1 | MODULE compute_NH_geopot_mod |
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2 | USE grid_param |
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3 | USE icosa, ONLY : rstd |
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4 | IMPLICIT NONE |
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5 | PRIVATE |
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6 | |
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7 | LOGICAL, SAVE :: debug_hevi_solver = .FALSE. |
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8 | |
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9 | REAL(rstd) :: pbot=1e5, rho_bot=100. ! for NH solver |
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10 | |
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11 | #include "../unstructured/unstructured.h90" |
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12 | |
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13 | PUBLIC :: compute_NH_geopot,compute_NH_geopot_unst, pbot, rho_bot |
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14 | |
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15 | CONTAINS |
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16 | |
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17 | #ifdef BEGIN_DYSL |
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18 | |
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19 | KERNEL(compute_NH_geopot) |
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20 | tau2_g=tau*tau/g |
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21 | g2=g*g |
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22 | gm2 = 1./g2 |
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23 | vreff = Treff*cpp/preff*kappa |
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24 | gamma = 1./(1.-kappa) |
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25 | |
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26 | BARRIER |
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27 | |
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28 | ! compute Phi_star |
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29 | SEQUENCE_C1 |
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30 | BODY('1,llm+1') |
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31 | Phi_star_il(CELL) = Phi_il(CELL) + tau*g2*(W_il(CELL)/m_il(CELL)-tau) |
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32 | END_BLOCK |
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33 | END_BLOCK |
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34 | |
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35 | ! Newton-Raphson iteration : Phi_il contains current guess value |
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36 | DO iter=1,2 ! 2 iterations should be enough |
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37 | ! Compute pressure, A_ik |
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38 | SELECT CASE(caldyn_thermo) |
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39 | CASE(thermo_theta) |
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40 | {% call() compute_p_and_Aik() %} |
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41 | X_ij = (cpp/preff)*kappa*theta(CELL)*rho_ij |
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42 | p_ik(CELL) = preff*(X_ij**gamma) |
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43 | c2_mik = gamma*p_ik(CELL)/(rho_ij*m_ik(CELL)) ! c^2 = gamma*R*T = gamma*p/rho |
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44 | {% endcall %} |
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45 | CASE(thermo_entropy) |
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46 | {% call() compute_p_and_Aik() %} |
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47 | X_ij = log(vreff*rho_ij) + theta(CELL)/cpp |
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48 | p_ik(CELL) = preff*exp(X_ij*gamma) |
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49 | c2_mik = gamma*p_ik(CELL)/(rho_ij*m_ik(CELL)) ! c^2 = gamma*R*T = gamma*p/rho |
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50 | {% endcall %} |
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51 | CASE DEFAULT |
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52 | PRINT *, 'caldyn_thermo not supported by compute_NH_geopot', caldyn_thermo |
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53 | STOP |
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54 | END SELECT |
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55 | |
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56 | ! NB : A(1), A(llm), R(1), R(llm+1) = 0 => x(l)=0 at l=1,llm+1 => flat, rigid top and bottom |
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57 | ! Solve -A(l-1)x(l-1) + B(l)x(l) - A(l)x(l+1) = R(l) using Thomas algorithm |
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58 | |
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59 | SEQUENCE_C1 |
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60 | ! Compute residual R_il and B_il |
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61 | PROLOGUE(1) |
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62 | ! bottom interface l=1 |
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63 | ml_g2 = gm2*m_il(CELL) |
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64 | B_il(CELL) = A_ik(CELL) + ml_g2 + tau2_g*rho_bot |
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65 | R_il(CELL) = ml_g2*( Phi_il(CELL)-Phi_star_il(CELL)) & |
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66 | + tau2_g*( p_ik(CELL)-pbot+rho_bot*(Phi_il(CELL)-PHI_BOT(HIDX(CELL))) ) |
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67 | END_BLOCK |
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68 | BODY('2,llm') |
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69 | ! inner interfaces |
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70 | ml_g2 = gm2*m_il(CELL) |
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71 | B_il(CELL) = A_ik(CELL)+A_ik(DOWN(CELL)) + ml_g2 |
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72 | R_il(CELL) = ml_g2*( Phi_il(CELL)-Phi_star_il(CELL)) & |
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73 | + tau2_g*(p_ik(CELL)-p_ik(DOWN(CELL))) |
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74 | ! consistency check : if Wil=0 and initial state is in hydrostatic balance |
