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! $Header: /home/cvsroot/LMDZ4/libf/dyn3d/ppm3d.F,v 1.1.1.1 2004/05/19 |
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! 12:53:07 lmdzadmin Exp $ |
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! From lin@explorer.gsfc.nasa.gov Wed Apr 15 17:44:44 1998 |
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! Date: Wed, 15 Apr 1998 11:37:03 -0400 |
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! From: lin@explorer.gsfc.nasa.gov |
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! To: Frederic.Hourdin@lmd.jussieu.fr |
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! Subject: 3D transport module of the GSFC CTM and GEOS GCM |
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! This code is sent to you by S-J Lin, DAO, NASA-GSFC |
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! Note: this version is intended for machines like CRAY |
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! -90. No multitasking directives implemented. |
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! ******************************************************************** |
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! TransPort Core for Goddard Chemistry Transport Model (G-CTM), Goddard |
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! Earth Observing System General Circulation Model (GEOS-GCM), and Data |
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! Assimilation System (GEOS-DAS). |
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! ******************************************************************** |
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! Purpose: given horizontal winds on a hybrid sigma-p surfaces, |
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! one call to tpcore updates the 3-D mixing ratio |
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! fields one time step (NDT). [vertical mass flux is computed |
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! internally consistent with the discretized hydrostatic mass |
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! continuity equation of the C-Grid GEOS-GCM (for IGD=1)]. |
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! Schemes: Multi-dimensional Flux Form Semi-Lagrangian (FFSL) scheme based |
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! on the van Leer or PPM. |
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! (see Lin and Rood 1996). |
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! Version 4.5 |
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! Last modified: Dec. 5, 1996 |
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! Major changes from version 4.0: a more general vertical hybrid sigma- |
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! pressure coordinate. |
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! Subroutines modified: xtp, ytp, fzppm, qckxyz |
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! Subroutines deleted: vanz |
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! Author: Shian-Jiann Lin |
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! mail address: |
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! Shian-Jiann Lin* |
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! Code 910.3, NASA/GSFC, Greenbelt, MD 20771 |
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! Phone: 301-286-9540 |
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! E-mail: lin@dao.gsfc.nasa.gov |
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! *affiliation: |
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! Joint Center for Earth Systems Technology |
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! The University of Maryland Baltimore County |
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! NASA - Goddard Space Flight Center |
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! References: |
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! 1. Lin, S.-J., and R. B. Rood, 1996: Multidimensional flux form semi- |
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! Lagrangian transport schemes. Mon. Wea. Rev., 124, 2046-2070. |
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! 2. Lin, S.-J., W. C. Chao, Y. C. Sud, and G. K. Walker, 1994: A class of |
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! the van Leer-type transport schemes and its applications to the moist- |
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! ure transport in a General Circulation Model. Mon. Wea. Rev., 122, |
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! 1575-1593. |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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| 1 |
SUBROUTINE ppm3d(igd, q, ps1, ps2, u, v, w, ndt, iord, jord, kord, nc, imr, & |
SUBROUTINE ppm3d(igd, q, ps1, ps2, u, v, w, ndt, iord, jord, kord, nc, imr, & |
| 2 |
jnp, j1, nlay, ap, bp, pt, ae, fill, dum, umax) |
jnp, j1, nlay, ap, bp, pt, ae, fill, dum, umax) |
| 3 |
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| 721 |
END SUBROUTINE ppm3d |
END SUBROUTINE ppm3d |
| 722 |
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| 723 |
! ****6***0*********0*********0*********0*********0*********0**********72 |
! ****6***0*********0*********0*********0*********0*********0**********72 |
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SUBROUTINE fzppm(imr, jnp, nlay, j1, dq, wz, p, dc, dqdt, ar, al, a6, flux, & |
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wk1, wk2, wz2, delp, kord) |
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PARAMETER (kmax=150) |
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PARAMETER (r23=2./3., r3=1./3.) |
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REAL wz(imr, jnp, nlay), p(imr, jnp, nlay), dc(imr, jnp, nlay), & |
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wk1(imr, *), delp(imr, jnp, nlay), dq(imr, jnp, nlay), & |
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dqdt(imr, jnp, nlay) |
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! Assuming JNP >= NLAY |
