[614] | 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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[658] | 6 | vreff = Treff*cpp/preff*kappa |
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[614] | 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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[658] | 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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[614] | 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 | ! bottom interface l=1 |
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[686] | 55 | ml_g2 = gm2*m_il(1,ij) |
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| 56 | B_il(1,ij) = A_ik(1,ij) + ml_g2 + tau2_g*rho_bot |
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| 57 | R_il(1,ij) = ml_g2*( Phi_il(1,ij)-Phi_star_il(1,ij)) & |
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| 58 | + tau2_g*( p_ik(1,ij)-pbot+rho_bot*(Phi_il(1,ij)-PHI_BOT(ij)) ) |
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[614] | 59 | DO l = 2,llm |
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| 60 | ! inner interfaces |
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| 61 | ml_g2 = gm2*m_il(l,ij) |
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| 62 | B_il(l,ij) = A_ik(l,ij)+A_ik(l-1,ij) + ml_g2 |
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| 63 | R_il(l,ij) = ml_g2*( Phi_il(l,ij)-Phi_star_il(l,ij)) & |
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| 64 | + tau2_g*(p_ik(l,ij)-p_ik(l-1,ij)) |
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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(l,ij) = Phi_il(l,ij) - 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 | ! top interface l=llm+1 |
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[686] | 70 | ml_g2 = gm2*m_il(llm+1,ij) |
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| 71 | B_il(llm+1,ij) = A_ik(llm+1 -1,ij) + ml_g2 |
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| 72 | R_il(llm+1,ij) = ml_g2*( Phi_il(llm+1,ij)-Phi_star_il(llm+1,ij)) & |
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| 73 | + tau2_g*( ptop-p_ik(llm+1 -1,ij) ) |
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[614] | 74 | ! |
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| 75 | ! Forward sweep : |
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| 76 | ! C(0)=0, C(l) = -A(l) / (B(l)+A(l-1)C(l-1)), |
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| 77 | ! 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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[686] | 78 | X_ij = 1./B_il(1,ij) |
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| 79 | C_ik(1,ij) = -A_ik(1,ij) * X_ij |
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| 80 | D_il(1,ij) = R_il(1,ij) * X_ij |
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[614] | 81 | DO l = 2,llm |
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| 82 | X_ij = 1./( B_il(l,ij) + A_ik(l-1,ij)*C_ik(l-1,ij) ) |
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| 83 | C_ik(l,ij) = -A_ik(l,ij) * X_ij |
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| 84 | D_il(l,ij) = (R_il(l,ij)+A_ik(l-1,ij)*D_il(l-1,ij)) * X_ij |
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| 85 | END DO |
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[686] | 86 | X_ij = 1./( B_il(llm+1,ij) + A_ik(llm+1 -1,ij)*C_ik(llm+1 -1,ij) ) |
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| 87 | D_il(llm+1,ij) = (R_il(llm+1,ij)+A_ik(llm+1 -1,ij)*D_il(llm+1 -1,ij)) * X_ij |
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[614] | 88 | ! Back substitution : |
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| 89 | ! x(i) = D(i)-C(i)x(i+1), x(llm+1)=0 |
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| 90 | ! + Newton-Raphson update |
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| 91 | ! top interface l=llm+1 |
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[686] | 92 | x_il(llm+1,ij) = D_il(llm+1,ij) |
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| 93 | Phi_il(llm+1,ij) = Phi_il(llm+1,ij) - x_il(llm+1,ij) |
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[614] | 94 | DO l = llm,1,-1 |
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| 95 | ! Back substitution at lower interfaces |
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| 96 | x_il(l,ij) = D_il(l,ij) - C_ik(l,ij)*x_il(l+1,ij) |
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| 97 | Phi_il(l,ij) = Phi_il(l,ij) - x_il(l,ij) |
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| 98 | END DO |
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| 99 | END DO |
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| 100 | !$OMP END DO |
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| 101 | IF(debug_hevi_solver) THEN |
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| 102 | PRINT *, '[hevi_solver] A,B', iter, MAXVAL(ABS(A_ik)),MAXVAL(ABS(B_il)) |
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| 103 | PRINT *, '[hevi_solver] C,D', iter, MAXVAL(ABS(C_ik)),MAXVAL(ABS(D_il)) |
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| 104 | DO l=1,llm+1 |
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[822] | 105 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] x_il', iter,l, MAXVAL(ABS(x_il(l,:))) |
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[614] | 106 | END DO |
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| 107 | DO l=1,llm+1 |
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[822] | 108 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] R_il', iter,l, MAXVAL(ABS(R_il(l,:))) |
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[614] | 109 | END DO |
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| 110 | END IF |
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| 111 | END DO ! Newton-Raphson |
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| 112 | !$OMP BARRIER |
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| 113 | debug_hevi_solver=.FALSE. |
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| 114 | !---------------------------- compute_NH_geopot ---------------------------------- |
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| 115 | !-------------------------------------------------------------------------- |
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