1 | MODULE compute_NH_geopot_mod |
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2 | USE grid_param, ONLY : llm |
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3 | IMPLICIT NONE |
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4 | PRIVATE |
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5 | |
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6 | LOGICAL, SAVE :: debug_hevi_solver = .FALSE. |
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7 | |
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8 | PUBLIC :: compute_NH_geopot |
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9 | |
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10 | CONTAINS |
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11 | |
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12 | SUBROUTINE compute_NH_geopot(tau, phis, m_ik, m_il, theta, W_il, Phi_il) |
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13 | USE icosa |
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14 | USE disvert_mod |
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15 | USE caldyn_vars_mod |
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16 | USE omp_para |
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17 | REAL(rstd), PARAMETER :: pbot=1e5, rho_bot=1e6 |
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18 | REAL(rstd),INTENT(IN) :: tau ! solve Phi-tau*dPhi/dt = Phi_rhs |
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19 | REAL(rstd),INTENT(IN) :: phis(iim*jjm) |
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20 | REAL(rstd),INTENT(IN) :: m_ik(iim*jjm,llm) |
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21 | REAL(rstd),INTENT(IN) :: m_il(iim*jjm,llm+1) |
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22 | REAL(rstd),INTENT(IN) :: theta(iim*jjm,llm) |
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23 | REAL(rstd),INTENT(IN) :: W_il(iim*jjm,llm+1) ! vertical momentum |
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24 | REAL(rstd),INTENT(INOUT) :: Phi_il(iim*jjm,llm+1) ! geopotential |
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25 | |
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26 | REAL(rstd) :: Phi_star_il(iim*jjm,llm+1) |
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27 | REAL(rstd) :: p_ik(iim*jjm,llm) ! pressure |
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28 | REAL(rstd) :: R_il(iim*jjm,llm+1) ! rhs of tridiag problem |
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29 | REAL(rstd) :: x_il(iim*jjm,llm+1) ! solution of tridiag problem |
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30 | REAL(rstd) :: A_ik(iim*jjm,llm) ! off-diagonal coefficients of tridiag problem |
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31 | REAL(rstd) :: B_il(iim*jjm,llm+1) ! diagonal coefficients of tridiag problem |
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32 | REAL(rstd) :: C_ik(iim*jjm,llm) ! Thomas algorithm |
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33 | REAL(rstd) :: D_il(iim*jjm,llm+1) ! Thomas algorithm |
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34 | REAL(rstd) :: gamma, rho_ij, X_ij, Y_ij |
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35 | REAL(rstd) :: wil, tau2_g, g2, gm2, ml_g2, c2_mik, vreff |
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36 | |
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37 | INTEGER :: iter, ij, l, ij_omp_begin_ext, ij_omp_end_ext |
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38 | |
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39 | CALL distrib_level(ij_begin_ext,ij_end_ext, ij_omp_begin_ext,ij_omp_end_ext) |
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40 | |
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41 | IF(dysl) THEN |
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42 | #define PHI_BOT(ij) phis(ij) |
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43 | #include "../kernels_hex/compute_NH_geopot.k90" |
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44 | #undef PHI_BOT |
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45 | ELSE |
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46 | ! FIXME : vertical OpenMP parallelism will not work |
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47 | |
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48 | tau2_g=tau*tau/g |
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49 | g2=g*g |
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50 | gm2 = g**-2 |
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51 | gamma = 1./(1.-kappa) |
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52 | |
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53 | ! compute Phi_star |
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54 | DO l=1,llm+1 |
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55 | !DIR$ SIMD |
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56 | DO ij=ij_begin_ext,ij_end_ext |
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57 | Phi_star_il(ij,l) = Phi_il(ij,l) + tau*g2*(W_il(ij,l)/m_il(ij,l)-tau) |
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58 | ENDDO |
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59 | ENDDO |
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60 | |
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61 | ! Newton-Raphson iteration : Phi_il contains current guess value |
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62 | DO iter=1,5 ! 2 iterations should be enough |
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63 | |
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64 | ! Compute pressure, A_ik |
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65 | DO l=1,llm |
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66 | !DIR$ SIMD |
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67 | DO ij=ij_begin_ext,ij_end_ext |
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68 | rho_ij = (g*m_ik(ij,l))/(Phi_il(ij,l+1)-Phi_il(ij,l)) |
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69 | X_ij = (cpp/preff)*kappa*theta(ij,l)*rho_ij |
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70 | p_ik(ij,l) = preff*(X_ij**gamma) |
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71 | 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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72 | A_ik(ij,l) = c2_mik*(tau/g*rho_ij)**2 |
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73 | ENDDO |
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74 | ENDDO |
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75 | |
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76 | ! Compute residual, B_il |
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77 | ! bottom interface l=1 |
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78 | !DIR$ SIMD |
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79 | DO ij=ij_begin_ext,ij_end_ext |
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80 | ml_g2 = gm2*m_il(ij,1) |
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81 | B_il(ij,1) = A_ik(ij,1) + ml_g2 + tau2_g*rho_bot |
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82 | R_il(ij,1) = ml_g2*( Phi_il(ij,1)-Phi_star_il(ij,1)) & |
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83 | + tau2_g*( p_ik(ij,1)-pbot+rho_bot*(Phi_il(ij,1)-phis(ij)) ) |
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84 | ENDDO |
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85 | ! inner interfaces |
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86 | DO l=2,llm |
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87 | !DIR$ SIMD |
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88 | DO ij=ij_begin_ext,ij_end_ext |
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89 | ml_g2 = gm2*m_il(ij,l) |
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90 | B_il(ij,l) = A_ik(ij,l)+A_ik(ij,l-1) + ml_g2 |
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91 | R_il(ij,l) = ml_g2*( Phi_il(ij,l)-Phi_star_il(ij,l)) & |