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75 | ! then Phi_star_il(CELL) = Phi_il(CELL) - tau^2*g^2 |
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76 | ! and residual = tau^2*(ml+(1/g)dl_pi)=0 |
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77 | END_BLOCK |
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78 | EPILOGUE('llm+1') |
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79 | ! top interface l=llm+1 |
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80 | ml_g2 = gm2*m_il(CELL) |
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81 | B_il(CELL) = A_ik(DOWN(CELL)) + ml_g2 |
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82 | R_il(CELL) = ml_g2*( Phi_il(CELL)-Phi_star_il(CELL)) & |
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83 | + tau2_g*( ptop-p_ik(DOWN(CELL)) ) |
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84 | END_BLOCK |
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85 | ! |
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86 | ! Forward sweep : |
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87 | ! C(0)=0, C(l) = -A(l) / (B(l)+A(l-1)C(l-1)), |
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88 | ! D(0)=0, D(l) = (R(l)+A(l-1)D(l-1)) / (B(l)+A(l-1)C(l-1)) |
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89 | PROLOGUE(1) |
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90 | X_ij = 1./B_il(CELL) |
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91 | C_ik(CELL) = -A_ik(CELL) * X_ij |
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92 | D_il(CELL) = R_il(CELL) * X_ij |
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93 | END_BLOCK |
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94 | BODY('2,llm') |
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95 | X_ij = 1./( B_il(CELL) + A_ik(DOWN(CELL))*C_ik(DOWN(CELL)) ) |
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96 | C_ik(CELL) = -A_ik(CELL) * X_ij |
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97 | D_il(CELL) = (R_il(CELL)+A_ik(DOWN(CELL))*D_il(DOWN(CELL))) * X_ij |
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98 | END_BLOCK |
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99 | EPILOGUE('llm+1') |
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100 | X_ij = 1./( B_il(CELL) + A_ik(DOWN(CELL))*C_ik(DOWN(CELL)) ) |
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101 | D_il(CELL) = (R_il(CELL)+A_ik(DOWN(CELL))*D_il(DOWN(CELL))) * X_ij |
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102 | ! Back substitution : |
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103 | ! x(i) = D(i)-C(i)x(i+1), x(llm+1)=0 |
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104 | ! + Newton-Raphson update |
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105 | ! top interface l=llm+1 |
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106 | x_il(CELL) = D_il(CELL) |
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107 | Phi_il(CELL) = Phi_il(CELL) - x_il(CELL) |
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108 | END_BLOCK |
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109 | BODY('llm,1,-1') |
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110 | ! Back substitution at lower interfaces |
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111 | x_il(CELL) = D_il(CELL) - C_ik(CELL)*x_il(UP(CELL)) |
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112 | Phi_il(CELL) = Phi_il(CELL) - x_il(CELL) |
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113 | END_BLOCK |
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114 | END_BLOCK |
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115 | |
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116 | IF(debug_hevi_solver) THEN |
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117 | PRINT *, '[hevi_solver] A,B', iter, MAXVAL(ABS(A_ik)),MAXVAL(ABS(B_il)) |
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118 | PRINT *, '[hevi_solver] C,D', iter, MAXVAL(ABS(C_ik)),MAXVAL(ABS(D_il)) |
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119 | DO l=1,llm+1 |
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120 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] x_il', iter,l, MAXVAL(ABS(x_il(l,:))) |
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121 | END DO |
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122 | DO l=1,llm+1 |
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123 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] R_il', iter,l, MAXVAL(ABS(R_il(l,:))) |
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124 | END DO |
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125 | END IF |
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126 | |
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127 | END DO ! Newton-Raphson |
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128 | |
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129 | BARRIER |
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130 | |
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131 | debug_hevi_solver=.FALSE. |
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132 | END_BLOCK |
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133 | |
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134 | #endif END_DYSL |
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135 | |
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136 | SUBROUTINE compute_NH_geopot_unst(tau, m_ik, m_il, theta, W_il, Phi_il) |
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137 | USE ISO_C_BINDING, only : C_DOUBLE, C_FLOAT |
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138 | USE disvert_mod, only : g,Treff,cpp,preff,kappa,caldyn_thermo,thermo_theta, & |
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139 | thermo_entropy |
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140 | USE disvert_mod, ONLY : ptop |
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141 | USE data_unstructured_mod, ONLY : enter_trace, exit_trace, & |
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142 | id_NH_geopot,debug_hevi_solver_, & |
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143 | PHI_BOT,pbot,rho_bot |
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144 | FIELD_MASS :: m_ik, theta ! IN*2 |
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145 | FIELD_GEOPOT :: m_il, W_il, Phi_il, Phi_star_il ! IN,INOUT*2, LOCAL |