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REAL ar(imr, *), al(imr, *), a6(imr, *), flux(imr, *), wk2(imr, *), & |
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wz2(imr, *) |
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jmr = jnp - 1 |
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imjm = imr*jnp |
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nlaym1 = nlay - 1 |
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lmt = kord - 3 |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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! Compute DC for PPM |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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DO k = 1, nlaym1 |
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DO i = 1, imjm |
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dqdt(i, 1, k) = p(i, 1, k+1) - p(i, 1, k) |
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END DO |
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END DO |
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DO k = 2, nlaym1 |
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DO i = 1, imjm |
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c0 = delp(i, 1, k)/(delp(i,1,k-1)+delp(i,1,k)+delp(i,1,k+1)) |
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c1 = (delp(i,1,k-1)+0.5*delp(i,1,k))/(delp(i,1,k+1)+delp(i,1,k)) |
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c2 = (delp(i,1,k+1)+0.5*delp(i,1,k))/(delp(i,1,k-1)+delp(i,1,k)) |
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tmp = c0*(c1*dqdt(i,1,k)+c2*dqdt(i,1,k-1)) |
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qmax = max(p(i,1,k-1), p(i,1,k), p(i,1,k+1)) - p(i, 1, k) |
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qmin = p(i, 1, k) - min(p(i,1,k-1), p(i,1,k), p(i,1,k+1)) |
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dc(i, 1, k) = sign(min(abs(tmp),qmax,qmin), tmp) |
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END DO |
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END DO |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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! Loop over latitudes (to save memory) |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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DO j = 1, jnp |
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IF ((j==2 .OR. j==jmr) .AND. j1/=2) GO TO 2000 |
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DO k = 1, nlay |
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DO i = 1, imr |
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wz2(i, k) = wz(i, j, k) |
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wk1(i, k) = p(i, j, k) |
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wk2(i, k) = delp(i, j, k) |
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flux(i, k) = dc(i, j, k) !this flux is actually the monotone slope |
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END DO |
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END DO |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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! Compute first guesses at cell interfaces |
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! First guesses are required to be continuous. |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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! three-cell parabolic subgrid distribution at model top |
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! two-cell parabolic with zero gradient subgrid distribution |
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! at the surface. |
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! First guess top edge value |
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DO i = 1, imr |
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! three-cell PPM |
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! Compute a,b, and c of q = aP**2 + bP + c using cell averages and delp |
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a = 3.*(dqdt(i,j,2)-dqdt(i,j,1)*(wk2(i,2)+wk2(i,3))/(wk2(i,1)+wk2(i, & |
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2)))/((wk2(i,2)+wk2(i,3))*(wk2(i,1)+wk2(i,2)+wk2(i,3))) |
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b = 2.*dqdt(i, j, 1)/(wk2(i,1)+wk2(i,2)) - r23*a*(2.*wk2(i,1)+wk2(i,2)) |
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al(i, 1) = wk1(i, 1) - wk2(i, 1)*(r3*a*wk2(i,1)+0.5*b) |
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al(i, 2) = wk2(i, 1)*(a*wk2(i,1)+b) + al(i, 1) |
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! Check if change sign |
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IF (wk1(i,1)*al(i,1)<=0.) THEN |
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al(i, 1) = 0. |
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flux(i, 1) = 0. |
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ELSE |
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flux(i, 1) = wk1(i, 1) - al(i, 1) |
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END IF |
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END DO |
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! Bottom |
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DO i = 1, imr |
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! 2-cell PPM with zero gradient right at the surface |
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fct = dqdt(i, j, nlaym1)*wk2(i, nlay)**2/((wk2(i,nlay)+wk2(i, & |
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nlaym1))*(2.*wk2(i,nlay)+wk2(i,nlaym1))) |
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ar(i, nlay) = wk1(i, nlay) + fct |
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al(i, nlay) = wk1(i, nlay) - (fct+fct) |
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IF (wk1(i,nlay)*ar(i,nlay)<=0.) ar(i, nlay) = 0. |
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flux(i, nlay) = ar(i, nlay) - wk1(i, nlay) |
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END DO |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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! 4th order interpolation in the interior. |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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DO k = 3, nlaym1 |
