1 | !> @file tridia_solver_mod.f90 |
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2 | !------------------------------------------------------------------------------! |
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3 | ! This file is part of the PALM model system. |
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4 | ! |
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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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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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17 | ! Copyright 1997-2019 Leibniz Universitaet Hannover |
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18 | !------------------------------------------------------------------------------! |
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19 | ! |
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20 | ! Current revisions: |
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21 | ! ------------------ |
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22 | ! |
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23 | ! |
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24 | ! Former revisions: |
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25 | ! ----------------- |
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26 | ! $Id: tridia_solver_mod.f90 3690 2019-01-22 22:56:42Z suehring $ |
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27 | ! OpenACC port for SPEC |
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28 | ! |
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29 | ! 3274 2018-09-24 15:42:55Z knoop |
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30 | ! Modularization of all bulk cloud physics code components |
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31 | ! |
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32 | ! 3241 2018-09-12 15:02:00Z raasch |
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33 | ! unused variables removed |
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34 | ! |
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35 | ! 2718 2018-01-02 08:49:38Z maronga |
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36 | ! Corrected "Former revisions" section |
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37 | ! |
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38 | ! 2696 2017-12-14 17:12:51Z kanani |
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39 | ! Change in file header (GPL part) |
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40 | ! |
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41 | ! 2119 2017-01-17 16:51:50Z raasch |
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42 | ! |
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43 | ! 2118 2017-01-17 16:38:49Z raasch |
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44 | ! OpenACC directives removed |
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45 | ! |
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46 | ! 2037 2016-10-26 11:15:40Z knoop |
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47 | ! Anelastic approximation implemented |
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48 | ! |
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49 | ! 2000 2016-08-20 18:09:15Z knoop |
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50 | ! Forced header and separation lines into 80 columns |
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51 | ! |
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52 | ! 1850 2016-04-08 13:29:27Z maronga |
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53 | ! Module renamed |
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54 | ! |
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55 | ! |
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56 | ! 1815 2016-04-06 13:49:59Z raasch |
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57 | ! cpp-switch intel11 removed |
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58 | ! |
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59 | ! 1808 2016-04-05 19:44:00Z raasch |
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60 | ! test output removed |
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61 | ! |
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62 | ! 1804 2016-04-05 16:30:18Z maronga |
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63 | ! Removed code for parameter file check (__check) |
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64 | ! |
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65 | ! 1682 2015-10-07 23:56:08Z knoop |
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66 | ! Code annotations made doxygen readable |
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67 | ! |
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68 | ! 1406 2014-05-16 13:47:01Z raasch |
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69 | ! bugfix for pgi 14.4: declare create moved after array declaration |
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70 | ! |
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71 | ! 1342 2014-03-26 17:04:47Z kanani |
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72 | ! REAL constants defined as wp-kind |
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73 | ! |
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74 | ! 1322 2014-03-20 16:38:49Z raasch |
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75 | ! REAL functions provided with KIND-attribute |
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76 | ! |
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77 | ! 1320 2014-03-20 08:40:49Z raasch |
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78 | ! ONLY-attribute added to USE-statements, |
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79 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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80 | ! kinds are defined in new module kinds, |
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81 | ! old module precision_kind is removed, |
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82 | ! revision history before 2012 removed, |
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83 | ! comment fields (!:) to be used for variable explanations added to |
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84 | ! all variable declaration statements |
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85 | ! |
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86 | ! 1257 2013-11-08 15:18:40Z raasch |
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87 | ! openacc loop and loop vector clauses removed, declare create moved after |
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88 | ! the FORTRAN declaration statement |
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89 | ! |
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90 | ! 1221 2013-09-10 08:59:13Z raasch |
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91 | ! dummy argument tri in 1d-routines replaced by tri_for_1d because of name |
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92 | ! conflict with arry tri in module arrays_3d |
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93 | ! |
