[1850] | 1 | !> @file tridia_solver_mod.f90 |
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[2000] | 2 | !------------------------------------------------------------------------------! |
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[2696] | 3 | ! This file is part of the PALM model system. |
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[1212] | 4 | ! |
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[2000] | 5 | ! PALM is free software: you can redistribute it and/or modify it under the |
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| 6 | ! terms of the GNU General Public License as published by the Free Software |
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| 7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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| 8 | ! version. |
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[1212] | 9 | ! |
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| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 13 | ! |
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| 14 | ! You should have received a copy of the GNU General Public License along with |
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| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 16 | ! |
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[3655] | 17 | ! Copyright 1997-2019 Leibniz Universitaet Hannover |
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[2000] | 18 | !------------------------------------------------------------------------------! |
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[1212] | 19 | ! |
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| 20 | ! Current revisions: |
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| 21 | ! ------------------ |
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[1851] | 22 | ! |
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[2119] | 23 | ! |
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[1321] | 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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| 26 | ! $Id: tridia_solver_mod.f90 4236 2019-09-25 11:26:18Z schwenkel $ |
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[4236] | 27 | ! Added missing OpenMP directives |
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| 28 | ! |
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| 29 | ! 4182 2019-08-22 15:20:23Z scharf |
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[4182] | 30 | ! Corrected "Former revisions" section |
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[4181] | 31 | ! |
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[4182] | 32 | ! 3761 2019-02-25 15:31:42Z raasch |
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[3761] | 33 | ! OpenACC modification to prevent compiler warning about unused variable |
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| 34 | ! |
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| 35 | ! 3690 2019-01-22 22:56:42Z knoop |
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[3634] | 36 | ! OpenACC port for SPEC |
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[1321] | 37 | ! |
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[4182] | 38 | ! 1212 2013-08-15 08:46:27Z raasch |
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| 39 | ! Initial revision. |
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| 40 | ! Routines have been moved to seperate module from former file poisfft to here. |
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| 41 | ! The tridiagonal matrix coefficients of array tri are calculated only once at |
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| 42 | ! the beginning, i.e. routine split is called within tridia_init. |
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| 43 | ! |
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| 44 | ! |
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[1212] | 45 | ! Description: |
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| 46 | ! ------------ |
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[1682] | 47 | !> solves the linear system of equations: |
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| 48 | !> |
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| 49 | !> -(4 pi^2(i^2/(dx^2*nnx^2)+j^2/(dy^2*nny^2))+ |
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| 50 | !> 1/(dzu(k)*dzw(k))+1/(dzu(k-1)*dzw(k)))*p(i,j,k)+ |
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| 51 | !> 1/(dzu(k)*dzw(k))*p(i,j,k+1)+1/(dzu(k-1)*dzw(k))*p(i,j,k-1)=d(i,j,k) |
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| 52 | !> |
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| 53 | !> by using the Thomas algorithm |
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[1212] | 54 | !------------------------------------------------------------------------------! |
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[4181] | 55 | |
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| 56 | #define __acc_fft_device ( defined( _OPENACC ) && ( defined ( __cuda_fft ) ) ) |
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| 57 | |
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[1682] | 58 | MODULE tridia_solver |
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| 59 | |
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[1212] | 60 | |
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[3274] | 61 | USE basic_constants_and_equations_mod, & |
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| 62 | ONLY: pi |
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| 63 | |
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[1320] | 64 | USE indices, & |
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| 65 | ONLY: nx, ny, nz |
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[1212] | 66 | |
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[1320] | 67 | USE kinds |
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| 68 | |
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| 69 | USE transpose_indices, & |
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| 70 | ONLY: nxl_z, nyn_z, nxr_z, nys_z |
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| 71 | |
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[1212] | 72 | IMPLICIT NONE |
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| 73 | |
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[1682] | 74 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ddzuw !< |
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[1212] | 75 | |
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| 76 | PRIVATE |
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| 77 | |
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| 78 | INTERFACE tridia_substi |
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| 79 | MODULE PROCEDURE tridia_substi |
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| 80 | END INTERFACE tridia_substi |
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| 81 | |
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[1216] | 82 | INTERFACE tridia_substi_overlap |
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| 83 | MODULE PROCEDURE tridia_substi_overlap |