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DO i = 1, imr |
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c1 = dqdt(i, j, k-1)*wk2(i, k-1)/(wk2(i,k-1)+wk2(i,k)) |
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c2 = 2./(wk2(i,k-2)+wk2(i,k-1)+wk2(i,k)+wk2(i,k+1)) |
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a1 = (wk2(i,k-2)+wk2(i,k-1))/(2.*wk2(i,k-1)+wk2(i,k)) |
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a2 = (wk2(i,k)+wk2(i,k+1))/(2.*wk2(i,k)+wk2(i,k-1)) |
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al(i, k) = wk1(i, k-1) + c1 + c2*(wk2(i,k)*(c1*(a1-a2)+a2*flux(i, & |
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k-1))-wk2(i,k-1)*a1*flux(i,k)) |
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END DO |
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END DO |
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DO i = 1, imr*nlaym1 |
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ar(i, 1) = al(i, 2) |
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END DO |
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DO i = 1, imr*nlay |
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a6(i, 1) = 3.*(wk1(i,1)+wk1(i,1)-(al(i,1)+ar(i,1))) |
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END DO |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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! Top & Bot always monotonic |
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CALL lmtppm(flux(1,1), a6(1,1), ar(1,1), al(1,1), wk1(1,1), imr, 0) |
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CALL lmtppm(flux(1,nlay), a6(1,nlay), ar(1,nlay), al(1,nlay), & |
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wk1(1,nlay), imr, 0) |
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! Interior depending on KORD |
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IF (lmt<=2) CALL lmtppm(flux(1,2), a6(1,2), ar(1,2), al(1,2), wk1(1,2), & |
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imr*(nlay-2), lmt) |
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! ****6***0*********0*********0*********0*********0*********0**********72 |
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DO i = 1, imr*nlaym1 |
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IF (wz2(i,1)>0.) THEN |
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cm = wz2(i, 1)/wk2(i, 1) |
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flux(i, 2) = ar(i, 1) + 0.5*cm*(al(i,1)-ar(i,1)+a6(i,1)*(1.-r23*cm)) |
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ELSE |
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cp = wz2(i, 1)/wk2(i, 2) |
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flux(i, 2) = al(i, 2) + 0.5*cp*(al(i,2)-ar(i,2)-a6(i,2)*(1.+r23*cp)) |
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END IF |
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END DO |
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DO i = 1, imr*nlaym1 |
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flux(i, 2) = wz2(i, 1)*flux(i, 2) |
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END DO |
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DO i = 1, imr |
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dq(i, j, 1) = dq(i, j, 1) - flux(i, 2) |
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dq(i, j, nlay) = dq(i, j, nlay) + flux(i, nlay) |
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END DO |
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DO k = 2, nlaym1 |
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DO i = 1, imr |
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dq(i, j, k) = dq(i, j, k) + flux(i, k) - flux(i, k+1) |
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END DO |
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END DO |
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2000 END DO |
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RETURN |
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END SUBROUTINE fzppm |
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SUBROUTINE xtp(imr, jnp, iml, j1, j2, jn, js, pu, dq, q, uc, fx1, xmass, & |
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iord) |
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DIMENSION uc(imr, *), dc(-iml:imr+iml+1), xmass(imr, jnp), fx1(imr+1), & |
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dq(imr, jnp), qtmp(-iml:imr+1+iml) |
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DIMENSION pu(imr, jnp), q(imr, jnp), isave(imr) |
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imp = imr + 1 |
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! van Leer at high latitudes |
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jvan = max(1, jnp/18) |
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j1vl = j1 + jvan |
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j2vl = j2 - jvan |
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DO j = j1, j2 |
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DO i = 1, imr |
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qtmp(i) = q(i, j) |
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END DO |
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IF (j>=jn .OR. j<=js) GO TO 2222 |
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! ************* Eulerian ********** |
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qtmp(0) = q(imr, j) |
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qtmp(-1) = q(imr-1, j) |
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qtmp(imp) = q(1, j) |
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qtmp(imp+1) = q(2, j) |
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IF (iord==1 .OR. j==j1 .OR. j==j2) THEN |
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DO i = 1, imr |
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iu = float(i) - uc(i, j) |
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fx1(i) = qtmp(iu) |
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END DO |