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94 | ! 1216 2013-08-26 09:31:42Z raasch |
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95 | ! +tridia_substi_overlap for handling overlapping fft / transposition |
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96 | ! |
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97 | ! 1212 2013-08-15 08:46:27Z raasch |
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98 | ! Initial revision. |
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99 | ! Routines have been moved to seperate module from former file poisfft to here. |
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100 | ! The tridiagonal matrix coefficients of array tri are calculated only once at |
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101 | ! the beginning, i.e. routine split is called within tridia_init. |
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102 | ! |
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103 | |
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104 | #define __acc_fft_device ( defined( _OPENACC ) && ( defined ( __cuda_fft ) ) ) |
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105 | |
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106 | ! |
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107 | ! Description: |
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108 | ! ------------ |
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109 | !> solves the linear system of equations: |
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110 | !> |
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111 | !> -(4 pi^2(i^2/(dx^2*nnx^2)+j^2/(dy^2*nny^2))+ |
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112 | !> 1/(dzu(k)*dzw(k))+1/(dzu(k-1)*dzw(k)))*p(i,j,k)+ |
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113 | !> 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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114 | !> |
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115 | !> by using the Thomas algorithm |
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116 | !------------------------------------------------------------------------------! |
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117 | MODULE tridia_solver |
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118 | |
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119 | |
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120 | USE basic_constants_and_equations_mod, & |
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121 | ONLY: pi |
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122 | |
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123 | USE indices, & |
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124 | ONLY: nx, ny, nz |
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125 | |
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126 | USE kinds |
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127 | |
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128 | USE transpose_indices, & |
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129 | ONLY: nxl_z, nyn_z, nxr_z, nys_z |
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130 | |
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131 | IMPLICIT NONE |
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132 | |
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133 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ddzuw !< |
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134 | |
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135 | PRIVATE |
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136 | |
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137 | INTERFACE tridia_substi |
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138 | MODULE PROCEDURE tridia_substi |
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139 | END INTERFACE tridia_substi |
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140 | |
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141 | INTERFACE tridia_substi_overlap |
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142 | MODULE PROCEDURE tridia_substi_overlap |
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143 | END INTERFACE tridia_substi_overlap |
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144 | |
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145 | PUBLIC tridia_substi, tridia_substi_overlap, tridia_init, tridia_1dd |
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146 | |
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147 | CONTAINS |
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148 | |
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149 | |
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150 | !------------------------------------------------------------------------------! |
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151 | ! Description: |
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152 | ! ------------ |
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153 | !> @todo Missing subroutine description. |
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154 | !------------------------------------------------------------------------------! |
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155 | SUBROUTINE tridia_init |
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156 | |
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157 | USE arrays_3d, & |
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158 | ONLY: ddzu_pres, ddzw, rho_air_zw, tri |
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159 | |
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160 | IMPLICIT NONE |
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161 | |
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162 | INTEGER(iwp) :: k !< |
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163 | |
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164 | ALLOCATE( ddzuw(0:nz-1,3) ) |
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165 | |
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166 | DO k = 0, nz-1 |
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167 | ddzuw(k,1) = ddzu_pres(k+1) * ddzw(k+1) * rho_air_zw(k) |
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168 | ddzuw(k,2) = ddzu_pres(k+2) * ddzw(k+1) * rho_air_zw(k+1) |
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169 | ddzuw(k,3) = -1.0_wp * & |
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170 | ( ddzu_pres(k+2) * ddzw(k+1) * rho_air_zw(k+1) + & |
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171 | ddzu_pres(k+1) * ddzw(k+1) * rho_air_zw(k) ) |
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172 | ENDDO |
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173 | ! |
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174 | !-- Calculate constant coefficients of the tridiagonal matrix |
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175 | CALL maketri |
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176 | CALL split |
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177 | |
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178 | #if __acc_fft_device |
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179 | !$ACC ENTER DATA & |
