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| 2 | ! gfortran -cpp -O3 -flto ex_5.f90 -o ex_5 |
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| 3 | ! ./ex_5 |
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| 4 | |
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| 5 | ! Assemble high-order interpolants over a uniform domain. |
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| 6 | ! |
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| 7 | |
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| 8 | # include "../src/ppr_1d.f90" |
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| 9 | |
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| 10 | program ex |
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| 11 | |
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| 12 | use ppr_1d |
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| 13 | |
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| 14 | implicit none |
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| 15 | |
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| 16 | integer, parameter :: npos = 43 ! no. edge |
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| 17 | integer, parameter :: nvar = 1 ! no. variables to build |
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| 18 | integer, parameter :: ndof = 1 ! no. FV DoF per cell |
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| 19 | integer :: ipos,jpos,mdof |
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| 20 | |
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| 21 | !------------------------------- domain discretisation ! |
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| 22 | real*8 :: xpos(npos),xdel(1) |
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| 23 | real*8 :: xmid,xhat,xloc,floc |
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| 24 | |
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| 25 | !-------------------------------- finite-volume arrays ! |
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| 26 | |
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| 27 | ! Arrays represent a "block" of finite-volume tracers |
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| 28 | ! to remap. The 1st dim. is the no. of DoF per cell, |
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| 29 | ! NDOF=1 is a standard finite-volume scheme where the |
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| 30 | ! data is specified as cell means. NDOF>1 is reserved |
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| 31 | ! for future use with DG-style schemes. NVAR is the |
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| 32 | ! number of tracers to remap. Processing tracers in a |
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| 33 | ! batch is typically more efficient than one-by-one. |
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| 34 | ! The last dim. is the no. cells (layers) in the grid. |
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| 35 | |
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| 36 | real*8 :: fdat(ndof,nvar,npos-1) |
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| 37 | |
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| 38 | !-------------------------------- reconstruction coeff ! |
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| 39 | |
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| 40 | ! Coeff. for the piecewise polynomial reconstruction. |
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| 41 | ! A polynomial is assembled for each cell w.r.t. a |
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| 42 | ! "local" cell coordinate system: each cell is mapped |
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| 43 | ! onto [-1,+1]. The interpolants can be evaluated by |
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| 44 | ! taking the product FHAT*BVEC, where BVEC is a basis |
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| 45 | ! vector assembled at the interpolation points. Basis |
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| 46 | ! vectors can eb assembled via calls to BFUN1D(). |
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| 47 | |
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| 48 | real*8 :: fhat( 5,nvar,npos-1) |
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| 49 | real*8 :: bvec( 5) |
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| 50 | real*8 :: spos( 5) |
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| 51 | |
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| 52 | !------------------------------ method data-structures ! |
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| 53 | type(rcon_work) :: work |
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| 54 | type(rcon_opts) :: opts |
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| 55 | type(rcon_ends) :: bc_l(nvar) |
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| 56 | type(rcon_ends) :: bc_r(nvar) |
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| 57 | |
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| 58 | !------------------------------ define a simple domain ! |
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| 59 | |
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| 60 | call linspace(0.d0,1.d0,npos,xpos) |
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| 61 | |
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| 62 | xdel(1) = (xpos(npos)& |
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| 63 | & - xpos( 1)) / (npos- 1) |
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| 64 | |
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| 65 | !------------------------------ setup some simple data ! |
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| 66 | |
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| 67 | do ipos = +1, npos-1 |
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| 68 | |
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| 69 | xmid = xpos(ipos+0) * 0.5d+0 & |
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| 70 | & + xpos(ipos+1) * 0.5d+0 |
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| 71 | |
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| 72 | fdat(1,1,ipos) = & |
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| 73 | & .8d+0 * exp( -75.0d+0 * (xmid - 0.275d+0) ** 2 ) & |
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| 74 | & + .9d+0 * exp(-100.0d+0 * (xmid - 0.500d+0) ** 2 ) & |
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| 75 | & + 1.d+0 * exp(-125.0d+0 * (xmid - 0.725d+0) ** 2 ) |
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| 76 | |
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| 77 | end do |
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| 78 | |
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| 79 | !------------------------------ specify method options ! |
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| 80 | |
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| 81 | opts%edge_meth = p5e_method ! 5th-order edge interp. |
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| 82 | opts%cell_meth = pqm_method ! PPM method in cells |
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| 83 | opts%cell_lims = mono_limit ! monotone limiter |
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| 84 | |
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| 85 | !------------------------------ set BC.'s at endpoints ! |
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| 86 | |
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| 87 | bc_l%bcopt = bcon_loose ! "loose" = extrapolate |
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| 88 | bc_r%bcopt = bcon_loose |
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| 89 | |
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| 90 | !------------------------------ init. method workspace ! |
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| 91 | |
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| 92 | call work%init(npos,nvar,opts) |
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| 93 | |
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| 94 | !------------------------------ build cell polynomials ! |
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| 95 | |
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| 96 | fhat = 0.d+0 |
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| 97 | |
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| 98 | mdof = ndof1d (opts%cell_meth) |
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| 99 | |
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| 100 | call rcon1d(npos,nvar,ndof,xdel, & |
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| 101 | & fdat,bc_l,bc_r,fhat, & |
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| 102 | & work,opts) |
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| 103 | |
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| 104 | !------------------------------ clear method workspace ! |
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| 105 | |
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| 106 | call work%free() |
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| 107 | |
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| 108 | !------------------------------ dump results to stdout ! |
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| 109 | |
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| 110 | print*,"Eval. PPR interpolant: " |
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| 111 | |
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| 112 | spos(1) = -1.0d+0 ! eval. at local points |
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| 113 | spos(2) = -0.5d+0 |
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| 114 | spos(3) = +0.0d+0 |
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| 115 | spos(4) = +0.5d+0 |
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| 116 | spos(5) = +1.0d+0 |
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| 117 | |
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| 118 | do ipos = +1, npos-1 |
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| 119 | do jpos = +1, +5 |
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| 120 | |
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| 121 | xmid = xpos(ipos+1)* 0.5d+0 & |
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| 122 | & + xpos(ipos+0)* 0.5d+0 |
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| 123 | |
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| 124 | xhat = xpos(ipos+1)* 0.5d+0 & |
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| 125 | & - xpos(ipos+0)* 0.5d+0 |
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| 126 | |
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| 127 | xloc = xmid + spos(jpos)*xhat |
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| 128 | |
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| 129 | call bfun1d(0,mdof,spos(jpos),bvec) |
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| 130 | |
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| 131 | floc = dot_product( & |
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| 132 | & fhat(+1:mdof,1,ipos),bvec(+1:mdof)) |
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| 133 | |
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| 134 | print *, xloc, floc |
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| 135 | |
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| 136 | end do |
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| 137 | end do |
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| 138 | |
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| 139 | end program |
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| 140 | |
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| 141 | |
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| 142 | |
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