p,VA,ady,wk,IAD) |
| 1304 |
REAL p(IMR,JNP),ady(IMR,JNP),VA(IMR,JNP) |
| 1305 |
REAL WK(IMR,-1:JNP+2) |
| 1306 |
C |
| 1307 |
JMR = JNP-1 |
| 1308 |
IMH = IMR/2 |
| 1309 |
do j=1,JNP |
| 1310 |
do i=1,IMR |
| 1311 |
wk(i,j) = p(i,j) |
| 1312 |
enddo |
| 1313 |
enddo |
| 1314 |
C Poles: |
| 1315 |
do i=1,IMH |
| 1316 |
wk(i, -1) = p(i+IMH,3) |
| 1317 |
wk(i+IMH,-1) = p(i,3) |
| 1318 |
wk(i, 0) = p(i+IMH,2) |
| 1319 |
wk(i+IMH,0) = p(i,2) |
| 1320 |
wk(i,JNP+1) = p(i+IMH,JMR) |
| 1321 |
wk(i+IMH,JNP+1) = p(i,JMR) |
| 1322 |
wk(i,JNP+2) = p(i+IMH,JNP-2) |
| 1323 |
wk(i+IMH,JNP+2) = p(i,JNP-2) |
| 1324 |
enddo |
| 1325 |
|
| 1326 |
IF(IAD.eq.2) then |
| 1327 |
do j=j1-1,j2+1 |
| 1328 |
do i=1,IMR |
| 1329 |
JP = NINT(VA(i,j)) |
| 1330 |
rv = JP - VA(i,j) |
| 1331 |
JP = j - JP |
| 1332 |
a1 = 0.5*(wk(i,jp+1)+wk(i,jp-1)) - wk(i,jp) |
| 1333 |
b1 = 0.5*(wk(i,jp+1)-wk(i,jp-1)) |
| 1334 |
ady(i,j) = wk(i,jp) + rv*(a1*rv + b1) - wk(i,j) |
| 1335 |
enddo |
| 1336 |
enddo |
| 1337 |
|
| 1338 |
ELSEIF(IAD.eq.1) then |
| 1339 |
do j=j1-1,j2+1 |
| 1340 |
do i=1,imr |
| 1341 |
JP = float(j)-VA(i,j) |
| 1342 |
ady(i,j) = VA(i,j)*(wk(i,jp)-wk(i,jp+1)) |
| 1343 |
enddo |
| 1344 |
enddo |
| 1345 |
ENDIF |
| 1346 |
C |
| 1347 |
if(j1.ne.2) then |
| 1348 |
sum1 = 0. |
| 1349 |
sum2 = 0. |
| 1350 |
do i=1,imr |
| 1351 |
sum1 = sum1 + ady(i,2) |
| 1352 |
sum2 = sum2 + ady(i,JMR) |
| 1353 |
enddo |
| 1354 |
sum1 = sum1 / IMR |
| 1355 |
sum2 = sum2 / IMR |
| 1356 |
C |
| 1357 |
do i=1,imr |
| 1358 |
ady(i, 2) = sum1 |
| 1359 |
ady(i,JMR) = sum2 |
| 1360 |
ady(i, 1) = sum1 |
| 1361 |
ady(i,JNP) = sum2 |
| 1362 |
enddo |
| 1363 |
else |
| 1364 |
C Poles: |
| 1365 |
sum1 = 0. |
| 1366 |
sum2 = 0. |
| 1367 |
do i=1,imr |
| 1368 |
sum1 = sum1 + ady(i,1) |
| 1369 |
sum2 = sum2 + ady(i,JNP) |
| 1370 |
enddo |
| 1371 |
sum1 = sum1 / IMR |
| 1372 |
sum2 = sum2 / IMR |
| 1373 |
C |
| 1374 |
do i=1,imr |
| 1375 |
ady(i, 1) = sum1 |
| 1376 |
ady(i,JNP) = sum2 |
| 1377 |
enddo |
| 1378 |
endif |
| 1379 |
C |
| 1380 |
return |
| 1381 |
end |
| 1382 |
C |
| 1383 |
subroutine xadv(IMR,JNP,j1,j2,p,UA,JS,JN,IML,adx,IAD) |
| 1384 |
REAL p(IMR,JNP),adx(IMR,JNP),qtmp(-IMR:IMR+IMR),UA(IMR,JNP) |
| 1385 |
C |
| 1386 |
JMR = JNP-1 |
| 1387 |
do 1309 j=j1,j2 |
| 1388 |
if(J.GT.JS .and. J.LT.JN) GO TO 1309 |
| 1389 |
C |
| 1390 |
do i=1,IMR |
| 1391 |
qtmp(i) = p(i,j) |