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| 84 | END INTERFACE tridia_substi_overlap |
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[1212] | 85 | |
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[1216] | 86 | PUBLIC tridia_substi, tridia_substi_overlap, tridia_init, tridia_1dd |
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| 87 | |
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[1212] | 88 | CONTAINS |
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| 89 | |
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| 90 | |
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[1682] | 91 | !------------------------------------------------------------------------------! |
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| 92 | ! Description: |
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| 93 | ! ------------ |
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| 94 | !> @todo Missing subroutine description. |
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| 95 | !------------------------------------------------------------------------------! |
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[1212] | 96 | SUBROUTINE tridia_init |
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| 97 | |
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[1320] | 98 | USE arrays_3d, & |
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[3761] | 99 | ONLY: ddzu_pres, ddzw, rho_air_zw |
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[1212] | 100 | |
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[3761] | 101 | #if defined( _OPENACC ) |
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| 102 | USE arrays_3d, & |
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| 103 | ONLY: tri |
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| 104 | #endif |
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| 105 | |
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[1212] | 106 | IMPLICIT NONE |
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| 107 | |
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[1682] | 108 | INTEGER(iwp) :: k !< |
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[1212] | 109 | |
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| 110 | ALLOCATE( ddzuw(0:nz-1,3) ) |
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| 111 | |
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| 112 | DO k = 0, nz-1 |
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[2037] | 113 | ddzuw(k,1) = ddzu_pres(k+1) * ddzw(k+1) * rho_air_zw(k) |
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| 114 | ddzuw(k,2) = ddzu_pres(k+2) * ddzw(k+1) * rho_air_zw(k+1) |
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[1342] | 115 | ddzuw(k,3) = -1.0_wp * & |
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[2037] | 116 | ( ddzu_pres(k+2) * ddzw(k+1) * rho_air_zw(k+1) + & |
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| 117 | ddzu_pres(k+1) * ddzw(k+1) * rho_air_zw(k) ) |
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[1212] | 118 | ENDDO |
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| 119 | ! |
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| 120 | !-- Calculate constant coefficients of the tridiagonal matrix |
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| 121 | CALL maketri |
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| 122 | CALL split |
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| 123 | |
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[3690] | 124 | #if __acc_fft_device |
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[3634] | 125 | !$ACC ENTER DATA & |
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| 126 | !$ACC COPYIN(ddzuw(0:nz-1,1:3)) & |
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| 127 | !$ACC COPYIN(tri(nxl_z:nxr_z,nys_z:nyn_z,0:nz-1,1:2)) |
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[3690] | 128 | #endif |
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[3634] | 129 | |
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[1212] | 130 | END SUBROUTINE tridia_init |
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| 131 | |
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| 132 | |
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| 133 | !------------------------------------------------------------------------------! |
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[1682] | 134 | ! Description: |
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| 135 | ! ------------ |
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| 136 | !> Computes the i- and j-dependent component of the matrix |
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| 137 | !> Provide the constant coefficients of the tridiagonal matrix for solution |
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| 138 | !> of the Poisson equation in Fourier space. |
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| 139 | !> The coefficients are computed following the method of |
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| 140 | !> Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
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| 141 | !> Siano's original version by discretizing the Poisson equation, |
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| 142 | !> before it is Fourier-transformed. |
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[1212] | 143 | !------------------------------------------------------------------------------! |
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[1682] | 144 | SUBROUTINE maketri |
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[1212] | 145 | |
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[1682] | 146 | |
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[1320] | 147 | USE arrays_3d, & |
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[2037] | 148 | ONLY: tric, rho_air |
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[1212] | 149 | |
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[1320] | 150 | USE control_parameters, & |
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| 151 | ONLY: ibc_p_b, ibc_p_t |
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| 152 | |
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| 153 | USE grid_variables, & |
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| 154 | ONLY: dx, dy |
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| 155 | |
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| 156 | |
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[1212] | 157 | IMPLICIT NONE |
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| 158 | |
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[1682] | 159 | INTEGER(iwp) :: i !< |
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| 160 | INTEGER(iwp) :: j !< |
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| 161 | INTEGER(iwp) :: k !< |
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| 162 | INTEGER(iwp) :: nnxh !< |
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| 163 | INTEGER(iwp) :: nnyh !< |
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[1212] | 164 | |
