[563] | 1 | !-------------------------------------------------------------------------- |
---|
| 2 | !---------------------------- compute_NH_geopot ---------------------------------- |
---|
| 3 | tau2_g=tau*tau/g |
---|
| 4 | g2=g*g |
---|
| 5 | gm2 = 1./g2 |
---|
[657] | 6 | vreff = Treff*cpp/preff*kappa |
---|
[563] | 7 | gamma = 1./(1.-kappa) |
---|
| 8 | !$OMP BARRIER |
---|
| 9 | ! compute Phi_star |
---|
| 10 | DO l = 1,llm+1 |
---|
[724] | 11 | !DIR$ SIMD |
---|
[563] | 12 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
---|
| 13 | Phi_star_il(ij,l) = Phi_il(ij,l) + tau*g2*(W_il(ij,l)/m_il(ij,l)-tau) |
---|
| 14 | END DO |
---|
| 15 | END DO |
---|
| 16 | ! Newton-Raphson iteration : Phi_il contains current guess value |
---|
| 17 | DO iter=1,2 ! 2 iterations should be enough |
---|
| 18 | ! Compute pressure, A_ik |
---|
| 19 | SELECT CASE(caldyn_thermo) |
---|
| 20 | CASE(thermo_theta) |
---|
| 21 | DO l = 1,llm |
---|
[724] | 22 | !DIR$ SIMD |
---|
[563] | 23 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
---|
| 24 | rho_ij = (g*m_ik(ij,l))/(Phi_il(ij,l+1)-Phi_il(ij,l)) |
---|
| 25 | X_ij = (cpp/preff)*kappa*theta(ij,l)*rho_ij |
---|
| 26 | p_ik(ij,l) = preff*(X_ij**gamma) |
---|
| 27 | c2_mik = gamma*p_ik(ij,l)/(rho_ij*m_ik(ij,l)) ! c^2 = gamma*R*T = gamma*p/rho |
---|
| 28 | A_ik(ij,l) = c2_mik*(tau/g*rho_ij)**2 |
---|
| 29 | END DO |
---|
| 30 | END DO |
---|
| 31 | CASE(thermo_entropy) |
---|
| 32 | DO l = 1,llm |
---|
[724] | 33 | !DIR$ SIMD |
---|
[563] | 34 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
---|
| 35 | rho_ij = (g*m_ik(ij,l))/(Phi_il(ij,l+1)-Phi_il(ij,l)) |
---|
[657] | 36 | X_ij = log(vreff*rho_ij) + theta(ij,l)/cpp |
---|
| 37 | p_ik(ij,l) = preff*exp(X_ij*gamma) |
---|
[563] | 38 | c2_mik = gamma*p_ik(ij,l)/(rho_ij*m_ik(ij,l)) ! c^2 = gamma*R*T = gamma*p/rho |
---|
| 39 | A_ik(ij,l) = c2_mik*(tau/g*rho_ij)**2 |
---|
| 40 | END DO |
---|
| 41 | END DO |
---|
| 42 | CASE DEFAULT |
---|
| 43 | PRINT *, 'caldyn_thermo not supported by compute_NH_geopot', caldyn_thermo |
---|
| 44 | STOP |
---|
| 45 | END SELECT |
---|
| 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 |
---|
| 47 | ! Solve -A(l-1)x(l-1) + B(l)x(l) - A(l)x(l+1) = R(l) using Thomas algorithm |
---|
| 48 | ! Compute residual R_il and B_il |
---|
[724] | 49 | !DIR$ SIMD |
---|
[563] | 50 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
---|
| 51 | ! bottom interface l=1 |
---|
| 52 | ml_g2 = gm2*m_il(ij,1) |
---|
| 53 | B_il(ij,1) = A_ik(ij,1) + ml_g2 + tau2_g*rho_bot |
---|
| 54 | R_il(ij,1) = ml_g2*( Phi_il(ij,1)-Phi_star_il(ij,1)) & |
---|
| 55 | + tau2_g*( p_ik(ij,1)-pbot+rho_bot*(Phi_il(ij,1)-PHI_BOT(ij)) ) |
---|
| 56 | END DO |
---|
| 57 | DO l = 2,llm |
---|
[724] | 58 | !DIR$ SIMD |
---|
[563] | 59 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
---|
| 60 | ! inner interfaces |
---|
| 61 | ml_g2 = gm2*m_il(ij,l) |
---|
| 62 | B_il(ij,l) = A_ik(ij,l)+A_ik(ij,l-1) + ml_g2 |
---|
| 63 | R_il(ij,l) = ml_g2*( Phi_il(ij,l)-Phi_star_il(ij,l)) & |
---|
| 64 | + tau2_g*(p_ik(ij,l)-p_ik(ij,l-1)) |
---|
| 65 | ! consistency check : if Wil=0 and initial state is in hydrostatic balance |