| 1392 |
enddo |
| 1393 |
C |
| 1394 |
do i=-IML,0 |
| 1395 |
qtmp(i) = p(IMR+i,j) |
| 1396 |
qtmp(IMR+1-i) = p(1-i,j) |
| 1397 |
enddo |
| 1398 |
C |
| 1399 |
IF(IAD.eq.2) THEN |
| 1400 |
DO i=1,IMR |
| 1401 |
IP = NINT(UA(i,j)) |
| 1402 |
ru = IP - UA(i,j) |
| 1403 |
IP = i - IP |
| 1404 |
a1 = 0.5*(qtmp(ip+1)+qtmp(ip-1)) - qtmp(ip) |
| 1405 |
b1 = 0.5*(qtmp(ip+1)-qtmp(ip-1)) |
| 1406 |
adx(i,j) = qtmp(ip) + ru*(a1*ru + b1) |
| 1407 |
enddo |
| 1408 |
ELSEIF(IAD.eq.1) then |
| 1409 |
DO i=1,IMR |
| 1410 |
iu = UA(i,j) |
| 1411 |
ru = UA(i,j) - iu |
| 1412 |
iiu = i-iu |
| 1413 |
if(UA(i,j).GE.0.) then |
| 1414 |
adx(i,j) = qtmp(iiu)+ru*(qtmp(iiu-1)-qtmp(iiu)) |
| 1415 |
else |
| 1416 |
adx(i,j) = qtmp(iiu)+ru*(qtmp(iiu)-qtmp(iiu+1)) |
| 1417 |
endif |
| 1418 |
enddo |
| 1419 |
ENDIF |
| 1420 |
C |
| 1421 |
do i=1,IMR |
| 1422 |
adx(i,j) = adx(i,j) - p(i,j) |
| 1423 |
enddo |
| 1424 |
1309 continue |
| 1425 |
C |
| 1426 |
C Eulerian upwind |
| 1427 |
C |
| 1428 |
do j=JS+1,JN-1 |
| 1429 |
C |
| 1430 |
do i=1,IMR |
| 1431 |
qtmp(i) = p(i,j) |
| 1432 |
enddo |
| 1433 |
C |
| 1434 |
qtmp(0) = p(IMR,J) |
| 1435 |
qtmp(IMR+1) = p(1,J) |
| 1436 |
C |
| 1437 |
IF(IAD.eq.2) THEN |
| 1438 |
qtmp(-1) = p(IMR-1,J) |
| 1439 |
qtmp(IMR+2) = p(2,J) |
| 1440 |
do i=1,imr |
| 1441 |
IP = NINT(UA(i,j)) |
| 1442 |
ru = IP - UA(i,j) |
| 1443 |
IP = i - IP |
| 1444 |
a1 = 0.5*(qtmp(ip+1)+qtmp(ip-1)) - qtmp(ip) |
| 1445 |
b1 = 0.5*(qtmp(ip+1)-qtmp(ip-1)) |
| 1446 |
adx(i,j) = qtmp(ip)- p(i,j) + ru*(a1*ru + b1) |
| 1447 |
enddo |
| 1448 |
ELSEIF(IAD.eq.1) then |
| 1449 |
C 1st order |
| 1450 |
DO i=1,IMR |
| 1451 |
IP = i - UA(i,j) |
| 1452 |
adx(i,j) = UA(i,j)*(qtmp(ip)-qtmp(ip+1)) |
| 1453 |
enddo |
| 1454 |
ENDIF |
| 1455 |
enddo |
| 1456 |
C |
| 1457 |
if(j1.ne.2) then |
| 1458 |
do i=1,IMR |
| 1459 |
adx(i, 2) = 0. |
| 1460 |
adx(i,JMR) = 0. |
| 1461 |
enddo |
| 1462 |
endif |
| 1463 |
C set cross term due to x-adv at the poles to zero. |
| 1464 |
do i=1,IMR |
| 1465 |
adx(i, 1) = 0. |
| 1466 |
adx(i,JNP) = 0. |
| 1467 |
enddo |
| 1468 |
return |
| 1469 |
end |
| 1470 |
C |
| 1471 |
subroutine lmtppm(DC,A6,AR,AL,P,IM,LMT) |
| 1472 |
C |
| 1473 |
C A6 = CURVATURE OF THE TEST PARABOLA |
| 1474 |
C AR = RIGHT EDGE VALUE OF THE TEST PARABOLA |
| 1475 |
C AL = LEFT EDGE VALUE OF THE TEST PARABOLA |
| 1476 |
C DC = 0.5 * MISMATCH |