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146 | NUM :: tau, gamma, tau2_g, tau2_g2, g2, gm2, vreff, Rd_preff |
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147 | INTEGER :: iter |
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148 | LOGICAL :: debug_hevi_solver |
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149 | DECLARE_INDICES |
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150 | NUM :: rho_ij, X_ij, Y_ij, wil, rho_c2_mik, c2_mik, ml_g2 |
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151 | #define COLUMN 0 |
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152 | #if COLUMN |
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153 | NUM1(llm) :: pk, Ak, Ck |
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154 | NUM1(llm+1):: Rl, Bl, Dl, xl |
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155 | #define p_ik(l,ij) pk(l) |
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156 | #define A_ik(l,ij) Ak(l) |
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157 | #define C_ik(l,ij) Ck(l) |
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158 | #define R_il(l,ij) Rl(l) |
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159 | #define B_il(l,ij) Bl(l) |
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160 | #define D_il(l,ij) Dl(l) |
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161 | #define x_il(l,ij) xl(l) |
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162 | #else |
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163 | FIELD_MASS :: p_ik, A_ik, C_ik |
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164 | FIELD_GEOPOT :: R_il, B_il, D_il, x_il |
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165 | #endif |
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166 | |
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167 | debug_hevi_solver=.FALSE. |
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168 | !$OMP MASTER |
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169 | debug_hevi_solver = debug_hevi_solver_ |
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170 | !$OMP END MASTER |
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171 | |
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172 | #define PHI_BOT(ij) Phi_bot |
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173 | START_TRACE(id_NH_geopot, 7,0,0) |
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174 | #include "../kernels_unst/compute_NH_geopot.k90" |
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175 | STOP_TRACE |
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176 | |
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177 | !$OMP MASTER |
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178 | debug_hevi_solver_ = debug_hevi_solver |
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179 | !$OMP END MASTER |
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180 | #undef PHI_BOT |
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181 | |
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182 | #if COLUMN |
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183 | #undef p_ik |
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184 | #undef A_ik |
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185 | #undef C_ik |
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186 | #undef R_il |
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187 | #undef B_il |
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188 | #undef D_il |
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189 | #undef x_il |
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190 | #endif |
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191 | #undef COLUMN |
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192 | END SUBROUTINE compute_NH_geopot_unst |
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193 | |
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194 | SUBROUTINE compute_NH_geopot(tau, phis, m_ik, m_il, theta, W_il, Phi_il) |
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195 | USE disvert_mod |
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196 | USE caldyn_vars_mod |
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197 | USE omp_para |
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198 | REAL(rstd),INTENT(IN) :: tau ! solve Phi-tau*dPhi/dt = Phi_rhs |
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199 | REAL(rstd),INTENT(IN) :: phis(iim*jjm) |
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200 | REAL(rstd),INTENT(IN) :: m_ik(iim*jjm,llm) |
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201 | REAL(rstd),INTENT(IN) :: m_il(iim*jjm,llm+1) |
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202 | REAL(rstd),INTENT(IN) :: theta(iim*jjm,llm) |
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203 | REAL(rstd),INTENT(IN) :: W_il(iim*jjm,llm+1) ! vertical momentum |
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204 | REAL(rstd),INTENT(INOUT) :: Phi_il(iim*jjm,llm+1) ! geopotential |
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205 | |
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206 | REAL(rstd) :: Phi_star_il(iim*jjm,llm+1) |
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207 | REAL(rstd) :: p_ik(iim*jjm,llm) ! pressure |
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208 | REAL(rstd) :: R_il(iim*jjm,llm+1) ! rhs of tridiag problem |
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209 | REAL(rstd) :: x_il(iim*jjm,llm+1) ! solution of tridiag problem |
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210 | REAL(rstd) :: A_ik(iim*jjm,llm) ! off-diagonal coefficients of tridiag problem |
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211 | REAL(rstd) :: B_il(iim*jjm,llm+1) ! diagonal coefficients of tridiag problem |
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212 | REAL(rstd) :: C_ik(iim*jjm,llm) ! Thomas algorithm |
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213 | REAL(rstd) :: D_il(iim*jjm,llm+1) ! Thomas algorithm |
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214 | REAL(rstd) :: gamma, rho_ij, X_ij, Y_ij |
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215 | REAL(rstd) :: wil, tau2_g, g2, gm2, ml_g2, c2_mik, vreff |
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216 | |