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180 | !$ACC COPYIN(ddzuw(0:nz-1,1:3)) & |
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181 | !$ACC COPYIN(tri(nxl_z:nxr_z,nys_z:nyn_z,0:nz-1,1:2)) |
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182 | #endif |
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183 | |
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184 | END SUBROUTINE tridia_init |
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185 | |
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186 | |
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187 | !------------------------------------------------------------------------------! |
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188 | ! Description: |
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189 | ! ------------ |
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190 | !> Computes the i- and j-dependent component of the matrix |
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191 | !> Provide the constant coefficients of the tridiagonal matrix for solution |
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192 | !> of the Poisson equation in Fourier space. |
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193 | !> The coefficients are computed following the method of |
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194 | !> Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
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195 | !> Siano's original version by discretizing the Poisson equation, |
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196 | !> before it is Fourier-transformed. |
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197 | !------------------------------------------------------------------------------! |
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198 | SUBROUTINE maketri |
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199 | |
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200 | |
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201 | USE arrays_3d, & |
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202 | ONLY: tric, rho_air |
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203 | |
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204 | USE control_parameters, & |
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205 | ONLY: ibc_p_b, ibc_p_t |
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206 | |
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207 | USE grid_variables, & |
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208 | ONLY: dx, dy |
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209 | |
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210 | |
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211 | IMPLICIT NONE |
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212 | |
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213 | INTEGER(iwp) :: i !< |
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214 | INTEGER(iwp) :: j !< |
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215 | INTEGER(iwp) :: k !< |
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216 | INTEGER(iwp) :: nnxh !< |
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217 | INTEGER(iwp) :: nnyh !< |
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218 | |
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219 | REAL(wp) :: ll(nxl_z:nxr_z,nys_z:nyn_z) !< |
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220 | |
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221 | |
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222 | nnxh = ( nx + 1 ) / 2 |
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223 | nnyh = ( ny + 1 ) / 2 |
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224 | |
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225 | DO j = nys_z, nyn_z |
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226 | DO i = nxl_z, nxr_z |
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227 | IF ( j >= 0 .AND. j <= nnyh ) THEN |
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228 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
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229 | ll(i,j) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * i ) / & |
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230 | REAL( nx+1, KIND=wp ) ) ) / ( dx * dx ) + & |
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231 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * j ) / & |
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232 | REAL( ny+1, KIND=wp ) ) ) / ( dy * dy ) |
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233 | ELSE |
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234 | ll(i,j) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * ( nx+1-i ) ) / & |
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235 | REAL( nx+1, KIND=wp ) ) ) / ( dx * dx ) + & |
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236 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * j ) / & |
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237 | REAL( ny+1, KIND=wp ) ) ) / ( dy * dy ) |
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238 | ENDIF |
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239 | ELSE |
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240 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
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241 | ll(i,j) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * i ) / & |
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242 | REAL( nx+1, KIND=wp ) ) ) / ( dx * dx ) + & |
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243 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * ( ny+1-j ) ) / & |
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244 | REAL( ny+1, KIND=wp ) ) ) / ( dy * dy ) |
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245 | ELSE |
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246 | ll(i,j) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * ( nx+1-i ) ) / & |
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247 | REAL( nx+1, KIND=wp ) ) ) / ( dx * dx ) + & |
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248 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * ( ny+1-j ) ) / & |
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249 | REAL( ny+1, KIND=wp ) ) ) / ( dy * dy ) |
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250 | ENDIF |
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251 | ENDIF |
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252 | ENDDO |
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253 | ENDDO |
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254 | |
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255 | DO k = 0, nz-1 |
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256 | DO j = nys_z, nyn_z |
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257 | DO i = nxl_z, nxr_z |
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258 | tric(i,j,k) = ddzuw(k,3) - ll(i,j) * rho_air(k+1) |
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259 | ENDDO |
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260 | ENDDO |
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261 | ENDDO |
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262 | |