| 1477 |
C P = CELL-AVERAGED VALUE |
| 1478 |
C IM = VECTOR LENGTH |
| 1479 |
C |
| 1480 |
C OPTIONS: |
| 1481 |
C |
| 1482 |
C LMT = 0: FULL MONOTONICITY |
| 1483 |
C LMT = 1: SEMI-MONOTONIC CONSTRAINT (NO UNDERSHOOTS) |
| 1484 |
C LMT = 2: POSITIVE-DEFINITE CONSTRAINT |
| 1485 |
C |
| 1486 |
parameter ( R12 = 1./12. ) |
| 1487 |
dimension A6(IM),AR(IM),AL(IM),P(IM),DC(IM) |
| 1488 |
C |
| 1489 |
if(LMT.eq.0) then |
| 1490 |
C Full constraint |
| 1491 |
do 100 i=1,IM |
| 1492 |
if(DC(i).eq.0.) then |
| 1493 |
AR(i) = p(i) |
| 1494 |
AL(i) = p(i) |
| 1495 |
A6(i) = 0. |
| 1496 |
else |
| 1497 |
da1 = AR(i) - AL(i) |
| 1498 |
da2 = da1**2 |
| 1499 |
A6DA = A6(i)*da1 |
| 1500 |
if(A6DA .lt. -da2) then |
| 1501 |
A6(i) = 3.*(AL(i)-p(i)) |
| 1502 |
AR(i) = AL(i) - A6(i) |
| 1503 |
elseif(A6DA .gt. da2) then |
| 1504 |
A6(i) = 3.*(AR(i)-p(i)) |
| 1505 |
AL(i) = AR(i) - A6(i) |
| 1506 |
endif |
| 1507 |
endif |
| 1508 |
100 continue |
| 1509 |
elseif(LMT.eq.1) then |
| 1510 |
C Semi-monotonic constraint |
| 1511 |
do 150 i=1,IM |
| 1512 |
if(abs(AR(i)-AL(i)) .GE. -A6(i)) go to 150 |
| 1513 |
if(p(i).lt.AR(i) .and. p(i).lt.AL(i)) then |
| 1514 |
AR(i) = p(i) |
| 1515 |
AL(i) = p(i) |
| 1516 |
A6(i) = 0. |
| 1517 |
elseif(AR(i) .gt. AL(i)) then |
| 1518 |
A6(i) = 3.*(AL(i)-p(i)) |
| 1519 |
AR(i) = AL(i) - A6(i) |
| 1520 |
else |
| 1521 |
A6(i) = 3.*(AR(i)-p(i)) |
| 1522 |
AL(i) = AR(i) - A6(i) |
| 1523 |
endif |
| 1524 |
150 continue |
| 1525 |
elseif(LMT.eq.2) then |
| 1526 |
do 250 i=1,IM |
| 1527 |
if(abs(AR(i)-AL(i)) .GE. -A6(i)) go to 250 |
| 1528 |
fmin = p(i) + 0.25*(AR(i)-AL(i))**2/A6(i) + A6(i)*R12 |
| 1529 |
if(fmin.ge.0.) go to 250 |
| 1530 |
if(p(i).lt.AR(i) .and. p(i).lt.AL(i)) then |
| 1531 |
AR(i) = p(i) |
| 1532 |
AL(i) = p(i) |
| 1533 |
A6(i) = 0. |
| 1534 |
elseif(AR(i) .gt. AL(i)) then |
| 1535 |
A6(i) = 3.*(AL(i)-p(i)) |
| 1536 |
AR(i) = AL(i) - A6(i) |
| 1537 |
else |
| 1538 |
A6(i) = 3.*(AR(i)-p(i)) |
| 1539 |
AL(i) = AR(i) - A6(i) |
| 1540 |
endif |
| 1541 |
250 continue |
| 1542 |
endif |
| 1543 |
return |
| 1544 |
end |
| 1545 |
C |
| 1546 |
subroutine A2C(U,V,IMR,JMR,j1,j2,CRX,CRY,dtdx5,DTDY5) |
| 1547 |
dimension U(IMR,*),V(IMR,*),CRX(IMR,*),CRY(IMR,*),DTDX5(*) |
| 1548 |
C |
| 1549 |
do 35 j=j1,j2 |
| 1550 |
do 35 i=2,IMR |
| 1551 |
35 CRX(i,J) = dtdx5(j)*(U(i,j)+U(i-1,j)) |
| 1552 |
C |
| 1553 |