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ELSE |
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CALL xmist(imr, iml, qtmp, dc) |
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dc(0) = dc(imr) |
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IF (iord==2 .OR. j<=j1vl .OR. j>=j2vl) THEN |
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DO i = 1, imr |
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iu = float(i) - uc(i, j) |
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fx1(i) = qtmp(iu) + dc(iu)*(sign(1.,uc(i,j))-uc(i,j)) |
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END DO |
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ELSE |
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CALL fxppm(imr, iml, uc(1,j), qtmp, dc, fx1, iord) |
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END IF |
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END IF |
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DO i = 1, imr |
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fx1(i) = fx1(i)*xmass(i, j) |
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END DO |
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GO TO 1309 |
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! ***** Conservative (flux-form) Semi-Lagrangian transport ***** |
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2222 CONTINUE |
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DO i = -iml, 0 |
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qtmp(i) = q(imr+i, j) |
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qtmp(imp-i) = q(1-i, j) |
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END DO |
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IF (iord==1 .OR. j==j1 .OR. j==j2) THEN |
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DO i = 1, imr |
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itmp = int(uc(i,j)) |
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isave(i) = i - itmp |
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iu = i - uc(i, j) |
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fx1(i) = (uc(i,j)-itmp)*qtmp(iu) |
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END DO |
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ELSE |
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CALL xmist(imr, iml, qtmp, dc) |
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DO i = -iml, 0 |
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dc(i) = dc(imr+i) |
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dc(imp-i) = dc(1-i) |
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END DO |
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DO i = 1, imr |
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itmp = int(uc(i,j)) |
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rut = uc(i, j) - itmp |
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isave(i) = i - itmp |
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iu = i - uc(i, j) |
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fx1(i) = rut*(qtmp(iu)+dc(iu)*(sign(1.,rut)-rut)) |
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END DO |
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END IF |
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DO i = 1, imr |
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IF (uc(i,j)>1.) THEN |
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! DIR$ NOVECTOR |
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DO ist = isave(i), i - 1 |
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fx1(i) = fx1(i) + qtmp(ist) |
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END DO |
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ELSE IF (uc(i,j)<-1.) THEN |
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DO ist = i, isave(i) - 1 |
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fx1(i) = fx1(i) - qtmp(ist) |
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END DO |
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! DIR$ VECTOR |
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END IF |
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END DO |
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DO i = 1, imr |
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fx1(i) = pu(i, j)*fx1(i) |
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END DO |
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! *************************************** |
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1309 fx1(imp) = fx1(1) |
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DO i = 1, imr |
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dq(i, j) = dq(i, j) + fx1(i) - fx1(i+1) |
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END DO |
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! *************************************** |
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END DO |
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RETURN |
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END SUBROUTINE xtp |
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SUBROUTINE fxppm(imr, iml, ut, p, dc, flux, iord) |
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PARAMETER (r3=1./3., r23=2./3.) |
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DIMENSION ut(*), flux(*), p(-iml:imr+iml+1), dc(-iml:imr+iml+1) |
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DIMENSION ar(0:imr), al(0:imr), a6(0:imr) |
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INTEGER lmt |
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! logical first |
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! data first /.true./ |
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! SAVE LMT |
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! if(first) then |
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! correction calcul de LMT a chaque passage pour pouvoir choisir |
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! plusieurs schemas PPM pour differents traceurs |
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! IF (IORD.LE.0) then |