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217 | INTEGER :: iter, ij, l, ij_omp_begin_ext, ij_omp_end_ext |
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218 | |
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219 | CALL distrib_level(ij_begin_ext,ij_end_ext, ij_omp_begin_ext,ij_omp_end_ext) |
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220 | |
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221 | IF(dysl) THEN |
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222 | #define PHI_BOT(ij) phis(ij) |
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223 | #include "../kernels_hex/compute_NH_geopot.k90" |
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224 | #undef PHI_BOT |
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225 | ELSE |
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226 | ! FIXME : vertical OpenMP parallelism will not work |
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227 | |
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228 | tau2_g=tau*tau/g |
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229 | g2=g*g |
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230 | gm2 = g**-2 |
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231 | gamma = 1./(1.-kappa) |
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232 | |
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233 | ! compute Phi_star |
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234 | DO l=1,llm+1 |
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235 | !DIR$ SIMD |
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236 | DO ij=ij_begin_ext,ij_end_ext |
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237 | Phi_star_il(ij,l) = Phi_il(ij,l) + tau*g2*(W_il(ij,l)/m_il(ij,l)-tau) |
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238 | ENDDO |
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239 | ENDDO |
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240 | |
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241 | ! Newton-Raphson iteration : Phi_il contains current guess value |
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242 | DO iter=1,5 ! 2 iterations should be enough |
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243 | |
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244 | ! Compute pressure, A_ik |
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245 | DO l=1,llm |
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246 | !DIR$ SIMD |
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247 | DO ij=ij_begin_ext,ij_end_ext |
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248 | rho_ij = (g*m_ik(ij,l))/(Phi_il(ij,l+1)-Phi_il(ij,l)) |
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249 | X_ij = (cpp/preff)*kappa*theta(ij,l)*rho_ij |
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250 | p_ik(ij,l) = preff*(X_ij**gamma) |
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251 | c2_mik = gamma*p_ik(ij,l)/(rho_ij*m_ik(ij,l)) ! c^2 = gamma*R*T = gamma*p/rho |
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252 | A_ik(ij,l) = c2_mik*(tau/g*rho_ij)**2 |
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253 | ENDDO |
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254 | ENDDO |
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255 | |
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256 | ! Compute residual, B_il |
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257 | ! bottom interface l=1 |
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258 | !DIR$ SIMD |
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259 | DO ij=ij_begin_ext,ij_end_ext |
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260 | ml_g2 = gm2*m_il(ij,1) |
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261 | B_il(ij,1) = A_ik(ij,1) + ml_g2 + tau2_g*rho_bot |
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262 | R_il(ij,1) = ml_g2*( Phi_il(ij,1)-Phi_star_il(ij,1)) & |
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263 | + tau2_g*( p_ik(ij,1)-pbot+rho_bot*(Phi_il(ij,1)-phis(ij)) ) |
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264 | ENDDO |
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265 | ! inner interfaces |
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266 | DO l=2,llm |
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267 | !DIR$ SIMD |
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268 | DO ij=ij_begin_ext,ij_end_ext |
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269 | ml_g2 = gm2*m_il(ij,l) |
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270 | B_il(ij,l) = A_ik(ij,l)+A_ik(ij,l-1) + ml_g2 |
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271 | R_il(ij,l) = ml_g2*( Phi_il(ij,l)-Phi_star_il(ij,l)) & |
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272 | + tau2_g*(p_ik(ij,l)-p_ik(ij,l-1)) |
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273 | ! consistency check : if Wil=0 and initial state is in hydrostatic balance |
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274 | ! then Phi_star_il(ij,l) = Phi_il(ij,l) - tau^2*g^2 |
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275 | ! and residual = tau^2*(ml+(1/g)dl_pi)=0 |
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276 | ENDDO |
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277 | ENDDO |
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278 | ! top interface l=llm+1 |
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279 | !DIR$ SIMD |
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280 | DO ij=ij_begin_ext,ij_end_ext |
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281 | ml_g2 = gm2*m_il(ij,llm+1) |
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282 | B_il(ij,llm+1) = A_ik(ij,llm) + ml_g2 |
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283 | R_il(ij,llm+1) = ml_g2*( Phi_il(ij,llm+1)-Phi_star_il(ij,llm+1)) & |
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284 | + tau2_g*( ptop-p_ik(ij,llm) ) |
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285 | ENDDO |
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286 | |
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287 | ! FIXME later |
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288 | ! the lines below modify the tridiag problem |
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289 | ! for flat, rigid boundary conditions at top and bottom : |