do 45 j=j1,j2 |
| 1554 |
45 CRX(1,J) = dtdx5(j)*(U(1,j)+U(IMR,j)) |
| 1555 |
C |
| 1556 |
do 55 i=1,IMR*JMR |
| 1557 |
55 CRY(i,2) = DTDY5*(V(i,2)+V(i,1)) |
| 1558 |
return |
| 1559 |
end |
| 1560 |
C |
| 1561 |
subroutine cosa(cosp,cose,JNP,PI,DP) |
| 1562 |
dimension cosp(*),cose(*) |
| 1563 |
JMR = JNP-1 |
| 1564 |
do 55 j=2,JNP |
| 1565 |
ph5 = -0.5*PI + (FLOAT(J-1)-0.5)*DP |
| 1566 |
55 cose(j) = cos(ph5) |
| 1567 |
C |
| 1568 |
JEQ = (JNP+1) / 2 |
| 1569 |
if(JMR .eq. 2*(JMR/2) ) then |
| 1570 |
do j=JNP, JEQ+1, -1 |
| 1571 |
cose(j) = cose(JNP+2-j) |
| 1572 |
enddo |
| 1573 |
else |
| 1574 |
C cell edge at equator. |
| 1575 |
cose(JEQ+1) = 1. |
| 1576 |
do j=JNP, JEQ+2, -1 |
| 1577 |
cose(j) = cose(JNP+2-j) |
| 1578 |
enddo |
| 1579 |
endif |
| 1580 |
C |
| 1581 |
do 66 j=2,JMR |
| 1582 |
66 cosp(j) = 0.5*(cose(j)+cose(j+1)) |
| 1583 |
cosp(1) = 0. |
| 1584 |
cosp(JNP) = 0. |
| 1585 |
return |
| 1586 |
end |
| 1587 |
C |
| 1588 |
subroutine cosc(cosp,cose,JNP,PI,DP) |
| 1589 |
dimension cosp(*),cose(*) |
| 1590 |
C |
| 1591 |
phi = -0.5*PI |
| 1592 |
do 55 j=2,JNP-1 |
| 1593 |
phi = phi + DP |
| 1594 |
55 cosp(j) = cos(phi) |
| 1595 |
cosp( 1) = 0. |
| 1596 |
cosp(JNP) = 0. |
| 1597 |
C |
| 1598 |
do 66 j=2,JNP |
| 1599 |
cose(j) = 0.5*(cosp(j)+cosp(j-1)) |
| 1600 |
66 CONTINUE |
| 1601 |
C |
| 1602 |
do 77 j=2,JNP-1 |
| 1603 |
cosp(j) = 0.5*(cose(j)+cose(j+1)) |
| 1604 |
77 CONTINUE |
| 1605 |
return |
| 1606 |
end |
| 1607 |
C |
| 1608 |
SUBROUTINE qckxyz (Q,qtmp,IMR,JNP,NLAY,j1,j2,cosp,acosp, |
| 1609 |
& cross,IC,NSTEP) |
| 1610 |
C |
| 1611 |
parameter( tiny = 1.E-60 ) |
| 1612 |
DIMENSION Q(IMR,JNP,NLAY),qtmp(IMR,JNP),cosp(*),acosp(*) |
| 1613 |
logical cross |
| 1614 |
C |
| 1615 |
NLAYM1 = NLAY-1 |
| 1616 |
len = IMR*(j2-j1+1) |
| 1617 |
ip = 0 |
| 1618 |
C |
| 1619 |
C Top layer |
| 1620 |
L = 1 |
| 1621 |
icr = 1 |
| 1622 |
call filns(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,ipy,tiny) |
| 1623 |
if(ipy.eq.0) goto 50 |
| 1624 |
call filew(q(1,1,L),qtmp,IMR,JNP,j1,j2,ipx,tiny) |
| 1625 |
if(ipx.eq.0) goto 50 |
| 1626 |
C |
| 1627 |
if(cross) then |
| 1628 |
call filcr(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,icr,tiny) |
| 1629 |
endif |
| 1630 |
if(icr.eq.0) goto 50 |
| 1631 |
C |
| 1632 |
C Vertical filling... |
| 1633 |
do i=1,len |
| 1634 |
IF( Q(i,j1,1).LT.0.) THEN |
| 1635 |