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! if(IMR.GE.144) then |
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! LMT = 0 |
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! elseif(IMR.GE.72) then |
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! LMT = 1 |
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! else |
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! LMT = 2 |
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! endif |
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! else |
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! LMT = IORD - 3 |
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! endif |
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lmt = iord - 3 |
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DO i = 1, imr |
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al(i) = 0.5*(p(i-1)+p(i)) + (dc(i-1)-dc(i))*r3 |
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END DO |
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DO i = 1, imr - 1 |
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ar(i) = al(i+1) |
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END DO |
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ar(imr) = al(1) |
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DO i = 1, imr |
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a6(i) = 3.*(p(i)+p(i)-(al(i)+ar(i))) |
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END DO |
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IF (lmt<=2) CALL lmtppm(dc(1), a6(1), ar(1), al(1), p(1), imr, lmt) |
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al(0) = al(imr) |
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ar(0) = ar(imr) |
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a6(0) = a6(imr) |
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DO i = 1, imr |
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IF (ut(i)>0.) THEN |
|
|
flux(i) = ar(i-1) + 0.5*ut(i)*(al(i-1)-ar(i-1)+a6(i-1)*(1.-r23*ut(i))) |
|
|
ELSE |
|
|
flux(i) = al(i) - 0.5*ut(i)*(ar(i)-al(i)+a6(i)*(1.+r23*ut(i))) |
|
|
END IF |
|
|
END DO |
|
|
RETURN |
|
|
END SUBROUTINE fxppm |
|
|
|
|
|
SUBROUTINE xmist(imr, iml, p, dc) |
|
|
PARAMETER (r24=1./24.) |
|
|
DIMENSION p(-iml:imr+1+iml), dc(-iml:imr+1+iml) |
|
|
|
|
|
DO i = 1, imr |
|
|
tmp = r24*(8.*(p(i+1)-p(i-1))+p(i-2)-p(i+2)) |
|
|
pmax = max(p(i-1), p(i), p(i+1)) - p(i) |
|
|
pmin = p(i) - min(p(i-1), p(i), p(i+1)) |
|
|
dc(i) = sign(min(abs(tmp),pmax,pmin), tmp) |
|
|
END DO |
|
|
RETURN |
|
|
END SUBROUTINE xmist |
|
|
|
|
|
SUBROUTINE ytp(imr, jnp, j1, j2, acosp, rcap, dq, p, vc, dc2, ymass, fx, a6, & |
|
|
ar, al, jord) |
|
|
DIMENSION p(imr, jnp), vc(imr, jnp), ymass(imr, jnp), dc2(imr, jnp), & |
|
|
dq(imr, jnp), acosp(jnp) |
|
|
! Work array |
|
|
DIMENSION fx(imr, jnp), ar(imr, jnp), al(imr, jnp), a6(imr, jnp) |
|
|
|
|
|
jmr = jnp - 1 |
|
|
len = imr*(j2-j1+2) |
|
|
|
|
|
IF (jord==1) THEN |
|
|
DO i = 1, len |
|
|
jt = float(j1) - vc(i, j1) |
|
|
fx(i, j1) = p(i, jt) |
|
|
END DO |
|
|
ELSE |
|
|
|
|
|
CALL ymist(imr, jnp, j1, p, dc2, 4) |
|
|
|
|
|
IF (jord<=0 .OR. jord>=3) THEN |
|
|
|
|
|
CALL fyppm(vc, p, dc2, fx, imr, jnp, j1, j2, a6, ar, al, jord) |
|
|
|
|
|
ELSE |
|
|
DO i = 1, len |
|
|
jt = float(j1) - vc(i, j1) |
|
|
fx(i, j1) = p(i, jt) + (sign(1.,vc(i,j1))-vc(i,j1))*dc2(i, jt) |
|
|
END DO |
|
|
END IF |
|
|
END IF |
|
|
|
|
|
DO i = 1, len |
|
|
fx(i, j1) = fx(i, j1)*ymass(i, j1) |
|
|
END DO |
|
|
|
|
|
DO j = j1, j2 |
|
|
DO i = 1, imr |
|
|
dq(i, j) = dq(i, j) + (fx(i,j)-fx(i,j+1))*acosp(j) |
|
|
END DO |
|
|
END DO |
|
|
|
|
|
! Poles |
|
|
sum1 = fx(imr, j1) |
|
|
sum2 = fx(imr, j2+1) |
|
|
DO i = 1, imr - 1 |
|
|
sum1 = sum1 + fx(i, j1) |
|
|
sum2 = sum2 + fx(i, j2+1) |
|
|
END DO |
|
|
|
|
|
sum1 = dq(1, 1) - sum1*rcap |
|
|
sum2 = dq(1, jnp) + sum2*rcap |
|
|
DO i = 1, imr |
|
|
dq(i, 1) = sum1 |
|
|
dq(i, jnp) = sum2 |
|
|
END DO |
|
|
|
|
|
IF (j1/=2) THEN |
|
|
DO i = 1, imr |
|
|
dq(i, 2) = sum1 |
|
|
dq(i, jmr) = sum2 |
|
|
END DO |
|
|
END IF |
|
|
|
|
|
RETURN |
|
|
END SUBROUTINE ytp |
|
|
|
|
|
SUBROUTINE ymist(imr, jnp, j1, p, dc, id) |
|
|
PARAMETER (r24=1./24.) |
|
|
DIMENSION p(imr, jnp), dc(imr, jnp) |
|
|
|
|
|
imh = imr/2 |
|
|
jmr = jnp - 1 |
|
|
ijm3 = imr*(jmr-3) |
|
|
|
|
|
IF (id==2) THEN |
|
|
DO i = 1, imr*(jmr-1) |
|
|
tmp = 0.25*(p(i,3)-p(i,1)) |
|
|
pmax = max(p(i,1), p(i,2), p(i,3)) - p(i, 2) |
|
|
pmin = p(i, 2) - min(p(i,1), p(i,2), p(i,3)) |
|
|
dc(i, 2) = sign(min(abs(tmp),pmin,pmax), tmp) |
|
|
END DO |
|
|
ELSE |
|
|
DO i = 1, imh |
|
|
! J=2 |
|
|
tmp = (8.*(p(i,3)-p(i,1))+p(i+imh,2)-p(i,4))*r24 |
|
|
pmax = max(p(i,1), p(i,2), p(i,3)) - p(i, 2) |
|
|
pmin = p(i, 2) - min(p(i,1), p(i,2), p(i,3)) |
|
|
dc(i, 2) = sign(min(abs(tmp),pmin,pmax), tmp) |
|
|
! J=JMR |
|
|
tmp = (8.*(p(i,jnp)-p(i,jmr-1))+p(i,jmr-2)-p(i+imh,jmr))*r24 |
|
|
pmax = max(p(i,jmr-1), p(i,jmr), p(i,jnp)) - p(i, jmr) |
|
|
pmin = p(i, jmr) - min(p(i,jmr-1), p(i,jmr), p(i,jnp)) |
|
|
dc(i, jmr) = sign(min(abs(tmp),pmin,pmax), tmp) |
|
|
END DO |
|
|
DO i = imh + 1, imr |
|
|
! J=2 |
|
|
tmp = (8.*(p(i,3)-p(i,1))+p(i-imh,2)-p(i,4))*r24 |
|
|
pmax = max(p(i,1), p(i,2), p(i,3)) - p(i, 2) |
|
|
pmin = p(i, 2) - min(p(i,1), p(i,2), p(i,3)) |
|
|
dc(i, 2) = sign(min(abs(tmp),pmin,pmax), tmp) |
|
|
! J=JMR |
|
|
tmp = (8.*(p(i,jnp)-p(i,jmr-1))+p(i,jmr-2)-p(i-imh,jmr))*r24 |
|
|
pmax = max(p(i,jmr-1), p(i,jmr), p(i,jnp)) - p(i, jmr) |
|
|
pmin = p(i, jmr) - min(p(i,jmr-1), p(i,jmr), p(i,jnp)) |
|
|
dc(i, jmr) = sign(min(abs(tmp),pmin,pmax), tmp) |
|
|
END DO |
|
|
|
|
|
DO i = 1, ijm3 |
|
|
tmp = (8.*(p(i,4)-p(i,2))+p(i,1)-p(i,5))*r24 |
|
|
pmax = max(p(i,2), p(i,3), p(i,4)) - p(i, 3) |
|
|
pmin = p(i, 3) - min(p(i,2), p(i,3), p(i,4)) |
|
|
dc(i, 3) = sign(min(abs(tmp),pmin,pmax), tmp) |
|
|
END DO |
|
|
END IF |
|
|
|
|
|
IF (j1/=2) THEN |
|
|
DO i = 1, imr |
|
|
dc(i, 1) = 0. |
|
|
dc(i, jnp) = 0. |
|
|
END DO |
|
|
ELSE |
|
|
! Determine slopes in polar caps for scalars! |
|
|
|
|
|
DO i = 1, imh |
|
|
! South |
|
|
tmp = 0.25*(p(i,2)-p(i+imh,2)) |
|
|
pmax = max(p(i,2), p(i,1), p(i+imh,2)) - p(i, 1) |
|
|