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[1682] | 165 | REAL(wp) :: ll(nxl_z:nxr_z,nys_z:nyn_z) !< |
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[1212] | 166 | |
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| 167 | |
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| 168 | nnxh = ( nx + 1 ) / 2 |
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| 169 | nnyh = ( ny + 1 ) / 2 |
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| 170 | |
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| 171 | DO j = nys_z, nyn_z |
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| 172 | DO i = nxl_z, nxr_z |
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| 173 | IF ( j >= 0 .AND. j <= nnyh ) THEN |
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| 174 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
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[1342] | 175 | ll(i,j) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * i ) / & |
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| 176 | REAL( nx+1, KIND=wp ) ) ) / ( dx * dx ) + & |
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| 177 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * j ) / & |
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| 178 | REAL( ny+1, KIND=wp ) ) ) / ( dy * dy ) |
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[1212] | 179 | ELSE |
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[1342] | 180 | ll(i,j) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * ( nx+1-i ) ) / & |
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| 181 | REAL( nx+1, KIND=wp ) ) ) / ( dx * dx ) + & |
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| 182 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * j ) / & |
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| 183 | REAL( ny+1, KIND=wp ) ) ) / ( dy * dy ) |
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[1212] | 184 | ENDIF |
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| 185 | ELSE |
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| 186 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
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[1342] | 187 | ll(i,j) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * i ) / & |
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| 188 | REAL( nx+1, KIND=wp ) ) ) / ( dx * dx ) + & |
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| 189 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * ( ny+1-j ) ) / & |
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| 190 | REAL( ny+1, KIND=wp ) ) ) / ( dy * dy ) |
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[1212] | 191 | ELSE |
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[1342] | 192 | ll(i,j) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * ( nx+1-i ) ) / & |
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| 193 | REAL( nx+1, KIND=wp ) ) ) / ( dx * dx ) + & |
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| 194 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * ( ny+1-j ) ) / & |
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| 195 | REAL( ny+1, KIND=wp ) ) ) / ( dy * dy ) |
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[1212] | 196 | ENDIF |
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| 197 | ENDIF |
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| 198 | ENDDO |
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| 199 | ENDDO |
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| 200 | |
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| 201 | DO k = 0, nz-1 |
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| 202 | DO j = nys_z, nyn_z |
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| 203 | DO i = nxl_z, nxr_z |
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[2037] | 204 | tric(i,j,k) = ddzuw(k,3) - ll(i,j) * rho_air(k+1) |
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[1212] | 205 | ENDDO |
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| 206 | ENDDO |
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| 207 | ENDDO |
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| 208 | |
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| 209 | IF ( ibc_p_b == 1 ) THEN |
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| 210 | DO j = nys_z, nyn_z |
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| 211 | DO i = nxl_z, nxr_z |
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| 212 | tric(i,j,0) = tric(i,j,0) + ddzuw(0,1) |
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| 213 | ENDDO |
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| 214 | ENDDO |
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| 215 | ENDIF |
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| 216 | IF ( ibc_p_t == 1 ) THEN |
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| 217 | DO j = nys_z, nyn_z |
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| 218 | DO i = nxl_z, nxr_z |
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| 219 | tric(i,j,nz-1) = tric(i,j,nz-1) + ddzuw(nz-1,2) |
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| 220 | ENDDO |
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| 221 | ENDDO |
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| 222 | ENDIF |
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| 223 | |
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| 224 | END SUBROUTINE maketri |
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| 225 | |
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| 226 | |
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| 227 | !------------------------------------------------------------------------------! |
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[1682] | 228 | ! Description: |
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| 229 | ! ------------ |
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| 230 | !> Substitution (Forward and Backward) (Thomas algorithm) |
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[1212] | 231 | !------------------------------------------------------------------------------! |
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[1682] | 232 | SUBROUTINE tridia_substi( ar ) |
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[1212] | 233 | |
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[1682] | 234 | |
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[1320] | 235 | USE arrays_3d, & |
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| 236 | ONLY: tri |
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[1212] | 237 | |
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[1320] | 238 | USE control_parameters, & |
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| 239 | ONLY: ibc_p_b, ibc_p_t |
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| 240 | |
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[1212] | 241 | IMPLICIT NONE |
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| 242 | |
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[1682] | 243 | INTEGER(iwp) :: i !< |
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| 244 | INTEGER(iwp) :: j !< |
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| 245 | INTEGER(iwp) :: k !< |