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92 | + tau2_g*(p_ik(ij,l)-p_ik(ij,l-1)) |
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93 | ! consistency check : if Wil=0 and initial state is in hydrostatic balance |
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94 | ! then Phi_star_il(ij,l) = Phi_il(ij,l) - tau^2*g^2 |
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95 | ! and residual = tau^2*(ml+(1/g)dl_pi)=0 |
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96 | ENDDO |
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97 | ENDDO |
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98 | ! top interface l=llm+1 |
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99 | !DIR$ SIMD |
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100 | DO ij=ij_begin_ext,ij_end_ext |
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101 | ml_g2 = gm2*m_il(ij,llm+1) |
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102 | B_il(ij,llm+1) = A_ik(ij,llm) + ml_g2 |
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103 | R_il(ij,llm+1) = ml_g2*( Phi_il(ij,llm+1)-Phi_star_il(ij,llm+1)) & |
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104 | + tau2_g*( ptop-p_ik(ij,llm) ) |
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105 | ENDDO |
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106 | |
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107 | ! FIXME later |
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108 | ! the lines below modify the tridiag problem |
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109 | ! for flat, rigid boundary conditions at top and bottom : |
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110 | ! zero out A(1), A(llm), R(1), R(llm+1) |
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111 | ! => x(l)=0 at l=1,llm+1 |
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112 | DO ij=ij_begin_ext,ij_end_ext |
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113 | A_ik(ij,1) = 0. |
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114 | A_ik(ij,llm) = 0. |
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115 | R_il(ij,1) = 0. |
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116 | R_il(ij,llm+1) = 0. |
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117 | ENDDO |
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118 | |
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119 | IF(debug_hevi_solver) THEN ! print Linf(residual) |
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120 | PRINT *, '[hevi_solver] R,p', iter, MAXVAL(ABS(R_il)), MAXVAL(p_ik) |
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121 | END IF |
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122 | |
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123 | ! 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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124 | ! Forward sweep : |
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125 | ! C(0)=0, C(l) = -A(l) / (B(l)+A(l-1)C(l-1)), |
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126 | ! 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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127 | ! bottom interface l=1 |
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128 | !DIR$ SIMD |
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129 | DO ij=ij_begin_ext,ij_end_ext |
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130 | X_ij = 1./B_il(ij,1) |
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131 | C_ik(ij,1) = -A_ik(ij,1) * X_ij |
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132 | D_il(ij,1) = R_il(ij,1) * X_ij |
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133 | ENDDO |
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134 | ! inner interfaces/layers |
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135 | DO l=2,llm |
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136 | !DIR$ SIMD |
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137 | DO ij=ij_begin_ext,ij_end_ext |
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138 | X_ij = 1./(B_il(ij,l) + A_ik(ij,l-1)*C_ik(ij,l-1)) |
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139 | C_ik(ij,l) = -A_ik(ij,l) * X_ij |
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140 | D_il(ij,l) = (R_il(ij,l)+A_ik(ij,l-1)*D_il(ij,l-1)) * X_ij |
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141 | ENDDO |
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142 | ENDDO |
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143 | ! top interface l=llm+1 |
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144 | !DIR$ SIMD |
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145 | DO ij=ij_begin_ext,ij_end_ext |
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146 | X_ij = 1./(B_il(ij,llm+1) + A_ik(ij,llm)*C_ik(ij,llm)) |
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147 | D_il(ij,llm+1) = (R_il(ij,llm+1)+A_ik(ij,llm)*D_il(ij,llm)) * X_ij |
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148 | ENDDO |
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149 | |
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150 | ! Back substitution : |
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151 | ! x(i) = D(i)-C(i)x(i+1), x(N+1)=0 |
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152 | ! + Newton-Raphson update |
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153 | x_il=0. ! FIXME |
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154 | ! top interface l=llm+1 |
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155 | !DIR$ SIMD |
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156 | DO ij=ij_begin_ext,ij_end_ext |
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157 | x_il(ij,llm+1) = D_il(ij,llm+1) |
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158 | Phi_il(ij,llm+1) = Phi_il(ij,llm+1) - x_il(ij,llm+1) |
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159 | ENDDO |
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160 | ! lower interfaces |
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161 | DO l=llm,1,-1 |
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162 | !DIR$ SIMD |
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163 | DO ij=ij_begin_ext,ij_end_ext |
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164 | x_il(ij,l) = D_il(ij,l) - C_ik(ij,l)*x_il(ij,l+1) |
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165 | Phi_il(ij,l) = Phi_il(ij,l) - x_il(ij,l) |
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166 | ENDDO |
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167 | ENDDO |
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168 | |
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169 | IF(debug_hevi_solver) THEN |
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170 | PRINT *, '[hevi_solver] A,B', iter, MAXVAL(ABS(A_ik)),MAXVAL(ABS(B_il)) |
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171 | PRINT *, '[hevi_solver] C,D', iter, MAXVAL(ABS(C_ik)),MAXVAL(ABS(D_il)) |
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172 | DO l=1,llm+1 |
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173 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] x', iter,l, MAXVAL(ABS(x_il(:,l))) |
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174 | END DO |
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175 | END IF |
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176 | |
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177 | END DO ! Newton-Raphson |
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178 | |
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179 | END IF ! dysl |
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180 | |
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181 | END SUBROUTINE compute_NH_geopot |
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182 | |
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183 | END MODULE compute_NH_geopot_mod |
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