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263 | IF ( ibc_p_b == 1 ) THEN |
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264 | DO j = nys_z, nyn_z |
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265 | DO i = nxl_z, nxr_z |
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266 | tric(i,j,0) = tric(i,j,0) + ddzuw(0,1) |
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267 | ENDDO |
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268 | ENDDO |
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269 | ENDIF |
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270 | IF ( ibc_p_t == 1 ) THEN |
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271 | DO j = nys_z, nyn_z |
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272 | DO i = nxl_z, nxr_z |
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273 | tric(i,j,nz-1) = tric(i,j,nz-1) + ddzuw(nz-1,2) |
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274 | ENDDO |
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275 | ENDDO |
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276 | ENDIF |
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277 | |
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278 | END SUBROUTINE maketri |
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279 | |
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280 | |
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281 | !------------------------------------------------------------------------------! |
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282 | ! Description: |
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283 | ! ------------ |
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284 | !> Substitution (Forward and Backward) (Thomas algorithm) |
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285 | !------------------------------------------------------------------------------! |
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286 | SUBROUTINE tridia_substi( ar ) |
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287 | |
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288 | |
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289 | USE arrays_3d, & |
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290 | ONLY: tri |
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291 | |
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292 | USE control_parameters, & |
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293 | ONLY: ibc_p_b, ibc_p_t |
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294 | |
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295 | IMPLICIT NONE |
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296 | |
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297 | INTEGER(iwp) :: i !< |
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298 | INTEGER(iwp) :: j !< |
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299 | INTEGER(iwp) :: k !< |
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300 | |
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301 | REAL(wp) :: ar(nxl_z:nxr_z,nys_z:nyn_z,1:nz) !< |
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302 | |
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303 | REAL(wp), DIMENSION(nxl_z:nxr_z,nys_z:nyn_z,0:nz-1) :: ar1 !< |
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304 | #if __acc_fft_device |
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305 | !$ACC DECLARE CREATE(ar1) |
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306 | #endif |
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307 | |
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308 | ! |
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309 | !-- Forward substitution |
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310 | #if __acc_fft_device |
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311 | !$ACC PARALLEL PRESENT(ar, ar1, tri) PRIVATE(i,j,k) |
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312 | #endif |
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313 | DO k = 0, nz - 1 |
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314 | #if __acc_fft_device |
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315 | !$ACC LOOP COLLAPSE(2) |
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316 | #endif |
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317 | DO j = nys_z, nyn_z |
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318 | DO i = nxl_z, nxr_z |
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319 | |
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320 | IF ( k == 0 ) THEN |
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321 | ar1(i,j,k) = ar(i,j,k+1) |
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322 | ELSE |
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323 | ar1(i,j,k) = ar(i,j,k+1) - tri(i,j,k,2) * ar1(i,j,k-1) |
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324 | ENDIF |
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325 | |
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326 | ENDDO |
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327 | ENDDO |
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328 | ENDDO |
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329 | #if __acc_fft_device |
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330 | !$ACC END PARALLEL |
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331 | #endif |
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332 | |
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333 | ! |
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334 | !-- Backward substitution |
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335 | !-- Note, the 1.0E-20 in the denominator is due to avoid divisions |
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336 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
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337 | !-- the model domain. |
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338 | #if __acc_fft_device |
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339 | !$ACC PARALLEL PRESENT(ar, ar1, ddzuw, tri) PRIVATE(i,j,k) |
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340 | #endif |
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341 | DO k = nz-1, 0, -1 |
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342 | #if __acc_fft_device |
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343 | !$ACC LOOP COLLAPSE(2) |
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344 | #endif |
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345 | DO j = nys_z, nyn_z |
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346 | DO i = nxl_z, nxr_z |
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347 | |
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348 | IF ( k == nz-1 ) THEN |
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349 | ar(i,j,k+1) = ar1(i,j,k) / ( tri(i,j,k,1) + 1.0E-20_wp ) |
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350 | ELSE |
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351 | ar(i,j,k+1) = ( ar1(i,j,k) - ddzuw(k,2) * ar(i,j,k+2) ) & |
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352 | / tri(i,j,k,1) |
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353 | ENDIF |