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[1212] | 246 | |
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[1682] | 247 | REAL(wp) :: ar(nxl_z:nxr_z,nys_z:nyn_z,1:nz) !< |
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[1212] | 248 | |
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[1682] | 249 | REAL(wp), DIMENSION(nxl_z:nxr_z,nys_z:nyn_z,0:nz-1) :: ar1 !< |
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[3690] | 250 | #if __acc_fft_device |
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[3634] | 251 | !$ACC DECLARE CREATE(ar1) |
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[3690] | 252 | #endif |
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[1212] | 253 | |
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[4236] | 254 | !$OMP PARALLEL PRIVATE(i,j,k) |
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| 255 | |
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[1212] | 256 | ! |
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| 257 | !-- Forward substitution |
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[3690] | 258 | #if __acc_fft_device |
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[3634] | 259 | !$ACC PARALLEL PRESENT(ar, ar1, tri) PRIVATE(i,j,k) |
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[3690] | 260 | #endif |
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[1212] | 261 | DO k = 0, nz - 1 |
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[3690] | 262 | #if __acc_fft_device |
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[3634] | 263 | !$ACC LOOP COLLAPSE(2) |
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[3690] | 264 | #endif |
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[4236] | 265 | !$OMP DO |
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[1212] | 266 | DO j = nys_z, nyn_z |
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| 267 | DO i = nxl_z, nxr_z |
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| 268 | |
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| 269 | IF ( k == 0 ) THEN |
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| 270 | ar1(i,j,k) = ar(i,j,k+1) |
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| 271 | ELSE |
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| 272 | ar1(i,j,k) = ar(i,j,k+1) - tri(i,j,k,2) * ar1(i,j,k-1) |
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| 273 | ENDIF |
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| 274 | |
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| 275 | ENDDO |
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| 276 | ENDDO |
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| 277 | ENDDO |
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[3690] | 278 | #if __acc_fft_device |
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[3634] | 279 | !$ACC END PARALLEL |
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[3690] | 280 | #endif |
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[1212] | 281 | |
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| 282 | ! |
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| 283 | !-- Backward substitution |
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| 284 | !-- Note, the 1.0E-20 in the denominator is due to avoid divisions |
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| 285 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
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| 286 | !-- the model domain. |
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[3690] | 287 | #if __acc_fft_device |
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[3634] | 288 | !$ACC PARALLEL PRESENT(ar, ar1, ddzuw, tri) PRIVATE(i,j,k) |
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[3690] | 289 | #endif |
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[1212] | 290 | DO k = nz-1, 0, -1 |
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[3690] | 291 | #if __acc_fft_device |
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[3634] | 292 | !$ACC LOOP COLLAPSE(2) |
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[3690] | 293 | #endif |
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[4236] | 294 | !$OMP DO |
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[1212] | 295 | DO j = nys_z, nyn_z |
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| 296 | DO i = nxl_z, nxr_z |
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| 297 | |
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| 298 | IF ( k == nz-1 ) THEN |
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[1342] | 299 | ar(i,j,k+1) = ar1(i,j,k) / ( tri(i,j,k,1) + 1.0E-20_wp ) |
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[1212] | 300 | ELSE |
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| 301 | ar(i,j,k+1) = ( ar1(i,j,k) - ddzuw(k,2) * ar(i,j,k+2) ) & |
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| 302 | / tri(i,j,k,1) |
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| 303 | ENDIF |
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| 304 | ENDDO |
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| 305 | ENDDO |
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| 306 | ENDDO |
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[3690] | 307 | #if __acc_fft_device |
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[3634] | 308 | !$ACC END PARALLEL |
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[3690] | 309 | #endif |
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[1212] | 310 | |
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[4236] | 311 | !$OMP END PARALLEL |
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| 312 | |
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[1212] | 313 | ! |
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| 314 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
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| 315 | !-- The respective values of ar should be zero at all k-levels if |
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| 316 | !-- acceleration of horizontally averaged vertical velocity is zero. |
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| 317 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
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| 318 | IF ( nys_z == 0 .AND. nxl_z == 0 ) THEN |
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[3690] | 319 | #if __acc_fft_device |
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[3634] | 320 | !$ACC PARALLEL LOOP PRESENT(ar) |
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[3690] | 321 | #endif |
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[1212] | 322 | DO k = 1, nz |
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[1342] | 323 | ar(nxl_z,nys_z,k) = 0.0_wp |
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[1212] | 324 | ENDDO |
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| 325 | ENDIF |
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| 326 | ENDIF |
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| 327 | |
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| 328 | END SUBROUTINE tridia_substi |
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| 329 | |
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| 330 | |