pmin = p(i, 1) - min(p(i,2), p(i,1), p(i+imh,2)) |
|
|
dc(i, 1) = sign(min(abs(tmp),pmax,pmin), tmp) |
|
|
! North. |
|
|
tmp = 0.25*(p(i+imh,jmr)-p(i,jmr)) |
|
|
pmax = max(p(i+imh,jmr), p(i,jnp), p(i,jmr)) - p(i, jnp) |
|
|
pmin = p(i, jnp) - min(p(i+imh,jmr), p(i,jnp), p(i,jmr)) |
|
|
dc(i, jnp) = sign(min(abs(tmp),pmax,pmin), tmp) |
|
|
END DO |
|
|
|
|
|
DO i = imh + 1, imr |
|
|
dc(i, 1) = -dc(i-imh, 1) |
|
|
dc(i, jnp) = -dc(i-imh, jnp) |
|
|
END DO |
|
|
END IF |
|
|
RETURN |
|
|
END SUBROUTINE ymist |
|
|
|
|
|
SUBROUTINE fyppm(vc, p, dc, flux, imr, jnp, j1, j2, a6, ar, al, jord) |
|
|
PARAMETER (r3=1./3., r23=2./3.) |
|
|
REAL vc(imr, *), flux(imr, *), p(imr, *), dc(imr, *) |
|
|
! Local work arrays. |
|
|
REAL ar(imr, jnp), al(imr, jnp), a6(imr, jnp) |
|
|
INTEGER lmt |
|
|
! logical first |
|
|
! data first /.true./ |
|
|
! SAVE LMT |
|
|
|
|
|
imh = imr/2 |
|
|
jmr = jnp - 1 |
|
|
j11 = j1 - 1 |
|
|
imjm1 = imr*(j2-j1+2) |
|
|
len = imr*(j2-j1+3) |
|
|
! if(first) then |
|
|
! IF(JORD.LE.0) then |
|
|
! if(JMR.GE.90) then |
|
|
! LMT = 0 |
|
|
! elseif(JMR.GE.45) then |
|
|
! LMT = 1 |
|
|
! else |
|
|
! LMT = 2 |
|
|
! endif |
|
|
! else |
|
|
! LMT = JORD - 3 |
|
|
! endif |
|
|
|
|
|
! first = .false. |
|
|
! endif |
|
|
|
|
|
! modifs pour pouvoir choisir plusieurs schemas PPM |
|
|
lmt = jord - 3 |
|
|
|
|
|
DO i = 1, imr*jmr |
|
|
al(i, 2) = 0.5*(p(i,1)+p(i,2)) + (dc(i,1)-dc(i,2))*r3 |
|
|
ar(i, 1) = al(i, 2) |
|
|
END DO |
|
|
|
|
|
! Poles: |
|
|
|
|
|
DO i = 1, imh |
|
|
al(i, 1) = al(i+imh, 2) |
|
|
al(i+imh, 1) = al(i, 2) |
|
|
|
|
|
ar(i, jnp) = ar(i+imh, jmr) |
|
|
ar(i+imh, jnp) = ar(i, jmr) |
|
|
END DO |
|
|
|
|
|
! cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
|
|
! Rajout pour LMDZ.3.3 |
|
|
! ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
|
|
ar(imr, 1) = al(1, 1) |
|
|
ar(imr, jnp) = al(1, jnp) |
|
|
! cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
|
|
|
|
|
|
|
|
DO i = 1, len |
|
|
a6(i, j11) = 3.*(p(i,j11)+p(i,j11)-(al(i,j11)+ar(i,j11))) |
|
|
END DO |
|
|
|
|
|
IF (lmt<=2) CALL lmtppm(dc(1,j11), a6(1,j11), ar(1,j11), al(1,j11), & |
|
|
p(1,j11), len, lmt) |
|
|
|
|
|
|
|
|
DO i = 1, imjm1 |
|
|
IF (vc(i,j1)>0.) THEN |
|
|
flux(i, j1) = ar(i, j11) + 0.5*vc(i, j1)*(al(i,j11)-ar(i,j11)+a6(i,j11) & |
|
|
*(1.-r23*vc(i,j1))) |
|
|
ELSE |
|
|
flux(i, j1) = al(i, j1) - 0.5*vc(i, j1)*(ar(i,j1)-al(i,j1)+a6(i,j1)*(1. & |
|
|
+r23*vc(i,j1))) |
|
|
END IF |
|
|
END DO |
|
|
RETURN |
|
|
END SUBROUTINE fyppm |
|
|
|
|
|
SUBROUTINE yadv(imr, jnp, j1, j2, p, va, ady, wk, iad) |
|
|
REAL p(imr, jnp), ady(imr, jnp), va(imr, jnp) |
|
|
REAL wk(imr, -1:jnp+2) |
|
|
|
|
|
jmr = jnp - 1 |
|
|
imh = imr/2 |
|
|
DO j = 1, jnp |
|
|
DO i = 1, imr |
|
|
wk(i, j) = p(i, j) |
|
|
END DO |
|
|
END DO |
|
|
! Poles: |
|
|
DO i = 1, imh |
|
|
wk(i, -1) = p(i+imh, 3) |
|
|
wk(i+imh, -1) = p(i, 3) |
|
|
wk(i, 0) = p(i+imh, 2) |
|
|
wk(i+imh, 0) = p(i, 2) |
|
|
wk(i, jnp+1) = p(i+imh, jmr) |
|
|
wk(i+imh, jnp+1) = p(i, jmr) |
|
|
wk(i, jnp+2) = p(i+imh, jnp-2) |
|
|
wk(i+imh, jnp+2) = p(i, jnp-2) |
|
|
END DO |
|
|
|
|
|
IF (iad==2) THEN |
|
|
DO j = j1 - 1, j2 + 1 |
|
|
DO i = 1, imr |
|
|
jp = nint(va(i,j)) |
|
|
rv = jp - va(i, j) |
|
|
jp = j - jp |
|
|
a1 = 0.5*(wk(i,jp+1)+wk(i,jp-1)) - wk(i, jp) |
|
|
b1 = 0.5*(wk(i,jp+1)-wk(i,jp-1)) |
|
|
ady(i, j) = wk(i, jp) + rv*(a1*rv+b1) - wk(i, j) |
|
|
END DO |
|
|
END DO |
|
|
|
|
|
ELSE IF (iad==1) THEN |
|
|
DO j = j1 - 1, j2 + 1 |
|
|
DO i = 1, imr |
|
|
jp = float(j) - va(i, j) |
|
|
ady(i, j) = va(i, j)*(wk(i,jp)-wk(i,jp+1)) |
|
|
END DO |
|
|
END DO |
|
|
END IF |
|
|
|
|
|
IF (j1/=2) THEN |
|
|
sum1 = 0. |
|
|
sum2 = 0. |
|
|
DO i = 1, imr |
|
|
sum1 = sum1 + ady(i, 2) |
|
|
sum2 = sum2 + ady(i, jmr) |
|
|
END DO |
|
|
sum1 = sum1/imr |
|
|
sum2 = sum2/imr |
|
|
|
|
|
DO i = 1, imr |
|
|
ady(i, 2) = sum1 |
|
|
ady(i, jmr) = sum2 |
|
|
ady(i, 1) = sum1 |
|
|
ady(i, jnp) = sum2 |
|
|
END DO |
|
|
ELSE |
|
|
! Poles: |
|
|
sum1 = 0. |
|
|
sum2 = 0. |
|
|
DO i = 1, imr |
|
|
sum1 = sum1 + ady(i, 1) |
|
|
sum2 = sum2 + ady(i, jnp) |
|
|
END DO |
|
|
sum1 = sum1/imr |
|
|
sum2 = sum2/imr |
|
|
|
|
|
DO i = 1, imr |
|
|
ady(i, 1) = sum1 |
|
|
ady(i, jnp) = sum2 |
|
|
END DO |
|
|
END IF |
|
|
|
|
|
RETURN |
|
|
END SUBROUTINE yadv |
|
|
|
|
|
SUBROUTINE xadv(imr, jnp, j1, j2, p, ua, js, jn, iml, adx, iad) |
|
|
REAL p(imr, jnp), adx(imr, jnp), qtmp(-imr:imr+imr), ua(imr, jnp) |
|
|
|
|
|
jmr = jnp - 1 |
|
|
DO j = j1, j2 |
|
|
IF (j>js .AND. j<jn) GO TO 1309 |
|
|
|
|
|
DO i = 1, imr |
|
|
qtmp(i) = p(i, j) |
|
|
END DO |
|
|
|
|
|
DO i = -iml, 0 |
|
|
qtmp(i) = p(imr+i, j) |
|
|
qtmp(imr+1-i) = p(1-i, j) |
|
|
END DO |
|
|
|
|
|
IF (iad==2) THEN |
|
|
DO i = 1, imr |
|
|
ip = nint(ua(i,j)) |
|
|
ru = ip - ua(i, j) |
|
|
ip = i - ip |
|
|
a1 = 0.5*(qtmp(ip+1)+qtmp(ip-1)) - qtmp(ip) |
|
|
b1 = 0.5*(qtmp(ip+1)-qtmp(ip-1)) |
|
|
adx(i, j) = qtmp(ip) + ru*(a1*ru+b1) |
|
|
END DO |
|
|
ELSE IF (iad==1) THEN |
|
|
DO i = 1, imr |
|
|
iu = ua(i, j) |
|
|
ru = ua(i, j) - iu |
|
|
iiu = i - iu |
|
|
IF (ua(i,j)>=0.) THEN |
|
|
adx(i, j) = qtmp(iiu) + ru*(qtmp(iiu-1)-qtmp(iiu)) |
|
|
ELSE |
|
|
adx(i, j) = qtmp(iiu) + ru*(qtmp(iiu)-qtmp(iiu+1)) |
|
|
END IF |
|
|
END DO |
|
|
END IF |
|
|
|
|
|
DO i = 1, imr |
|
|
adx(i, j) = adx(i, j) - p(i, j) |
|
|
END DO |
|
|
1309 END DO |
|
|
|
|
|
! Eulerian upwind |
|
|
|
|
|
DO j = js + 1, jn - 1 |
|
|
|
|
|
DO i = 1, imr |
|
|
qtmp(i) = p(i, j) |
|
|
END DO |
|
|
|
|
|
qtmp(0) = p(imr, j) |
|
|
qtmp(imr+1) = p(1, j) |
|
|
|
|
|
IF (iad==2) THEN |
|
|
qtmp(-1) = p(imr-1, j) |
|
|
qtmp(imr+2) = p(2, j) |
|
|
DO i = 1, imr |
|
|
ip = nint(ua(i,j)) |
|
|
ru = ip - ua(i, j) |
|
|
ip = i - ip |
|
|
a1 = 0.5*(qtmp(ip+1)+qtmp(ip-1)) - qtmp(ip) |
|
|
b1 = 0.5*(qtmp(ip+1)-qtmp(ip-1)) |
|
|
adx(i, j) = qtmp(ip) - p(i, j) + ru*(a1*ru+b1) |
|
|
END DO |
|
|
ELSE IF (iad==1) THEN |
|
|
! 1st order |
|
|
DO i = 1, imr |
|
|
ip = i - ua(i, j) |
|
|
adx(i, j) = ua(i, j)*(qtmp(ip)-qtmp(ip+1)) |
|
|
END DO |
|
|
END IF |
|
|
END DO |
|
|
|
|
|
IF (j1/=2) THEN |
|
|
DO i = 1, imr |
|
|
adx(i, 2) = 0. |
|
|
adx(i, jmr) = 0. |
|
|
END DO |
|
|
END IF |
|
|