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354 | ENDDO |
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355 | ENDDO |
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356 | ENDDO |
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357 | #if __acc_fft_device |
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358 | !$ACC END PARALLEL |
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359 | #endif |
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360 | |
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361 | ! |
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362 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
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363 | !-- The respective values of ar should be zero at all k-levels if |
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364 | !-- acceleration of horizontally averaged vertical velocity is zero. |
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365 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
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366 | IF ( nys_z == 0 .AND. nxl_z == 0 ) THEN |
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367 | #if __acc_fft_device |
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368 | !$ACC PARALLEL LOOP PRESENT(ar) |
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369 | #endif |
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370 | DO k = 1, nz |
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371 | ar(nxl_z,nys_z,k) = 0.0_wp |
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372 | ENDDO |
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373 | ENDIF |
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374 | ENDIF |
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375 | |
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376 | END SUBROUTINE tridia_substi |
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377 | |
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378 | |
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379 | !------------------------------------------------------------------------------! |
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380 | ! Description: |
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381 | ! ------------ |
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382 | !> Substitution (Forward and Backward) (Thomas algorithm) |
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383 | !------------------------------------------------------------------------------! |
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384 | SUBROUTINE tridia_substi_overlap( ar, jj ) |
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385 | |
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386 | |
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387 | USE arrays_3d, & |
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388 | ONLY: tri |
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389 | |
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390 | USE control_parameters, & |
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391 | ONLY: ibc_p_b, ibc_p_t |
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392 | |
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393 | IMPLICIT NONE |
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394 | |
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395 | INTEGER(iwp) :: i !< |
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396 | INTEGER(iwp) :: j !< |
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397 | INTEGER(iwp) :: jj !< |
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398 | INTEGER(iwp) :: k !< |
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399 | |
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400 | REAL(wp) :: ar(nxl_z:nxr_z,nys_z:nyn_z,1:nz) !< |
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401 | |
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402 | REAL(wp), DIMENSION(nxl_z:nxr_z,nys_z:nyn_z,0:nz-1) :: ar1 !< |
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403 | |
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404 | ! |
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405 | !-- Forward substitution |
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406 | DO k = 0, nz - 1 |
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407 | DO j = nys_z, nyn_z |
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408 | DO i = nxl_z, nxr_z |
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409 | |
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410 | IF ( k == 0 ) THEN |
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411 | ar1(i,j,k) = ar(i,j,k+1) |
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412 | ELSE |
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413 | ar1(i,j,k) = ar(i,j,k+1) - tri(i,jj,k,2) * ar1(i,j,k-1) |
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414 | ENDIF |
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415 | |
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416 | ENDDO |
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417 | ENDDO |
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418 | ENDDO |
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419 | |
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420 | ! |
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421 | !-- Backward substitution |
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422 | !-- Note, the 1.0E-20 in the denominator is due to avoid divisions |
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423 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
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424 | !-- the model domain. |
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425 | DO k = nz-1, 0, -1 |
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426 | DO j = nys_z, nyn_z |
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427 | DO i = nxl_z, nxr_z |
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428 | |
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429 | IF ( k == nz-1 ) THEN |
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430 | ar(i,j,k+1) = ar1(i,j,k) / ( tri(i,jj,k,1) + 1.0E-20_wp ) |
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431 | ELSE |
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432 | ar(i,j,k+1) = ( ar1(i,j,k) - ddzuw(k,2) * ar(i,j,k+2) ) & |
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433 | / tri(i,jj,k,1) |
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434 | ENDIF |
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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 | ! |
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440 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
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441 | !-- The respective values of ar should be zero at all k-levels if |
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442 | !-- acceleration of horizontally averaged vertical velocity is zero. |
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443 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
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444 | IF ( nys_z == 0 .AND. nxl_z == 0 ) THEN |