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[1216] | 331 | !------------------------------------------------------------------------------! |
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[1682] | 332 | ! Description: |
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| 333 | ! ------------ |
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| 334 | !> Substitution (Forward and Backward) (Thomas algorithm) |
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[1216] | 335 | !------------------------------------------------------------------------------! |
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[1682] | 336 | SUBROUTINE tridia_substi_overlap( ar, jj ) |
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[1216] | 337 | |
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[1682] | 338 | |
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[1320] | 339 | USE arrays_3d, & |
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| 340 | ONLY: tri |
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[1216] | 341 | |
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[1320] | 342 | USE control_parameters, & |
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| 343 | ONLY: ibc_p_b, ibc_p_t |
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| 344 | |
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[1216] | 345 | IMPLICIT NONE |
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| 346 | |
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[1682] | 347 | INTEGER(iwp) :: i !< |
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| 348 | INTEGER(iwp) :: j !< |
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| 349 | INTEGER(iwp) :: jj !< |
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| 350 | INTEGER(iwp) :: k !< |
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[1216] | 351 | |
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[1682] | 352 | REAL(wp) :: ar(nxl_z:nxr_z,nys_z:nyn_z,1:nz) !< |
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[1216] | 353 | |
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[1682] | 354 | REAL(wp), DIMENSION(nxl_z:nxr_z,nys_z:nyn_z,0:nz-1) :: ar1 !< |
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[1216] | 355 | |
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| 356 | ! |
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| 357 | !-- Forward substitution |
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| 358 | DO k = 0, nz - 1 |
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| 359 | DO j = nys_z, nyn_z |
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| 360 | DO i = nxl_z, nxr_z |
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| 361 | |
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| 362 | IF ( k == 0 ) THEN |
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| 363 | ar1(i,j,k) = ar(i,j,k+1) |
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| 364 | ELSE |
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| 365 | ar1(i,j,k) = ar(i,j,k+1) - tri(i,jj,k,2) * ar1(i,j,k-1) |
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| 366 | ENDIF |
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| 367 | |
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| 368 | ENDDO |
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| 369 | ENDDO |
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| 370 | ENDDO |
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| 371 | |
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| 372 | ! |
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| 373 | !-- Backward substitution |
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| 374 | !-- Note, the 1.0E-20 in the denominator is due to avoid divisions |
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| 375 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
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| 376 | !-- the model domain. |
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| 377 | DO k = nz-1, 0, -1 |
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| 378 | DO j = nys_z, nyn_z |
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| 379 | DO i = nxl_z, nxr_z |
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| 380 | |
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| 381 | IF ( k == nz-1 ) THEN |
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[1342] | 382 | ar(i,j,k+1) = ar1(i,j,k) / ( tri(i,jj,k,1) + 1.0E-20_wp ) |
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[1216] | 383 | ELSE |
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| 384 | ar(i,j,k+1) = ( ar1(i,j,k) - ddzuw(k,2) * ar(i,j,k+2) ) & |
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| 385 | / tri(i,jj,k,1) |
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| 386 | ENDIF |
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| 387 | ENDDO |
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| 388 | ENDDO |
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| 389 | ENDDO |
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| 390 | |
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| 391 | ! |
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| 392 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
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| 393 | !-- The respective values of ar should be zero at all k-levels if |
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| 394 | !-- acceleration of horizontally averaged vertical velocity is zero. |
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| 395 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
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| 396 | IF ( nys_z == 0 .AND. nxl_z == 0 ) THEN |
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| 397 | DO k = 1, nz |
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[1342] | 398 | ar(nxl_z,nys_z,k) = 0.0_wp |
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[1216] | 399 | ENDDO |
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| 400 | ENDIF |
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| 401 | ENDIF |
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| 402 | |
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| 403 | END SUBROUTINE tridia_substi_overlap |
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| 404 | |
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| 405 | |
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[1212] | 406 | !------------------------------------------------------------------------------! |
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[1682] | 407 | ! Description: |
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| 408 | ! ------------ |
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| 409 | !> Splitting of the tridiagonal matrix (Thomas algorithm) |
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[1212] | 410 | !------------------------------------------------------------------------------! |
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[1682] | 411 | SUBROUTINE split |
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[1212] | 412 | |
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[1682] | 413 | |