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290 | ! zero out A(1), A(llm), R(1), R(llm+1) |
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291 | ! => x(l)=0 at l=1,llm+1 |
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292 | DO ij=ij_begin_ext,ij_end_ext |
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293 | A_ik(ij,1) = 0. |
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294 | A_ik(ij,llm) = 0. |
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295 | R_il(ij,1) = 0. |
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296 | R_il(ij,llm+1) = 0. |
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297 | ENDDO |
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298 | |
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299 | IF(debug_hevi_solver) THEN ! print Linf(residual) |
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300 | PRINT *, '[hevi_solver] R,p', iter, MAXVAL(ABS(R_il)), MAXVAL(p_ik) |
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301 | END IF |
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302 | |
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303 | ! Solve -A(l-1)x(l-1) + B(l)x(l) - A(l)x(l+1) = R(l) using Thomas algorithm |
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304 | ! Forward sweep : |
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305 | ! C(0)=0, C(l) = -A(l) / (B(l)+A(l-1)C(l-1)), |
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306 | ! D(0)=0, D(l) = (R(l)+A(l-1)D(l-1)) / (B(l)+A(l-1)C(l-1)) |
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307 | ! bottom interface l=1 |
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308 | !DIR$ SIMD |
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309 | DO ij=ij_begin_ext,ij_end_ext |
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310 | X_ij = 1./B_il(ij,1) |
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311 | C_ik(ij,1) = -A_ik(ij,1) * X_ij |
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312 | D_il(ij,1) = R_il(ij,1) * X_ij |
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313 | ENDDO |
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314 | ! inner interfaces/layers |
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315 | DO l=2,llm |
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316 | !DIR$ SIMD |
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317 | DO ij=ij_begin_ext,ij_end_ext |
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318 | X_ij = 1./(B_il(ij,l) + A_ik(ij,l-1)*C_ik(ij,l-1)) |
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319 | C_ik(ij,l) = -A_ik(ij,l) * X_ij |
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320 | D_il(ij,l) = (R_il(ij,l)+A_ik(ij,l-1)*D_il(ij,l-1)) * X_ij |
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321 | ENDDO |
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322 | ENDDO |
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323 | ! top interface l=llm+1 |
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324 | !DIR$ SIMD |
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325 | DO ij=ij_begin_ext,ij_end_ext |
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326 | X_ij = 1./(B_il(ij,llm+1) + A_ik(ij,llm)*C_ik(ij,llm)) |
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327 | D_il(ij,llm+1) = (R_il(ij,llm+1)+A_ik(ij,llm)*D_il(ij,llm)) * X_ij |
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328 | ENDDO |
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329 | |
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330 | ! Back substitution : |
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331 | ! x(i) = D(i)-C(i)x(i+1), x(N+1)=0 |
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332 | ! + Newton-Raphson update |
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333 | x_il=0. ! FIXME |
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334 | ! top interface l=llm+1 |
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335 | !DIR$ SIMD |
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336 | DO ij=ij_begin_ext,ij_end_ext |
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337 | x_il(ij,llm+1) = D_il(ij,llm+1) |
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338 | Phi_il(ij,llm+1) = Phi_il(ij,llm+1) - x_il(ij,llm+1) |
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339 | ENDDO |
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340 | ! lower interfaces |
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341 | DO l=llm,1,-1 |
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342 | !DIR$ SIMD |
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343 | DO ij=ij_begin_ext,ij_end_ext |
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344 | x_il(ij,l) = D_il(ij,l) - C_ik(ij,l)*x_il(ij,l+1) |
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345 | Phi_il(ij,l) = Phi_il(ij,l) - x_il(ij,l) |
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346 | ENDDO |
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347 | ENDDO |
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348 | |
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349 | IF(debug_hevi_solver) THEN |
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350 | PRINT *, '[hevi_solver] A,B', iter, MAXVAL(ABS(A_ik)),MAXVAL(ABS(B_il)) |
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351 | PRINT *, '[hevi_solver] C,D', iter, MAXVAL(ABS(C_ik)),MAXVAL(ABS(D_il)) |
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352 | DO l=1,llm+1 |
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353 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] x', iter,l, MAXVAL(ABS(x_il(:,l))) |
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354 | END DO |
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355 | END IF |
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356 | |
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357 | END DO ! Newton-Raphson |
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358 | |
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359 | END IF ! dysl |
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360 | |
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361 | END SUBROUTINE compute_NH_geopot |
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362 | |
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363 | END MODULE compute_NH_geopot_mod |
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