1 | !-------------------------------------------------------------------------- |
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2 | !---------------------------- compute_NH_geopot ---------------------------------- |
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3 | tau2_g=tau*tau/g |
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4 | g2=g*g |
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5 | gm2 = 1./g2 |
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6 | vreff = Treff*cpp/preff*kappa |
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7 | gamma = 1./(1.-kappa) |
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8 | !$OMP BARRIER |
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9 | ! compute Phi_star |
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10 | DO l = 1,llm+1 |
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11 | !DIR$ SIMD |
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12 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
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13 | Phi_star_il(ij,l) = Phi_il(ij,l) + tau*g2*(W_il(ij,l)/m_il(ij,l)-tau) |
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14 | END DO |
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15 | END DO |
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16 | ! Newton-Raphson iteration : Phi_il contains current guess value |
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17 | DO iter=1,2 ! 2 iterations should be enough |
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18 | ! Compute pressure, A_ik |
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19 | SELECT CASE(caldyn_thermo) |
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20 | CASE(thermo_theta) |
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21 | DO l = 1,llm |
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22 | !DIR$ SIMD |
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23 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
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24 | rho_ij = (g*m_ik(ij,l))/(Phi_il(ij,l+1)-Phi_il(ij,l)) |
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25 | X_ij = (cpp/preff)*kappa*theta(ij,l)*rho_ij |
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26 | p_ik(ij,l) = preff*(X_ij**gamma) |
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27 | 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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28 | A_ik(ij,l) = c2_mik*(tau/g*rho_ij)**2 |
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29 | END DO |
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30 | END DO |
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31 | CASE(thermo_entropy) |
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32 | DO l = 1,llm |
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33 | !DIR$ SIMD |
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34 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
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35 | rho_ij = (g*m_ik(ij,l))/(Phi_il(ij,l+1)-Phi_il(ij,l)) |
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36 | X_ij = log(vreff*rho_ij) + theta(ij,l)/cpp |
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37 | p_ik(ij,l) = preff*exp(X_ij*gamma) |
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38 | 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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39 | A_ik(ij,l) = c2_mik*(tau/g*rho_ij)**2 |
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40 | END DO |
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41 | END DO |
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42 | CASE DEFAULT |
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43 | PRINT *, 'caldyn_thermo not supported by compute_NH_geopot', caldyn_thermo |
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44 | STOP |
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45 | END SELECT |
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46 | ! 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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47 | ! 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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48 | ! Compute residual R_il and B_il |
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49 | !DIR$ SIMD |
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50 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
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51 | ! bottom interface l=1 |
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52 | ml_g2 = gm2*m_il(ij,1) |
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53 | B_il(ij,1) = A_ik(ij,1) + ml_g2 + tau2_g*rho_bot |
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54 | R_il(ij,1) = ml_g2*( Phi_il(ij,1)-Phi_star_il(ij,1)) & |
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55 | + tau2_g*( p_ik(ij,1)-pbot+rho_bot*(Phi_il(ij,1)-PHI_BOT(ij)) ) |
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56 | END DO |
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57 | DO l = 2,llm |
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58 | !DIR$ SIMD |
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59 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
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60 | ! inner interfaces |
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61 | ml_g2 = gm2*m_il(ij,l) |
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62 | B_il(ij,l) = A_ik(ij,l)+A_ik(ij,l-1) + ml_g2 |
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63 | R_il(ij,l) = ml_g2*( Phi_il(ij,l)-Phi_star_il(ij,l)) & |
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64 | + tau2_g*(p_ik(ij,l)-p_ik(ij,l-1)) |
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65 | ! consistency check : if Wil=0 and initial state is in hydrostatic balance |
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66 | ! then Phi_star_il(ij,l) = Phi_il(ij,l) - tau^2*g^2 |
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67 | ! and residual = tau^2*(ml+(1/g)dl_pi)=0 |
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68 | END DO |
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69 | END DO |
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70 | !DIR$ SIMD |
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71 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
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72 | ! top interface l=llm+1 |
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73 | ml_g2 = gm2*m_il(ij,llm+1) |
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74 | B_il(ij,llm+1) = A_ik(ij,llm+1 -1) + ml_g2 |
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75 | R_il(ij,llm+1) = ml_g2*( Phi_il(ij,llm+1)-Phi_star_il(ij,llm+1)) & |
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76 | + tau2_g*( ptop-p_ik(ij,llm+1 -1) ) |
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77 | END DO |
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78 | ! |
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79 | ! Forward sweep : |
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80 | ! C(0)=0, C(l) = -A(l) / (B(l)+A(l-1)C(l-1)), |
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81 | ! 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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82 | !DIR$ SIMD |
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83 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
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84 | X_ij = 1./B_il(ij,1) |
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85 | C_ik(ij,1) = -A_ik(ij,1) * X_ij |
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86 | D_il(ij,1) = R_il(ij,1) * X_ij |
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87 | END DO |
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88 | DO l = 2,llm |
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89 | !DIR$ SIMD |
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90 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
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91 | X_ij = 1./( B_il(ij,l) + A_ik(ij,l-1)*C_ik(ij,l-1) ) |
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92 | C_ik(ij,l) = -A_ik(ij,l) * X_ij |
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93 | D_il(ij,l) = (R_il(ij,l)+A_ik(ij,l-1)*D_il(ij,l-1)) * X_ij |
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94 | END DO |
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95 | END DO |
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96 | !DIR$ SIMD |
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97 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
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98 | X_ij = 1./( B_il(ij,llm+1) + A_ik(ij,llm+1 -1)*C_ik(ij,llm+1 -1) ) |
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99 | D_il(ij,llm+1) = (R_il(ij,llm+1)+A_ik(ij,llm+1 -1)*D_il(ij,llm+1 -1)) * X_ij |
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100 | ! Back substitution : |
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101 | ! x(i) = D(i)-C(i)x(i+1), x(llm+1)=0 |
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102 | ! + Newton-Raphson update |
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103 | ! top interface l=llm+1 |
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104 | x_il(ij,llm+1) = D_il(ij,llm+1) |
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105 | Phi_il(ij,llm+1) = Phi_il(ij,llm+1) - x_il(ij,llm+1) |
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106 | END DO |
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107 | DO l = llm,1,-1 |
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108 | !DIR$ SIMD |
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109 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
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110 | ! Back substitution at lower interfaces |
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111 | x_il(ij,l) = D_il(ij,l) - C_ik(ij,l)*x_il(ij,l+1) |
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112 | Phi_il(ij,l) = Phi_il(ij,l) - x_il(ij,l) |
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113 | END DO |
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114 | END DO |
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115 | IF(debug_hevi_solver) THEN |
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116 | PRINT *, '[hevi_solver] A,B', iter, MAXVAL(ABS(A_ik)),MAXVAL(ABS(B_il)) |
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117 | PRINT *, '[hevi_solver] C,D', iter, MAXVAL(ABS(C_ik)),MAXVAL(ABS(D_il)) |
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118 | DO l=1,llm+1 |
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119 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] x_il', iter,l, MAXVAL(ABS(x_il(l,:))) |
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120 | END DO |
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121 | DO l=1,llm+1 |
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122 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] R_il', iter,l, MAXVAL(ABS(R_il(l,:))) |
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123 | END DO |
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124 | END IF |
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125 | END DO ! Newton-Raphson |
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126 | !$OMP BARRIER |
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127 | debug_hevi_solver=.FALSE. |
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128 | !---------------------------- compute_NH_geopot ---------------------------------- |
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129 | !-------------------------------------------------------------------------- |
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