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[1320] | 414 | USE arrays_3d, & |
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| 415 | ONLY: tri, tric |
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[1212] | 416 | |
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| 417 | IMPLICIT NONE |
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| 418 | |
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[1682] | 419 | INTEGER(iwp) :: i !< |
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| 420 | INTEGER(iwp) :: j !< |
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| 421 | INTEGER(iwp) :: k !< |
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[1212] | 422 | ! |
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| 423 | !-- Splitting |
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| 424 | DO j = nys_z, nyn_z |
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| 425 | DO i = nxl_z, nxr_z |
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| 426 | tri(i,j,0,1) = tric(i,j,0) |
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| 427 | ENDDO |
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| 428 | ENDDO |
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| 429 | |
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| 430 | DO k = 1, nz-1 |
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| 431 | DO j = nys_z, nyn_z |
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| 432 | DO i = nxl_z, nxr_z |
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| 433 | tri(i,j,k,2) = ddzuw(k,1) / tri(i,j,k-1,1) |
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| 434 | tri(i,j,k,1) = tric(i,j,k) - ddzuw(k-1,2) * tri(i,j,k,2) |
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| 435 | ENDDO |
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| 436 | ENDDO |
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| 437 | ENDDO |
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| 438 | |
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| 439 | END SUBROUTINE split |
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| 440 | |
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| 441 | |
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| 442 | !------------------------------------------------------------------------------! |
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[1682] | 443 | ! Description: |
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| 444 | ! ------------ |
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| 445 | !> Solves the linear system of equations for a 1d-decomposition along x (see |
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| 446 | !> tridia) |
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| 447 | !> |
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| 448 | !> @attention when using the intel compilers older than 12.0, array tri must |
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| 449 | !> be passed as an argument to the contained subroutines. Otherwise |
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| 450 | !> addres faults will occur. This feature can be activated with |
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| 451 | !> cpp-switch __intel11 |
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| 452 | !> On NEC, tri should not be passed (except for routine substi_1dd) |
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| 453 | !> because this causes very bad performance. |
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[1212] | 454 | !------------------------------------------------------------------------------! |
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[1682] | 455 | |
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| 456 | SUBROUTINE tridia_1dd( ddx2, ddy2, nx, ny, j, ar, tri_for_1d ) |
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[1212] | 457 | |
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[1682] | 458 | |
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[1320] | 459 | USE arrays_3d, & |
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[2037] | 460 | ONLY: ddzu_pres, ddzw, rho_air, rho_air_zw |
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[1212] | 461 | |
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[1320] | 462 | USE control_parameters, & |
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| 463 | ONLY: ibc_p_b, ibc_p_t |
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[1212] | 464 | |
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| 465 | IMPLICIT NONE |
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| 466 | |
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[1682] | 467 | INTEGER(iwp) :: i !< |
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| 468 | INTEGER(iwp) :: j !< |
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| 469 | INTEGER(iwp) :: k !< |
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| 470 | INTEGER(iwp) :: nnyh !< |
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| 471 | INTEGER(iwp) :: nx !< |
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| 472 | INTEGER(iwp) :: ny !< |
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[1212] | 473 | |
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[1682] | 474 | REAL(wp) :: ddx2 !< |
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| 475 | REAL(wp) :: ddy2 !< |
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[1212] | 476 | |
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[1682] | 477 | REAL(wp), DIMENSION(0:nx,1:nz) :: ar !< |
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| 478 | REAL(wp), DIMENSION(5,0:nx,0:nz-1) :: tri_for_1d !< |
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[1212] | 479 | |
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| 480 | |
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| 481 | nnyh = ( ny + 1 ) / 2 |
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| 482 | |
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| 483 | ! |
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| 484 | !-- Define constant elements of the tridiagonal matrix. |
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| 485 | !-- The compiler on SX6 does loop exchange. If 0:nx is a high power of 2, |
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| 486 | !-- the exchanged loops create bank conflicts. The following directive |
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| 487 | !-- prohibits loop exchange and the loops perform much better. |
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| 488 | !CDIR NOLOOPCHG |
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| 489 | DO k = 0, nz-1 |
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| 490 | DO i = 0,nx |
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[2037] | 491 | tri_for_1d(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) * rho_air_zw(k) |
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| 492 | tri_for_1d(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) * rho_air_zw(k+1) |
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[1212] | 493 | ENDDO |
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| 494 | ENDDO |