ip = ip + 1 |
| 1636 |
Q(i,j1,2) = Q(i,j1,2) + Q(i,j1,1) |
| 1637 |
Q(i,j1,1) = 0. |
| 1638 |
endif |
| 1639 |
enddo |
| 1640 |
C |
| 1641 |
50 continue |
| 1642 |
DO 225 L = 2,NLAYM1 |
| 1643 |
icr = 1 |
| 1644 |
C |
| 1645 |
call filns(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,ipy,tiny) |
| 1646 |
if(ipy.eq.0) goto 225 |
| 1647 |
call filew(q(1,1,L),qtmp,IMR,JNP,j1,j2,ipx,tiny) |
| 1648 |
if(ipx.eq.0) go to 225 |
| 1649 |
if(cross) then |
| 1650 |
call filcr(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,icr,tiny) |
| 1651 |
endif |
| 1652 |
if(icr.eq.0) goto 225 |
| 1653 |
C |
| 1654 |
do i=1,len |
| 1655 |
IF( Q(I,j1,L).LT.0.) THEN |
| 1656 |
C |
| 1657 |
ip = ip + 1 |
| 1658 |
C From above |
| 1659 |
qup = Q(I,j1,L-1) |
| 1660 |
qly = -Q(I,j1,L) |
| 1661 |
dup = min(qly,qup) |
| 1662 |
Q(I,j1,L-1) = qup - dup |
| 1663 |
Q(I,j1,L ) = dup-qly |
| 1664 |
C Below |
| 1665 |
Q(I,j1,L+1) = Q(I,j1,L+1) + Q(I,j1,L) |
| 1666 |
Q(I,j1,L) = 0. |
| 1667 |
ENDIF |
| 1668 |
ENDDO |
| 1669 |
225 CONTINUE |
| 1670 |
C |
| 1671 |
C BOTTOM LAYER |
| 1672 |
sum = 0. |
| 1673 |
L = NLAY |
| 1674 |
C |
| 1675 |
call filns(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,ipy,tiny) |
| 1676 |
if(ipy.eq.0) goto 911 |
| 1677 |
call filew(q(1,1,L),qtmp,IMR,JNP,j1,j2,ipx,tiny) |
| 1678 |
if(ipx.eq.0) goto 911 |
| 1679 |
C |
| 1680 |
call filcr(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,icr,tiny) |
| 1681 |
if(icr.eq.0) goto 911 |
| 1682 |
C |
| 1683 |
DO I=1,len |
| 1684 |
IF( Q(I,j1,L).LT.0.) THEN |
| 1685 |
ip = ip + 1 |
| 1686 |
c |
| 1687 |
C From above |
| 1688 |
C |
| 1689 |
qup = Q(I,j1,NLAYM1) |
| 1690 |
qly = -Q(I,j1,L) |
| 1691 |
dup = min(qly,qup) |
| 1692 |
Q(I,j1,NLAYM1) = qup - dup |
| 1693 |
C From "below" the surface. |
| 1694 |
sum = sum + qly-dup |
| 1695 |
Q(I,j1,L) = 0. |
| 1696 |
ENDIF |
| 1697 |
ENDDO |
| 1698 |
C |
| 1699 |
911 continue |
| 1700 |
C |
| 1701 |
if(ip.gt.IMR) then |
| 1702 |
write(6,*) 'IC=',IC,' STEP=',NSTEP, |
| 1703 |
& ' Vertical filling pts=',ip |
| 1704 |
endif |
| 1705 |
C |
| 1706 |
if(sum.gt.1.e-25) then |
| 1707 |
write(6,*) IC,NSTEP,' Mass source from the ground=',sum |
| 1708 |
endif |
| 1709 |
RETURN |
| 1710 |
END |
| 1711 |
C |
| 1712 |
subroutine filcr(q,IMR,JNP,j1,j2,cosp,acosp,icr,tiny) |
| 1713 |
dimension q(IMR,*),cosp(*),acosp(*) |
| 1714 |