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445 | DO k = 1, nz |
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446 | ar(nxl_z,nys_z,k) = 0.0_wp |
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447 | ENDDO |
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448 | ENDIF |
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449 | ENDIF |
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450 | |
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451 | END SUBROUTINE tridia_substi_overlap |
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452 | |
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453 | |
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454 | !------------------------------------------------------------------------------! |
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455 | ! Description: |
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456 | ! ------------ |
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457 | !> Splitting of the tridiagonal matrix (Thomas algorithm) |
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458 | !------------------------------------------------------------------------------! |
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459 | SUBROUTINE split |
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460 | |
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461 | |
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462 | USE arrays_3d, & |
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463 | ONLY: tri, tric |
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464 | |
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465 | IMPLICIT NONE |
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466 | |
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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 | ! |
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471 | !-- Splitting |
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472 | DO j = nys_z, nyn_z |
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473 | DO i = nxl_z, nxr_z |
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474 | tri(i,j,0,1) = tric(i,j,0) |
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475 | ENDDO |
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476 | ENDDO |
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477 | |
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478 | DO k = 1, nz-1 |
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479 | DO j = nys_z, nyn_z |
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480 | DO i = nxl_z, nxr_z |
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481 | tri(i,j,k,2) = ddzuw(k,1) / tri(i,j,k-1,1) |
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482 | tri(i,j,k,1) = tric(i,j,k) - ddzuw(k-1,2) * tri(i,j,k,2) |
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483 | ENDDO |
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484 | ENDDO |
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485 | ENDDO |
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486 | |
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487 | END SUBROUTINE split |
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488 | |
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489 | |
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490 | !------------------------------------------------------------------------------! |
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491 | ! Description: |
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492 | ! ------------ |
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493 | !> Solves the linear system of equations for a 1d-decomposition along x (see |
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494 | !> tridia) |
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495 | !> |
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496 | !> @attention when using the intel compilers older than 12.0, array tri must |
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497 | !> be passed as an argument to the contained subroutines. Otherwise |
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498 | !> addres faults will occur. This feature can be activated with |
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499 | !> cpp-switch __intel11 |
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500 | !> On NEC, tri should not be passed (except for routine substi_1dd) |
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501 | !> because this causes very bad performance. |
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502 | !------------------------------------------------------------------------------! |
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503 | |
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504 | SUBROUTINE tridia_1dd( ddx2, ddy2, nx, ny, j, ar, tri_for_1d ) |
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505 | |
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506 | |
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507 | USE arrays_3d, & |
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508 | ONLY: ddzu_pres, ddzw, rho_air, rho_air_zw |
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509 | |
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510 | USE control_parameters, & |
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511 | ONLY: ibc_p_b, ibc_p_t |
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512 | |
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513 | IMPLICIT NONE |
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514 | |
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515 | INTEGER(iwp) :: i !< |
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516 | INTEGER(iwp) :: j !< |
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517 | INTEGER(iwp) :: k !< |
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518 | INTEGER(iwp) :: nnyh !< |
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519 | INTEGER(iwp) :: nx !< |
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520 | INTEGER(iwp) :: ny !< |
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521 | |
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522 | REAL(wp) :: ddx2 !< |
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523 | REAL(wp) :: ddy2 !< |
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524 | |
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525 | REAL(wp), DIMENSION(0:nx,1:nz) :: ar !< |
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526 | REAL(wp), DIMENSION(5,0:nx,0:nz-1) :: tri_for_1d !< |
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527 | |
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528 | |
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529 | nnyh = ( ny + 1 ) / 2 |
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530 | |
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531 | ! |
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532 | !-- Define constant elements of the tridiagonal matrix. |
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533 | !-- The compiler on SX6 does loop exchange. If 0:nx is a high power of 2, |
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534 | !-- the exchanged loops create bank conflicts. The following directive |