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| 495 | |
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| 496 | IF ( j <= nnyh ) THEN |
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| 497 | CALL maketri_1dd( j ) |
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| 498 | ELSE |
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| 499 | CALL maketri_1dd( ny+1-j ) |
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| 500 | ENDIF |
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[1815] | 501 | |
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[1212] | 502 | CALL split_1dd |
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[1221] | 503 | CALL substi_1dd( ar, tri_for_1d ) |
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[1212] | 504 | |
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| 505 | CONTAINS |
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| 506 | |
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[1682] | 507 | |
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| 508 | !------------------------------------------------------------------------------! |
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| 509 | ! Description: |
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| 510 | ! ------------ |
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| 511 | !> computes the i- and j-dependent component of the matrix |
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| 512 | !------------------------------------------------------------------------------! |
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[1212] | 513 | SUBROUTINE maketri_1dd( j ) |
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| 514 | |
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| 515 | IMPLICIT NONE |
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| 516 | |
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[1682] | 517 | INTEGER(iwp) :: i !< |
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| 518 | INTEGER(iwp) :: j !< |
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| 519 | INTEGER(iwp) :: k !< |
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| 520 | INTEGER(iwp) :: nnxh !< |
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[1212] | 521 | |
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[1682] | 522 | REAL(wp) :: a !< |
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| 523 | REAL(wp) :: c !< |
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[1212] | 524 | |
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[1682] | 525 | REAL(wp), DIMENSION(0:nx) :: l !< |
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[1320] | 526 | |
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[1212] | 527 | |
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| 528 | nnxh = ( nx + 1 ) / 2 |
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| 529 | ! |
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| 530 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
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| 531 | !-- Fourier space. The coefficients are computed following the method of |
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| 532 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
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| 533 | !-- Siano's original version by discretizing the Poisson equation, |
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| 534 | !-- before it is Fourier-transformed |
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| 535 | DO i = 0, nx |
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| 536 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
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[1342] | 537 | l(i) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * i ) / & |
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| 538 | REAL( nx+1, KIND=wp ) ) ) * ddx2 + & |
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| 539 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * j ) / & |
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| 540 | REAL( ny+1, KIND=wp ) ) ) * ddy2 |
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[1212] | 541 | ELSE |
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[1342] | 542 | l(i) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * ( nx+1-i ) ) / & |
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| 543 | REAL( nx+1, KIND=wp ) ) ) * ddx2 + & |
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| 544 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * j ) / & |
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| 545 | REAL( ny+1, KIND=wp ) ) ) * ddy2 |
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[1212] | 546 | ENDIF |
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| 547 | ENDDO |
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| 548 | |
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| 549 | DO k = 0, nz-1 |
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| 550 | DO i = 0, nx |
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[2037] | 551 | a = -1.0_wp * ddzu_pres(k+2) * ddzw(k+1) * rho_air_zw(k+1) |
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| 552 | c = -1.0_wp * ddzu_pres(k+1) * ddzw(k+1) * rho_air_zw(k) |
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| 553 | tri_for_1d(1,i,k) = a + c - l(i) * rho_air(k+1) |
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[1212] | 554 | ENDDO |
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| 555 | ENDDO |
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| 556 | IF ( ibc_p_b == 1 ) THEN |
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| 557 | DO i = 0, nx |
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[1221] | 558 | tri_for_1d(1,i,0) = tri_for_1d(1,i,0) + tri_for_1d(2,i,0) |
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[1212] | 559 | ENDDO |
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| 560 | ENDIF |
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| 561 | IF ( ibc_p_t == 1 ) THEN |
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| 562 | DO i = 0, nx |
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[1221] | 563 | tri_for_1d(1,i,nz-1) = tri_for_1d(1,i,nz-1) + tri_for_1d(3,i,nz-1) |
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[1212] | 564 | ENDDO |
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| 565 | ENDIF |
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| 566 | |
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| 567 | END SUBROUTINE maketri_1dd |
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| 568 | |
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| 569 | |
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[1682] | 570 | !------------------------------------------------------------------------------! |
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| 571 | ! Description: |
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| 572 | ! ------------ |
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| 573 | !> Splitting of the tridiagonal matrix (Thomas algorithm) |
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| 574 | !------------------------------------------------------------------------------! |