! set cross term due to x-adv at the poles to zero. |
|
|
DO i = 1, imr |
|
|
adx(i, 1) = 0. |
|
|
adx(i, jnp) = 0. |
|
|
END DO |
|
|
RETURN |
|
|
END SUBROUTINE xadv |
|
|
|
|
|
SUBROUTINE lmtppm(dc, a6, ar, al, p, im, lmt) |
|
|
|
|
|
! A6 = CURVATURE OF THE TEST PARABOLA |
|
|
! AR = RIGHT EDGE VALUE OF THE TEST PARABOLA |
|
|
! AL = LEFT EDGE VALUE OF THE TEST PARABOLA |
|
|
! DC = 0.5 * MISMATCH |
|
|
! P = CELL-AVERAGED VALUE |
|
|
! IM = VECTOR LENGTH |
|
|
|
|
|
! OPTIONS: |
|
|
|
|
|
! LMT = 0: FULL MONOTONICITY |
|
|
! LMT = 1: SEMI-MONOTONIC CONSTRAINT (NO UNDERSHOOTS) |
|
|
! LMT = 2: POSITIVE-DEFINITE CONSTRAINT |
|
|
|
|
|
PARAMETER (r12=1./12.) |
|
|
DIMENSION a6(im), ar(im), al(im), p(im), dc(im) |
|
|
|
|
|
IF (lmt==0) THEN |
|
|
! Full constraint |
|
|
DO i = 1, im |
|
|
IF (dc(i)==0.) THEN |
|
|
ar(i) = p(i) |
|
|
al(i) = p(i) |
|
|
a6(i) = 0. |
|
|
ELSE |
|
|
da1 = ar(i) - al(i) |
|
|
da2 = da1**2 |
|
|
a6da = a6(i)*da1 |
|
|
IF (a6da<-da2) THEN |
|
|
a6(i) = 3.*(al(i)-p(i)) |
|
|
ar(i) = al(i) - a6(i) |
|
|
ELSE IF (a6da>da2) THEN |
|
|
a6(i) = 3.*(ar(i)-p(i)) |
|
|
al(i) = ar(i) - a6(i) |
|
|
END IF |
|
|
END IF |
|
|
END DO |
|
|
ELSE IF (lmt==1) THEN |
|
|
! Semi-monotonic constraint |
|
|
DO i = 1, im |
|
|
IF (abs(ar(i)-al(i))>=-a6(i)) GO TO 150 |
|
|
IF (p(i)<ar(i) .AND. p(i)<al(i)) THEN |
|
|
ar(i) = p(i) |
|
|
al(i) = p(i) |
|
|
a6(i) = 0. |
|
|
ELSE IF (ar(i)>al(i)) THEN |
|
|
a6(i) = 3.*(al(i)-p(i)) |
|
|
ar(i) = al(i) - a6(i) |
|
|
ELSE |
|
|
a6(i) = 3.*(ar(i)-p(i)) |
|
|
al(i) = ar(i) - a6(i) |
|
|
END IF |
|
|
150 END DO |
|
|
ELSE IF (lmt==2) THEN |
|
|
DO i = 1, im |
|
|
IF (abs(ar(i)-al(i))>=-a6(i)) GO TO 250 |
|
|
fmin = p(i) + 0.25*(ar(i)-al(i))**2/a6(i) + a6(i)*r12 |
|
|
IF (fmin>=0.) GO TO 250 |
|
|
IF (p(i)<ar(i) .AND. p(i)<al(i)) THEN |
|
|
ar(i) = p(i) |
|
|
al(i) = p(i) |
|
|
a6(i) = 0. |
|
|
ELSE IF (ar(i)>al(i)) THEN |
|
|
a6(i) = 3.*(al(i)-p(i)) |
|
|
ar(i) = al(i) - a6(i) |
|
|
ELSE |
|
|
a6(i) = 3.*(ar(i)-p(i)) |
|
|
al(i) = ar(i) - a6(i) |
|
|
END IF |
|
|
250 END DO |
|
|
END IF |
|
|
RETURN |
|
|
END SUBROUTINE lmtppm |
|
|
|
|
|
SUBROUTINE a2c(u, v, imr, jmr, j1, j2, crx, cry, dtdx5, dtdy5) |
|
|
DIMENSION u(imr, *), v(imr, *), crx(imr, *), cry(imr, *), dtdx5(*) |
|
|
|
|
|
DO j = j1, j2 |
|
|
DO i = 2, imr |
|
|
crx(i, j) = dtdx5(j)*(u(i,j)+u(i-1,j)) |
|
|
END DO |
|
|
END DO |
|
|
|
|
|
DO j = j1, j2 |
|
|
crx(1, j) = dtdx5(j)*(u(1,j)+u(imr,j)) |
|
|
END DO |
|
|
|
|
|
DO i = 1, imr*jmr |
|
|
cry(i, 2) = dtdy5*(v(i,2)+v(i,1)) |
|
|
END DO |
|
|
RETURN |
|
|
END SUBROUTINE a2c |
|
|
|
|
|
SUBROUTINE cosa(cosp, cose, jnp, pi, dp) |
|
|
DIMENSION cosp(*), cose(*) |
|
|
|
|
|
jmr = jnp - 1 |
|
|
DO j = 2, jnp |
|
|
ph5 = -0.5*pi + (float(j-1)-0.5)*dp |
|
|
cose(j) = cos(ph5) |
|
|
END DO |
|
|
|
|
|
jeq = (jnp+1)/2 |
|
|
IF (jmr==2*(jmr/2)) THEN |
|
|
DO j = jnp, jeq + 1, -1 |
|
|
cose(j) = cose(jnp+2-j) |
|
|
END DO |
|
|
ELSE |
|
|
! cell edge at equator. |
|
|
cose(jeq+1) = 1. |
|
|
DO j = jnp, jeq + 2, -1 |
|
|
cose(j) = cose(jnp+2-j) |
|
|
END DO |
|
|
END IF |
|
|
|
|
|
DO j = 2, jmr |
|
|
cosp(j) = 0.5*(cose(j)+cose(j+1)) |
|
|
END DO |
|
|
cosp(1) = 0. |
|
|
cosp(jnp) = 0. |
|
|
RETURN |
|
|
END SUBROUTINE cosa |
|
|
|
|
|
SUBROUTINE cosc(cosp, cose, jnp, pi, dp) |
|
|
DIMENSION cosp(*), cose(*) |
|
|
|
|
|
phi = -0.5*pi |
|
|
DO j = 2, jnp - 1 |
|
|
phi = phi + dp |
|
|
cosp(j) = cos(phi) |
|
|
END DO |
|
|
cosp(1) = 0. |
|
|
cosp(jnp) = 0. |
|
|
|
|
|
DO j = 2, jnp |
|
|
cose(j) = 0.5*(cosp(j)+cosp(j-1)) |
|
|
END DO |
|
|
|
|
|
DO j = 2, jnp - 1 |
|
|
cosp(j) = 0.5*(cose(j)+cose(j+1)) |
|
|
END DO |
|
|
RETURN |
|
|
END SUBROUTINE cosc |
|
|
|
|
|
SUBROUTINE qckxyz(q, qtmp, imr, jnp, nlay, j1, j2, cosp, acosp, cross, ic, & |
|
|
nstep) |
|
|
|
|
|
PARAMETER (tiny=1.E-60) |
|
|
DIMENSION q(imr, jnp, nlay), qtmp(imr, jnp), cosp(*), acosp(*) |
|
|
LOGICAL cross |
|
|
|
|
|
nlaym1 = nlay - 1 |
|
|
len = imr*(j2-j1+1) |
|
|
ip = 0 |
|
|
|
|
|
! Top layer |
|
|
l = 1 |
|
|
icr = 1 |
|
|
CALL filns(q(1,1,l), imr, jnp, j1, j2, cosp, acosp, ipy, tiny) |
|
|
IF (ipy==0) GO TO 50 |
|
|
CALL filew(q(1,1,l), qtmp, imr, jnp, j1, j2, ipx, tiny) |
|
|
IF (ipx==0) GO TO 50 |
|
|
|
|
|
IF (cross) THEN |
|
|
CALL filcr(q(1,1,l), imr, jnp, j1, j2, cosp, acosp, icr, tiny) |
|
|
END IF |
|
|
IF (icr==0) GO TO 50 |
|
|
|
|
|
! Vertical filling... |
|
|
DO i = 1, len |
|
|
IF (q(i,j1,1)<0.) THEN |
|
|
ip = ip + 1 |
|
|
q(i, j1, 2) = q(i, j1, 2) + q(i, j1, 1) |
|
|
q(i, j1, 1) = 0. |
|
|
END IF |
|
|
END DO |
|
|
|
|
|
50 CONTINUE |
|
|
DO l = 2, nlaym1 |
|
|
icr = 1 |
|
|
|
|
|
CALL filns(q(1,1,l), imr, jnp, j1, j2, cosp, acosp, ipy, tiny) |
|
|
IF (ipy==0) GO TO 225 |
|
|
CALL filew(q(1,1,l), qtmp, imr, jnp, j1, j2, ipx, tiny) |
|
|
IF (ipx==0) GO TO 225 |
|
|
IF (cross) THEN |
|
|
CALL filcr(q(1,1,l), imr, jnp, j1, j2, cosp, acosp, icr, tiny) |
|
|
END IF |
|
|
IF (icr==0) GO TO 225 |
|
|
|
|
|
DO i = 1, len |
|
|
IF (q(i,j1,l)<0.) THEN |
|
|
|
|
|
ip = ip + 1 |
|
|
! From above |
|
|
qup = q(i, j1, l-1) |
|
|
qly = -q(i, j1, l) |
|
|
dup = min(qly, qup) |
|
|
q(i, j1, l-1) = qup - dup |
|
|
q(i, j1, l) = dup - qly |
|
|
! Below |
|
|
q(i, j1, l+1) = q(i, j1, l+1) + q(i, j1, l) |
|
|
q(i, j1, l) = 0. |
|
|
END IF |
|
|
END DO |
|
|
225 END DO |
|
|
|
|
|
! BOTTOM LAYER |
|
|
sum = 0. |
|
|
l = nlay |
|
|
|
|
|
CALL filns(q(1,1,l), imr, jnp, j1, j2, cosp, acosp, ipy, tiny) |
|
|
IF (ipy==0) GO TO 911 |
|
|
CALL filew(q(1,1,l), qtmp, imr, jnp, j1, j2, ipx, tiny) |
|
|
IF (ipx==0) GO TO 911 |
|
|
|
|
|
CALL filcr(q(1,1,l), imr, jnp, j1, j2, cosp, acosp, icr, tiny) |
|
|
IF (icr==0) GO TO 911 |
|
|
|
|
|
DO i = 1, len |
|
|
IF (q(i,j1,l)<0.) THEN |
|
|
ip = ip + 1 |
|
|
|
|
|
! From above |
|
|
|
|
|
qup = q(i, j1, nlaym1) |
|
|
qly = -q(i, j1, l) |
|
|
dup = min(qly, qup) |
|
|
q(i, j1, nlaym1) = qup - dup |
|
|
! From "below" the surface. |
|
|
sum = sum + qly - dup |
|
|
q(i, j1, l) = 0. |
|
|
END IF |
|
|
END DO |
|
|
|
|
|
911 CONTINUE |
|
|
|
|
|
IF (ip>imr) THEN |
|
|
WRITE (6, *) 'IC=', ic, ' STEP=', nstep, ' Vertical filling pts=', ip |
|
|
END IF |
|
|
|
|
|
IF (sum>1.E-25) THEN |
|
|
WRITE (6, *) ic, nstep, ' Mass source from the ground=', sum |