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535 | !-- prohibits loop exchange and the loops perform much better. |
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536 | !CDIR NOLOOPCHG |
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537 | DO k = 0, nz-1 |
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538 | DO i = 0,nx |
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539 | tri_for_1d(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) * rho_air_zw(k) |
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540 | tri_for_1d(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) * rho_air_zw(k+1) |
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541 | ENDDO |
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542 | ENDDO |
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543 | |
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544 | IF ( j <= nnyh ) THEN |
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545 | CALL maketri_1dd( j ) |
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546 | ELSE |
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547 | CALL maketri_1dd( ny+1-j ) |
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548 | ENDIF |
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549 | |
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550 | CALL split_1dd |
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551 | CALL substi_1dd( ar, tri_for_1d ) |
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552 | |
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553 | CONTAINS |
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554 | |
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555 | |
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556 | !------------------------------------------------------------------------------! |
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557 | ! Description: |
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558 | ! ------------ |
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559 | !> computes the i- and j-dependent component of the matrix |
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560 | !------------------------------------------------------------------------------! |
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561 | SUBROUTINE maketri_1dd( j ) |
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562 | |
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563 | IMPLICIT NONE |
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564 | |
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565 | INTEGER(iwp) :: i !< |
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566 | INTEGER(iwp) :: j !< |
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567 | INTEGER(iwp) :: k !< |
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568 | INTEGER(iwp) :: nnxh !< |
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569 | |
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570 | REAL(wp) :: a !< |
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571 | REAL(wp) :: c !< |
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572 | |
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573 | REAL(wp), DIMENSION(0:nx) :: l !< |
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574 | |
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575 | |
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576 | nnxh = ( nx + 1 ) / 2 |
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577 | ! |
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578 | !-- Provide the tridiagonal matrix for solution of the Poisson equation in |
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579 | !-- Fourier space. The coefficients are computed following the method of |
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580 | !-- Schmidt et al. (DFVLR-Mitteilung 84-15), which departs from Stephan |
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581 | !-- Siano's original version by discretizing the Poisson equation, |
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582 | !-- before it is Fourier-transformed |
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583 | DO i = 0, nx |
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584 | IF ( i >= 0 .AND. i <= nnxh ) THEN |
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585 | l(i) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * i ) / & |
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586 | REAL( nx+1, KIND=wp ) ) ) * ddx2 + & |
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587 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * j ) / & |
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588 | REAL( ny+1, KIND=wp ) ) ) * ddy2 |
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589 | ELSE |
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590 | l(i) = 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * ( nx+1-i ) ) / & |
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591 | REAL( nx+1, KIND=wp ) ) ) * ddx2 + & |
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592 | 2.0_wp * ( 1.0_wp - COS( ( 2.0_wp * pi * j ) / & |
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593 | REAL( ny+1, KIND=wp ) ) ) * ddy2 |
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594 | ENDIF |
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595 | ENDDO |
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596 | |
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597 | DO k = 0, nz-1 |
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598 | DO i = 0, nx |
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599 | a = -1.0_wp * ddzu_pres(k+2) * ddzw(k+1) * rho_air_zw(k+1) |
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600 | c = -1.0_wp * ddzu_pres(k+1) * ddzw(k+1) * rho_air_zw(k) |
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601 | tri_for_1d(1,i,k) = a + c - l(i) * rho_air(k+1) |
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602 | ENDDO |
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603 | ENDDO |
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604 | IF ( ibc_p_b == 1 ) THEN |
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605 | DO i = 0, nx |
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606 | tri_for_1d(1,i,0) = tri_for_1d(1,i,0) + tri_for_1d(2,i,0) |
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607 | ENDDO |
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608 | ENDIF |
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609 | IF ( ibc_p_t == 1 ) THEN |
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610 | DO i = 0, nx |
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611 | 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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612 | ENDDO |
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613 | ENDIF |
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614 | |
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615 | END SUBROUTINE maketri_1dd |
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616 | |
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617 | |
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618 | !------------------------------------------------------------------------------! |