---|
| 66 | ! then Phi_star_il(ij,l) = Phi_il(ij,l) - tau^2*g^2 |
---|
| 67 | ! and residual = tau^2*(ml+(1/g)dl_pi)=0 |
---|
| 68 | END DO |
---|
| 69 | END DO |
---|
[724] | 70 | !DIR$ SIMD |
---|
[563] | 71 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
---|
| 72 | ! top interface l=llm+1 |
---|
| 73 | ml_g2 = gm2*m_il(ij,llm+1) |
---|
| 74 | B_il(ij,llm+1) = A_ik(ij,llm+1 -1) + ml_g2 |
---|
| 75 | R_il(ij,llm+1) = ml_g2*( Phi_il(ij,llm+1)-Phi_star_il(ij,llm+1)) & |
---|
| 76 | + tau2_g*( ptop-p_ik(ij,llm+1 -1) ) |
---|
| 77 | END DO |
---|
| 78 | ! |
---|
| 79 | ! Forward sweep : |
---|
| 80 | ! C(0)=0, C(l) = -A(l) / (B(l)+A(l-1)C(l-1)), |
---|
| 81 | ! D(0)=0, D(l) = (R(l)+A(l-1)D(l-1)) / (B(l)+A(l-1)C(l-1)) |
---|
[724] | 82 | !DIR$ SIMD |
---|
[563] | 83 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
---|
| 84 | X_ij = 1./B_il(ij,1) |
---|
| 85 | C_ik(ij,1) = -A_ik(ij,1) * X_ij |
---|
| 86 | D_il(ij,1) = R_il(ij,1) * X_ij |
---|
| 87 | END DO |
---|
| 88 | DO l = 2,llm |
---|
[724] | 89 | !DIR$ SIMD |
---|
[563] | 90 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
---|
| 91 | X_ij = 1./( B_il(ij,l) + A_ik(ij,l-1)*C_ik(ij,l-1) ) |
---|
| 92 | C_ik(ij,l) = -A_ik(ij,l) * X_ij |
---|
| 93 | D_il(ij,l) = (R_il(ij,l)+A_ik(ij,l-1)*D_il(ij,l-1)) * X_ij |
---|
| 94 | END DO |
---|
| 95 | END DO |
---|
[724] | 96 | !DIR$ SIMD |
---|
[563] | 97 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
---|
| 98 | X_ij = 1./( B_il(ij,llm+1) + A_ik(ij,llm+1 -1)*C_ik(ij,llm+1 -1) ) |
---|
| 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 |
---|
| 100 | ! Back substitution : |
---|
| 101 | ! x(i) = D(i)-C(i)x(i+1), x(llm+1)=0 |
---|
| 102 | ! + Newton-Raphson update |
---|
| 103 | ! top interface l=llm+1 |
---|
| 104 | x_il(ij,llm+1) = D_il(ij,llm+1) |
---|
| 105 | Phi_il(ij,llm+1) = Phi_il(ij,llm+1) - x_il(ij,llm+1) |
---|
| 106 | END DO |
---|
| 107 | DO l = llm,1,-1 |
---|
[724] | 108 | !DIR$ SIMD |
---|
[563] | 109 | DO ij=ij_omp_begin_ext,ij_omp_end_ext |
---|
| 110 | ! Back substitution at lower interfaces |
---|
| 111 | x_il(ij,l) = D_il(ij,l) - C_ik(ij,l)*x_il(ij,l+1) |
---|
| 112 | Phi_il(ij,l) = Phi_il(ij,l) - x_il(ij,l) |
---|
| 113 | END DO |
---|
| 114 | END DO |
---|
| 115 | IF(debug_hevi_solver) THEN |
---|
| 116 | PRINT *, '[hevi_solver] A,B', iter, MAXVAL(ABS(A_ik)),MAXVAL(ABS(B_il)) |
---|
| 117 | PRINT *, '[hevi_solver] C,D', iter, MAXVAL(ABS(C_ik)),MAXVAL(ABS(D_il)) |
---|
| 118 | DO l=1,llm+1 |
---|
[821] | 119 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] x_il', iter,l, MAXVAL(ABS(x_il(l,:))) |
---|
[563] | 120 | END DO |
---|
| 121 | DO l=1,llm+1 |
---|
[821] | 122 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] R_il', iter,l, MAXVAL(ABS(R_il(l,:))) |
---|
[563] | 123 | END DO |
---|
| 124 | END IF |
---|
| 125 | END DO ! Newton-Raphson |
---|
| 126 | !$OMP BARRIER |
---|
| 127 | debug_hevi_solver=.FALSE. |
---|
| 128 | !---------------------------- compute_NH_geopot ---------------------------------- |
---|
| 129 | !-------------------------------------------------------------------------- |
---|