icr = 0 |
| 1715 |
do 65 j=j1+1,j2-1 |
| 1716 |
DO 50 i=1,IMR-1 |
| 1717 |
IF(q(i,j).LT.0.) THEN |
| 1718 |
icr = 1 |
| 1719 |
dq = - q(i,j)*cosp(j) |
| 1720 |
C N-E |
| 1721 |
dn = q(i+1,j+1)*cosp(j+1) |
| 1722 |
d0 = max(0.,dn) |
| 1723 |
d1 = min(dq,d0) |
| 1724 |
q(i+1,j+1) = (dn - d1)*acosp(j+1) |
| 1725 |
dq = dq - d1 |
| 1726 |
C S-E |
| 1727 |
ds = q(i+1,j-1)*cosp(j-1) |
| 1728 |
d0 = max(0.,ds) |
| 1729 |
d2 = min(dq,d0) |
| 1730 |
q(i+1,j-1) = (ds - d2)*acosp(j-1) |
| 1731 |
q(i,j) = (d2 - dq)*acosp(j) + tiny |
| 1732 |
endif |
| 1733 |
50 continue |
| 1734 |
if(icr.eq.0 .and. q(IMR,j).ge.0.) goto 65 |
| 1735 |
DO 55 i=2,IMR |
| 1736 |
IF(q(i,j).LT.0.) THEN |
| 1737 |
icr = 1 |
| 1738 |
dq = - q(i,j)*cosp(j) |
| 1739 |
C N-W |
| 1740 |
dn = q(i-1,j+1)*cosp(j+1) |
| 1741 |
d0 = max(0.,dn) |
| 1742 |
d1 = min(dq,d0) |
| 1743 |
q(i-1,j+1) = (dn - d1)*acosp(j+1) |
| 1744 |
dq = dq - d1 |
| 1745 |
C S-W |
| 1746 |
ds = q(i-1,j-1)*cosp(j-1) |
| 1747 |
d0 = max(0.,ds) |
| 1748 |
d2 = min(dq,d0) |
| 1749 |
q(i-1,j-1) = (ds - d2)*acosp(j-1) |
| 1750 |
q(i,j) = (d2 - dq)*acosp(j) + tiny |
| 1751 |
endif |
| 1752 |
55 continue |
| 1753 |
C ***************************************** |
| 1754 |
C i=1 |
| 1755 |
i=1 |
| 1756 |
IF(q(i,j).LT.0.) THEN |
| 1757 |
icr = 1 |
| 1758 |
dq = - q(i,j)*cosp(j) |
| 1759 |
C N-W |
| 1760 |
dn = q(IMR,j+1)*cosp(j+1) |
| 1761 |
d0 = max(0.,dn) |
| 1762 |
d1 = min(dq,d0) |
| 1763 |
q(IMR,j+1) = (dn - d1)*acosp(j+1) |
| 1764 |
dq = dq - d1 |
| 1765 |
C S-W |
| 1766 |
ds = q(IMR,j-1)*cosp(j-1) |
| 1767 |
d0 = max(0.,ds) |
| 1768 |
d2 = min(dq,d0) |
| 1769 |
q(IMR,j-1) = (ds - d2)*acosp(j-1) |
| 1770 |
q(i,j) = (d2 - dq)*acosp(j) + tiny |
| 1771 |
endif |
| 1772 |
C ***************************************** |
| 1773 |
C i=IMR |
| 1774 |
i=IMR |
| 1775 |
IF(q(i,j).LT.0.) THEN |
| 1776 |
icr = 1 |
| 1777 |
dq = - q(i,j)*cosp(j) |
| 1778 |
C N-E |
| 1779 |
dn = q(1,j+1)*cosp(j+1) |
| 1780 |
d0 = max(0.,dn) |
| 1781 |
d1 = min(dq,d0) |
| 1782 |
q(1,j+1) = (dn - d1)*acosp(j+1) |
| 1783 |
dq = dq - d1 |
| 1784 |
C S-E |
| 1785 |
ds = q(1,j-1)*cosp(j-1) |
| 1786 |
d0 = max(0.,ds) |
| 1787 |
d2 = min(dq,d0) |
| 1788 |
q(1,j-1) = (ds - d2)*acosp(j-1) |
| 1789 |
q(i,j) = (d2 - dq)*acosp(j) + tiny |
| 1790 |
endif |
| 1791 |
C ***************************************** |
| 1792 |
65 continue |
| 1793 |