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619 | ! Description: |
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620 | ! ------------ |
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621 | !> Splitting of the tridiagonal matrix (Thomas algorithm) |
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622 | !------------------------------------------------------------------------------! |
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623 | SUBROUTINE split_1dd |
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624 | |
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625 | IMPLICIT NONE |
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626 | |
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627 | INTEGER(iwp) :: i !< |
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628 | INTEGER(iwp) :: k !< |
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629 | |
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630 | |
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631 | ! |
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632 | !-- Splitting |
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633 | DO i = 0, nx |
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634 | tri_for_1d(4,i,0) = tri_for_1d(1,i,0) |
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635 | ENDDO |
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636 | DO k = 1, nz-1 |
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637 | DO i = 0, nx |
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638 | tri_for_1d(5,i,k) = tri_for_1d(2,i,k) / tri_for_1d(4,i,k-1) |
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639 | 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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640 | ENDDO |
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641 | ENDDO |
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642 | |
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643 | END SUBROUTINE split_1dd |
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644 | |
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645 | |
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646 | !------------------------------------------------------------------------------! |
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647 | ! Description: |
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648 | ! ------------ |
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649 | !> Substitution (Forward and Backward) (Thomas algorithm) |
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650 | !------------------------------------------------------------------------------! |
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651 | SUBROUTINE substi_1dd( ar, tri_for_1d ) |
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652 | |
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653 | |
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654 | IMPLICIT NONE |
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655 | |
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656 | INTEGER(iwp) :: i !< |
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657 | INTEGER(iwp) :: k !< |
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658 | |
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659 | REAL(wp), DIMENSION(0:nx,nz) :: ar !< |
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660 | REAL(wp), DIMENSION(0:nx,0:nz-1) :: ar1 !< |
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661 | REAL(wp), DIMENSION(5,0:nx,0:nz-1) :: tri_for_1d !< |
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662 | |
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663 | ! |
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664 | !-- Forward substitution |
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665 | DO i = 0, nx |
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666 | ar1(i,0) = ar(i,1) |
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667 | ENDDO |
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668 | DO k = 1, nz-1 |
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669 | DO i = 0, nx |
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670 | ar1(i,k) = ar(i,k+1) - tri_for_1d(5,i,k) * ar1(i,k-1) |
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671 | ENDDO |
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672 | ENDDO |
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673 | |
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674 | ! |
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675 | !-- Backward substitution |
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676 | !-- Note, the add of 1.0E-20 in the denominator is due to avoid divisions |
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677 | !-- by zero appearing if the pressure bc is set to neumann at the top of |
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678 | !-- the model domain. |
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679 | DO i = 0, nx |
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680 | ar(i,nz) = ar1(i,nz-1) / ( tri_for_1d(4,i,nz-1) + 1.0E-20_wp ) |
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681 | ENDDO |
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682 | DO k = nz-2, 0, -1 |
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683 | DO i = 0, nx |
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684 | ar(i,k+1) = ( ar1(i,k) - tri_for_1d(3,i,k) * ar(i,k+2) ) & |
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685 | / tri_for_1d(4,i,k) |
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686 | ENDDO |
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687 | ENDDO |
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688 | |
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689 | ! |
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690 | !-- Indices i=0, j=0 correspond to horizontally averaged pressure. |
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691 | !-- The respective values of ar should be zero at all k-levels if |
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692 | !-- acceleration of horizontally averaged vertical velocity is zero. |
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693 | IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN |
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694 | IF ( j == 0 ) THEN |
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695 | DO k = 1, nz |
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696 | ar(0,k) = 0.0_wp |
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697 | ENDDO |
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698 | ENDIF |
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699 | ENDIF |
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700 | |
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701 | END SUBROUTINE substi_1dd |
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702 | |
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703 | END SUBROUTINE tridia_1dd |
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704 | |
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705 | |
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706 | END MODULE tridia_solver |
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