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