C |
| 1794 |
do i=1,IMR |
| 1795 |
if(q(i,j1).lt.0. .or. q(i,j2).lt.0.) then |
| 1796 |
icr = 1 |
| 1797 |
goto 80 |
| 1798 |
endif |
| 1799 |
enddo |
| 1800 |
C |
| 1801 |
80 continue |
| 1802 |
C |
| 1803 |
if(q(1,1).lt.0. .or. q(1,jnp).lt.0.) then |
| 1804 |
icr = 1 |
| 1805 |
endif |
| 1806 |
C |
| 1807 |
return |
| 1808 |
end |
| 1809 |
C |
| 1810 |
subroutine filns(q,IMR,JNP,j1,j2,cosp,acosp,ipy,tiny) |
| 1811 |
dimension q(IMR,*),cosp(*),acosp(*) |
| 1812 |
c logical first |
| 1813 |
c data first /.true./ |
| 1814 |
c save cap1 |
| 1815 |
C |
| 1816 |
c if(first) then |
| 1817 |
DP = 4.*ATAN(1.)/float(JNP-1) |
| 1818 |
CAP1 = IMR*(1.-COS((j1-1.5)*DP))/DP |
| 1819 |
c first = .false. |
| 1820 |
c endif |
| 1821 |
C |
| 1822 |
ipy = 0 |
| 1823 |
do 55 j=j1+1,j2-1 |
| 1824 |
DO 55 i=1,IMR |
| 1825 |
IF(q(i,j).LT.0.) THEN |
| 1826 |
ipy = 1 |
| 1827 |
dq = - q(i,j)*cosp(j) |
| 1828 |
C North |
| 1829 |
dn = q(i,j+1)*cosp(j+1) |
| 1830 |
d0 = max(0.,dn) |
| 1831 |
d1 = min(dq,d0) |
| 1832 |
q(i,j+1) = (dn - d1)*acosp(j+1) |
| 1833 |
dq = dq - d1 |
| 1834 |
C South |
| 1835 |
ds = q(i,j-1)*cosp(j-1) |
| 1836 |
d0 = max(0.,ds) |
| 1837 |
d2 = min(dq,d0) |
| 1838 |
q(i,j-1) = (ds - d2)*acosp(j-1) |
| 1839 |
q(i,j) = (d2 - dq)*acosp(j) + tiny |
| 1840 |
endif |
| 1841 |
55 continue |
| 1842 |
C |
| 1843 |
do i=1,imr |
| 1844 |
IF(q(i,j1).LT.0.) THEN |
| 1845 |
ipy = 1 |
| 1846 |
dq = - q(i,j1)*cosp(j1) |
| 1847 |
C North |
| 1848 |
dn = q(i,j1+1)*cosp(j1+1) |
| 1849 |
d0 = max(0.,dn) |
| 1850 |
d1 = min(dq,d0) |
| 1851 |
q(i,j1+1) = (dn - d1)*acosp(j1+1) |
| 1852 |
q(i,j1) = (d1 - dq)*acosp(j1) + tiny |
| 1853 |
endif |
| 1854 |
enddo |
| 1855 |
C |
| 1856 |
j = j2 |
| 1857 |
do i=1,imr |
| 1858 |
IF(q(i,j).LT.0.) THEN |
| 1859 |
ipy = 1 |
| 1860 |
dq = - q(i,j)*cosp(j) |
| 1861 |
C South |
| 1862 |
ds = q(i,j-1)*cosp(j-1) |
| 1863 |
d0 = max(0.,ds) |
| 1864 |
d2 = min(dq,d0) |
| 1865 |
q(i,j-1) = (ds - d2)*acosp(j-1) |
| 1866 |
q(i,j) = (d2 - dq)*acosp(j) + tiny |
| 1867 |
endif |
| 1868 |
enddo |
| 1869 |
C |
| 1870 |
C Check Poles. |
| 1871 |
if(q(1,1).lt.0.) then |
| 1872 |
dq = q(1,1)*cap1/float(IMR)*acosp(j1) |
| 1873 |
do i=1,imr |
| 1874 |
q(i,1) = 0. |
| 1875 |
q(i,j1) = q(i,j1) + dq |
| 1876 |
if(q(i,j1).lt.0.) ipy = 1 |
| 1877 |
enddo |
| 1878 |
endif |
| 1879 |
C |
| 1880 |
if(q(1,JNP).lt.0.) then |
| 1881 |