|
|
END IF |
|
|
RETURN |
|
|
END SUBROUTINE qckxyz |
|
|
|
|
|
SUBROUTINE filcr(q, imr, jnp, j1, j2, cosp, acosp, icr, tiny) |
|
|
DIMENSION q(imr, *), cosp(*), acosp(*) |
|
|
|
|
|
icr = 0 |
|
|
DO j = j1 + 1, j2 - 1 |
|
|
DO i = 1, imr - 1 |
|
|
IF (q(i,j)<0.) THEN |
|
|
icr = 1 |
|
|
dq = -q(i, j)*cosp(j) |
|
|
! N-E |
|
|
dn = q(i+1, j+1)*cosp(j+1) |
|
|
d0 = max(0., dn) |
|
|
d1 = min(dq, d0) |
|
|
q(i+1, j+1) = (dn-d1)*acosp(j+1) |
|
|
dq = dq - d1 |
|
|
! S-E |
|
|
ds = q(i+1, j-1)*cosp(j-1) |
|
|
d0 = max(0., ds) |
|
|
d2 = min(dq, d0) |
|
|
q(i+1, j-1) = (ds-d2)*acosp(j-1) |
|
|
q(i, j) = (d2-dq)*acosp(j) + tiny |
|
|
END IF |
|
|
END DO |
|
|
IF (icr==0 .AND. q(imr,j)>=0.) GO TO 65 |
|
|
DO i = 2, imr |
|
|
IF (q(i,j)<0.) THEN |
|
|
icr = 1 |
|
|
dq = -q(i, j)*cosp(j) |
|
|
! N-W |
|
|
dn = q(i-1, j+1)*cosp(j+1) |
|
|
d0 = max(0., dn) |
|
|
d1 = min(dq, d0) |
|
|
q(i-1, j+1) = (dn-d1)*acosp(j+1) |
|
|
dq = dq - d1 |
|
|
! S-W |
|
|
ds = q(i-1, j-1)*cosp(j-1) |
|
|
d0 = max(0., ds) |
|
|
d2 = min(dq, d0) |
|
|
q(i-1, j-1) = (ds-d2)*acosp(j-1) |
|
|
q(i, j) = (d2-dq)*acosp(j) + tiny |
|
|
END IF |
|
|
END DO |
|
|
! ***************************************** |
|
|
! i=1 |
|
|
i = 1 |
|
|
IF (q(i,j)<0.) THEN |
|
|
icr = 1 |
|
|
dq = -q(i, j)*cosp(j) |
|
|
! N-W |
|
|
dn = q(imr, j+1)*cosp(j+1) |
|
|
d0 = max(0., dn) |
|
|
d1 = min(dq, d0) |
|
|
q(imr, j+1) = (dn-d1)*acosp(j+1) |
|
|
dq = dq - d1 |
|
|
! S-W |
|
|
ds = q(imr, j-1)*cosp(j-1) |
|
|
d0 = max(0., ds) |
|
|
d2 = min(dq, d0) |
|
|
q(imr, j-1) = (ds-d2)*acosp(j-1) |
|
|
q(i, j) = (d2-dq)*acosp(j) + tiny |
|
|
END IF |
|
|
! ***************************************** |
|
|
! i=IMR |
|
|
i = imr |
|
|
IF (q(i,j)<0.) THEN |
|
|
icr = 1 |
|
|
dq = -q(i, j)*cosp(j) |
|
|
! N-E |
|
|
dn = q(1, j+1)*cosp(j+1) |
|
|
d0 = max(0., dn) |
|
|
d1 = min(dq, d0) |
|
|
q(1, j+1) = (dn-d1)*acosp(j+1) |
|
|
dq = dq - d1 |
|
|
! S-E |
|
|
ds = q(1, j-1)*cosp(j-1) |
|
|
d0 = max(0., ds) |
|
|
d2 = min(dq, d0) |
|
|
q(1, j-1) = (ds-d2)*acosp(j-1) |
|
|
q(i, j) = (d2-dq)*acosp(j) + tiny |
|
|
END IF |
|
|
! ***************************************** |
|
|
65 END DO |
|
|
|
|
|
DO i = 1, imr |
|
|
IF (q(i,j1)<0. .OR. q(i,j2)<0.) THEN |
|
|
icr = 1 |
|
|
GO TO 80 |
|
|
END IF |
|
|
END DO |
|
|
|
|
|
80 CONTINUE |
|
|
|
|
|
IF (q(1,1)<0. .OR. q(1,jnp)<0.) THEN |
|
|
icr = 1 |
|
|
END IF |
|
|
|
|
|
RETURN |
|
|
END SUBROUTINE filcr |
|
|
|
|
|
SUBROUTINE filns(q, imr, jnp, j1, j2, cosp, acosp, ipy, tiny) |
|
|
DIMENSION q(imr, *), cosp(*), acosp(*) |
|
|
! logical first |
|
|
! data first /.true./ |
|
|
! save cap1 |
|
|
|
|
|
! if(first) then |
|
|
dp = 4.*atan(1.)/float(jnp-1) |
|
|
cap1 = imr*(1.-cos((j1-1.5)*dp))/dp |
|
|
! first = .false. |
|
|
! endif |
|
|
|
|
|
ipy = 0 |
|
|
DO j = j1 + 1, j2 - 1 |
|
|
DO i = 1, imr |
|
|
IF (q(i,j)<0.) THEN |
|
|
ipy = 1 |
|
|
dq = -q(i, j)*cosp(j) |
|
|
! North |
|
|
dn = q(i, j+1)*cosp(j+1) |
|
|
d0 = max(0., dn) |
|
|
d1 = min(dq, d0) |
|
|
q(i, j+1) = (dn-d1)*acosp(j+1) |
|
|
dq = dq - d1 |
|
|
! South |
|
|
ds = q(i, j-1)*cosp(j-1) |
|
|
d0 = max(0., ds) |
|
|
d2 = min(dq, d0) |
|
|
q(i, j-1) = (ds-d2)*acosp(j-1) |
|
|
q(i, j) = (d2-dq)*acosp(j) + tiny |
|
|
END IF |
|
|
END DO |
|
|
END DO |
|
|
|
|
|
DO i = 1, imr |
|
|
IF (q(i,j1)<0.) THEN |
|
|
ipy = 1 |
|
|
dq = -q(i, j1)*cosp(j1) |
|
|
! North |
|
|
dn = q(i, j1+1)*cosp(j1+1) |
|
|
d0 = max(0., dn) |
|
|
d1 = min(dq, d0) |
|
|
q(i, j1+1) = (dn-d1)*acosp(j1+1) |
|
|
q(i, j1) = (d1-dq)*acosp(j1) + tiny |
|
|
END IF |
|
|
END DO |
|
|
|
|
|
j = j2 |
|
|
DO i = 1, imr |
|
|
IF (q(i,j)<0.) THEN |
|
|
ipy = 1 |
|
|
dq = -q(i, j)*cosp(j) |
|
|
! South |
|
|
ds = q(i, j-1)*cosp(j-1) |
|
|
d0 = max(0., ds) |
|
|
d2 = min(dq, d0) |
|
|
q(i, j-1) = (ds-d2)*acosp(j-1) |
|
|
q(i, j) = (d2-dq)*acosp(j) + tiny |
|
|
END IF |
|
|
END DO |
|
|
|
|
|
! Check Poles. |
|
|
IF (q(1,1)<0.) THEN |
|
|
dq = q(1, 1)*cap1/float(imr)*acosp(j1) |
|
|
DO i = 1, imr |
|
|
q(i, 1) = 0. |
|
|
q(i, j1) = q(i, j1) + dq |
|
|
IF (q(i,j1)<0.) ipy = 1 |
|
|
END DO |
|
|
END IF |
|
|
|
|
|
IF (q(1,jnp)<0.) THEN |
|
|
dq = q(1, jnp)*cap1/float(imr)*acosp(j2) |
|
|
DO i = 1, imr |
|
|
q(i, jnp) = 0. |
|
|
q(i, j2) = q(i, j2) + dq |
|
|
IF (q(i,j2)<0.) ipy = 1 |
|
|
END DO |
|
|
END IF |
|
|
|
|
|
RETURN |
|
|
END SUBROUTINE filns |
|
|
|
|
|
SUBROUTINE filew(q, qtmp, imr, jnp, j1, j2, ipx, tiny) |
|
|
DIMENSION q(imr, *), qtmp(jnp, imr) |
|
|
|
|
|
ipx = 0 |
|
|
! Copy & swap direction for vectorization. |
|
|
DO i = 1, imr |
|
|
DO j = j1, j2 |
|
|
qtmp(j, i) = q(i, j) |
|
|
END DO |
|
|
END DO |
|
|
|
|
|
DO i = 2, imr - 1 |
|
|
DO j = j1, j2 |
|
|
IF (qtmp(j,i)<0.) THEN |
|
|
ipx = 1 |
|
|
! west |
|
|
d0 = max(0., qtmp(j,i-1)) |
|
|
d1 = min(-qtmp(j,i), d0) |
|
|
qtmp(j, i-1) = qtmp(j, i-1) - d1 |
|
|
qtmp(j, i) = qtmp(j, i) + d1 |
|
|
! east |
|
|
d0 = max(0., qtmp(j,i+1)) |
|
|
d2 = min(-qtmp(j,i), d0) |
|
|
qtmp(j, i+1) = qtmp(j, i+1) - d2 |
|
|
qtmp(j, i) = qtmp(j, i) + d2 + tiny |
|
|
END IF |
|
|
END DO |
|
|
END DO |
|
|
|
|
|
i = 1 |
|
|
DO j = j1, j2 |
|
|
IF (qtmp(j,i)<0.) THEN |
|
|
ipx = 1 |
|
|
! west |
|
|
d0 = max(0., qtmp(j,imr)) |
|
|
d1 = min(-qtmp(j,i), d0) |
|
|
qtmp(j, imr) = qtmp(j, imr) - d1 |
|
|
qtmp(j, i) = qtmp(j, i) + d1 |
|
|
! east |
|
|
d0 = max(0., qtmp(j,i+1)) |
|
|
d2 = min(-qtmp(j,i), d0) |
|
|
qtmp(j, i+1) = qtmp(j, i+1) - d2 |
|
|
|
|
|
qtmp(j, i) = qtmp(j, i) + d2 + tiny |
|
|
END IF |
|
|
END DO |
|
|
i = imr |
|
|
DO j = j1, j2 |
|
|
IF (qtmp(j,i)<0.) THEN |
|
|
ipx = 1 |
|
|
! west |
|
|
d0 = max(0., qtmp(j,i-1)) |
|
|
d1 = min(-qtmp(j,i), d0) |
|
|
qtmp(j, i-1) = qtmp(j, i-1) - d1 |
|
|
qtmp(j, i) = qtmp(j, i) + d1 |
|
|
! east |
|
|
d0 = max(0., qtmp(j,1)) |
|
|
d2 = min(-qtmp(j,i), d0) |
|
|
qtmp(j, 1) = qtmp(j, 1) - d2 |
|
|
|
|
|
qtmp(j, i) = qtmp(j, i) + d2 + tiny |
|
|
END IF |
|
|
END DO |
|
|
|
|
|
IF (ipx/=0) THEN |
|
|
DO j = j1, j2 |
|
|
DO i = 1, imr |
|
|
q(i, j) = qtmp(j, i) |
|
|
END DO |
|
|
END DO |
|
|
ELSE |
|
|
|
|
|
! Poles. |
|
|
IF (q(1,1)<0 .OR. q(1,jnp)<0.) ipx = 1 |
|
|
END IF |
|
|
RETURN |
|
|
END SUBROUTINE filew |
|
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