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[1212] | 575 | SUBROUTINE split_1dd |
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| 576 | |
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| 577 | IMPLICIT NONE |
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| 578 | |
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[1682] | 579 | INTEGER(iwp) :: i !< |
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| 580 | INTEGER(iwp) :: k !< |
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[1212] | 581 | |
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| 582 | |
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| 583 | ! |
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| 584 | !-- Splitting |
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| 585 | DO i = 0, nx |
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[1221] | 586 | tri_for_1d(4,i,0) = tri_for_1d(1,i,0) |
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[1212] | 587 | ENDDO |
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| 588 | DO k = 1, nz-1 |
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| 589 | DO i = 0, nx |
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[1221] | 590 | tri_for_1d(5,i,k) = tri_for_1d(2,i,k) / tri_for_1d(4,i,k-1) |
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| 591 | tri_for_1d(4,i,k) = tri_for_1d(1,i,k) - tri_for_1d(3,i,k-1) * tri_for_1d(5,i,k) |
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[1212] | 592 | ENDDO |
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| 593 | ENDDO |
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| 594 | |
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| 595 | END SUBROUTINE split_1dd |
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| 596 | |
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| 597 | |
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| 598 | !------------------------------------------------------------------------------! |
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[1682] | 599 | ! Description: |
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| 600 | ! ------------ |
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| 601 | !> Substitution (Forward and Backward) (Thomas algorithm) |
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[1212] | 602 | !------------------------------------------------------------------------------! |
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[1682] | 603 | SUBROUTINE substi_1dd( ar, tri_for_1d ) |
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[1212] | 604 | |
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[1682] | 605 | |
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[1212] | 606 | IMPLICIT NONE |
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| 607 | |
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[1682] | 608 | INTEGER(iwp) :: i !< |
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| 609 | INTEGER(iwp) :: k !< |
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[1212] | 610 | |
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[1682] | 611 | REAL(wp), DIMENSION(0:nx,nz) :: ar !< |
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| 612 | REAL(wp), DIMENSION(0:nx,0:nz-1) :: ar1 !< |
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| 613 | REAL(wp), DIMENSION(5,0:nx,0:nz-1) :: tri_for_1d !< |
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[1212] | 614 | |
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| 615 | ! |
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| 616 | !-- Forward substitution |
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| 617 | DO i = 0, nx |
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| 618 | ar1(i,0) = ar(i,1) |
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| 619 | ENDDO |
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| 620 | DO k = 1, nz-1 |
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| 621 | DO i = 0, nx |
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[1221] | 622 | ar1(i,k) = ar(i,k+1) - tri_for_1d(5,i,k) * ar1(i,k-1) |
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[1212] | 623 | ENDDO |
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| 624 | ENDDO |
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| 625 | |
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| 626 | ! |
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| 627 | !-- Backward substitution |
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| 628 | !-- Note, the add of 1.0E-20 in the denominator is due to avoid divisions |
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| 629 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
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| 630 | !-- the model domain. |
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| 631 | DO i = 0, nx |
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[1342] | 632 | ar(i,nz) = ar1(i,nz-1) / ( tri_for_1d(4,i,nz-1) + 1.0E-20_wp ) |
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[1212] | 633 | ENDDO |
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| 634 | DO k = nz-2, 0, -1 |
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| 635 | DO i = 0, nx |
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[1221] | 636 | ar(i,k+1) = ( ar1(i,k) - tri_for_1d(3,i,k) * ar(i,k+2) ) & |
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| 637 | / tri_for_1d(4,i,k) |
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[1212] | 638 | ENDDO |
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| 639 | ENDDO |
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| 640 | |
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| 641 | ! |
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| 642 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
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| 643 | !-- The respective values of ar should be zero at all k-levels if |
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| 644 | !-- acceleration of horizontally averaged vertical velocity is zero. |
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| 645 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
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| 646 | IF ( j == 0 ) THEN |
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| 647 | DO k = 1, nz |
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[1342] | 648 | ar(0,k) = 0.0_wp |
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[1212] | 649 | ENDDO |
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| 650 | ENDIF |
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| 651 | ENDIF |
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| 652 | |
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| 653 | END SUBROUTINE substi_1dd |
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| 654 | |
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| 655 | END SUBROUTINE tridia_1dd |
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| 656 | |
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| 657 | |
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| 658 | END MODULE tridia_solver |
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