dq = q(1,JNP)*cap1/float(IMR)*acosp(j2) |
| 1882 |
do i=1,imr |
| 1883 |
q(i,JNP) = 0. |
| 1884 |
q(i,j2) = q(i,j2) + dq |
| 1885 |
if(q(i,j2).lt.0.) ipy = 1 |
| 1886 |
enddo |
| 1887 |
endif |
| 1888 |
C |
| 1889 |
return |
| 1890 |
end |
| 1891 |
C |
| 1892 |
subroutine filew(q,qtmp,IMR,JNP,j1,j2,ipx,tiny) |
| 1893 |
dimension q(IMR,*),qtmp(JNP,IMR) |
| 1894 |
C |
| 1895 |
ipx = 0 |
| 1896 |
C Copy & swap direction for vectorization. |
| 1897 |
do 25 i=1,imr |
| 1898 |
do 25 j=j1,j2 |
| 1899 |
25 qtmp(j,i) = q(i,j) |
| 1900 |
C |
| 1901 |
do 55 i=2,imr-1 |
| 1902 |
do 55 j=j1,j2 |
| 1903 |
if(qtmp(j,i).lt.0.) then |
| 1904 |
ipx = 1 |
| 1905 |
c west |
| 1906 |
d0 = max(0.,qtmp(j,i-1)) |
| 1907 |
d1 = min(-qtmp(j,i),d0) |
| 1908 |
qtmp(j,i-1) = qtmp(j,i-1) - d1 |
| 1909 |
qtmp(j,i) = qtmp(j,i) + d1 |
| 1910 |
c east |
| 1911 |
d0 = max(0.,qtmp(j,i+1)) |
| 1912 |
d2 = min(-qtmp(j,i),d0) |
| 1913 |
qtmp(j,i+1) = qtmp(j,i+1) - d2 |
| 1914 |
qtmp(j,i) = qtmp(j,i) + d2 + tiny |
| 1915 |
endif |
| 1916 |
55 continue |
| 1917 |
c |
| 1918 |
i=1 |
| 1919 |
do 65 j=j1,j2 |
| 1920 |
if(qtmp(j,i).lt.0.) then |
| 1921 |
ipx = 1 |
| 1922 |
c west |
| 1923 |
d0 = max(0.,qtmp(j,imr)) |
| 1924 |
d1 = min(-qtmp(j,i),d0) |
| 1925 |
qtmp(j,imr) = qtmp(j,imr) - d1 |
| 1926 |
qtmp(j,i) = qtmp(j,i) + d1 |
| 1927 |
c east |
| 1928 |
d0 = max(0.,qtmp(j,i+1)) |
| 1929 |
d2 = min(-qtmp(j,i),d0) |
| 1930 |
qtmp(j,i+1) = qtmp(j,i+1) - d2 |
| 1931 |
c |
| 1932 |
qtmp(j,i) = qtmp(j,i) + d2 + tiny |
| 1933 |
endif |
| 1934 |
65 continue |
| 1935 |
i=IMR |
| 1936 |
do 75 j=j1,j2 |
| 1937 |
if(qtmp(j,i).lt.0.) then |
| 1938 |
ipx = 1 |
| 1939 |
c west |
| 1940 |
d0 = max(0.,qtmp(j,i-1)) |
| 1941 |
d1 = min(-qtmp(j,i),d0) |
| 1942 |
qtmp(j,i-1) = qtmp(j,i-1) - d1 |
| 1943 |
qtmp(j,i) = qtmp(j,i) + d1 |
| 1944 |
c east |
| 1945 |
d0 = max(0.,qtmp(j,1)) |
| 1946 |
d2 = min(-qtmp(j,i),d0) |
| 1947 |
qtmp(j,1) = qtmp(j,1) - d2 |
| 1948 |
c |
| 1949 |
qtmp(j,i) = qtmp(j,i) + d2 + tiny |
| 1950 |
endif |
| 1951 |
75 continue |
| 1952 |
C |
| 1953 |
if(ipx.ne.0) then |
| 1954 |
do 85 j=j1,j2 |
| 1955 |
do 85 i=1,imr |
| 1956 |
85 q(i,j) = qtmp(j,i) |
| 1957 |
else |
| 1958 |
C |
| 1959 |
C Poles. |
| 1960 |
if(q(1,1).lt.0. or. q(1,JNP).lt.0.) ipx = 1 |
| 1961 |
endif |
| 1962 |
return |
| 1963 |
end |
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