[859] | 1 | MODULE compute_NH_geopot_mod |
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[939] | 2 | USE grid_param |
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[980] | 3 | USE icosa, ONLY : rstd |
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[859] | 4 | IMPLICIT NONE |
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| 5 | PRIVATE |
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| 6 | |
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| 7 | LOGICAL, SAVE :: debug_hevi_solver = .FALSE. |
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[980] | 8 | |
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| 9 | REAL(rstd) :: pbot=1e5, rho_bot=100. ! for NH solver |
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[859] | 10 | |
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[878] | 11 | #include "../unstructured/unstructured.h90" |
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[859] | 12 | |
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[980] | 13 | PUBLIC :: compute_NH_geopot,compute_NH_geopot_unst, pbot, rho_bot |
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[878] | 14 | |
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[859] | 15 | CONTAINS |
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| 16 | |
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[878] | 17 | #ifdef BEGIN_DYSL |
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| 18 | |
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| 19 | KERNEL(compute_NH_geopot) |
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| 20 | tau2_g=tau*tau/g |
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| 21 | g2=g*g |
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| 22 | gm2 = 1./g2 |
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| 23 | vreff = Treff*cpp/preff*kappa |
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| 24 | gamma = 1./(1.-kappa) |
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| 25 | |
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| 26 | BARRIER |
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| 27 | |
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| 28 | ! compute Phi_star |
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| 29 | SEQUENCE_C1 |
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| 30 | BODY('1,llm+1') |
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| 31 | Phi_star_il(CELL) = Phi_il(CELL) + tau*g2*(W_il(CELL)/m_il(CELL)-tau) |
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| 32 | END_BLOCK |
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| 33 | END_BLOCK |
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| 34 | |
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| 35 | ! Newton-Raphson iteration : Phi_il contains current guess value |
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| 36 | DO iter=1,2 ! 2 iterations should be enough |
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| 37 | ! Compute pressure, A_ik |
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| 38 | SELECT CASE(caldyn_thermo) |
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| 39 | CASE(thermo_theta) |
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| 40 | {% call() compute_p_and_Aik() %} |
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| 41 | X_ij = (cpp/preff)*kappa*theta(CELL)*rho_ij |
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| 42 | p_ik(CELL) = preff*(X_ij**gamma) |
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| 43 | c2_mik = gamma*p_ik(CELL)/(rho_ij*m_ik(CELL)) ! c^2 = gamma*R*T = gamma*p/rho |
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| 44 | {% endcall %} |
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| 45 | CASE(thermo_entropy) |
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| 46 | {% call() compute_p_and_Aik() %} |
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| 47 | X_ij = log(vreff*rho_ij) + theta(CELL)/cpp |
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| 48 | p_ik(CELL) = preff*exp(X_ij*gamma) |
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| 49 | c2_mik = gamma*p_ik(CELL)/(rho_ij*m_ik(CELL)) ! c^2 = gamma*R*T = gamma*p/rho |
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| 50 | {% endcall %} |
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| 51 | CASE DEFAULT |
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| 52 | PRINT *, 'caldyn_thermo not supported by compute_NH_geopot', caldyn_thermo |
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| 53 | STOP |
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| 54 | END SELECT |
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| 55 | |
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| 56 | ! 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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| 57 | ! 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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| 58 | |
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| 59 | SEQUENCE_C1 |
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| 60 | ! Compute residual R_il and B_il |
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| 61 | PROLOGUE(1) |
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| 62 | ! bottom interface l=1 |
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| 63 | ml_g2 = gm2*m_il(CELL) |
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| 64 | B_il(CELL) = A_ik(CELL) + ml_g2 + tau2_g*rho_bot |
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| 65 | R_il(CELL) = ml_g2*( Phi_il(CELL)-Phi_star_il(CELL)) & |
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| 66 | + tau2_g*( p_ik(CELL)-pbot+rho_bot*(Phi_il(CELL)-PHI_BOT(HIDX(CELL))) ) |
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| 67 | END_BLOCK |
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| 68 | BODY('2,llm') |
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| 69 | ! inner interfaces |
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| 70 | ml_g2 = gm2*m_il(CELL) |
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| 71 | B_il(CELL) = A_ik(CELL)+A_ik(DOWN(CELL)) + ml_g2 |
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| 72 | R_il(CELL) = ml_g2*( Phi_il(CELL)-Phi_star_il(CELL)) & |
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| 73 | + tau2_g*(p_ik(CELL)-p_ik(DOWN(CELL))) |
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| 74 | ! consistency check : if Wil=0 and initial state is in hydrostatic balance |
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| 75 | ! then Phi_star_il(CELL) = Phi_il(CELL) - tau^2*g^2 |
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| 76 | ! and residual = tau^2*(ml+(1/g)dl_pi)=0 |
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| 77 | END_BLOCK |
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| 78 | EPILOGUE('llm+1') |
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| 79 | ! top interface l=llm+1 |
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| 80 | ml_g2 = gm2*m_il(CELL) |
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| 81 | B_il(CELL) = A_ik(DOWN(CELL)) + ml_g2 |
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| 82 | R_il(CELL) = ml_g2*( Phi_il(CELL)-Phi_star_il(CELL)) & |
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| 83 | + tau2_g*( ptop-p_ik(DOWN(CELL)) ) |
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| 84 | END_BLOCK |
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| 85 | ! |
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| 86 | ! Forward sweep : |
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| 87 | ! C(0)=0, C(l) = -A(l) / (B(l)+A(l-1)C(l-1)), |
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| 88 | ! 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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| 89 | PROLOGUE(1) |
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| 90 | X_ij = 1./B_il(CELL) |
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| 91 | C_ik(CELL) = -A_ik(CELL) * X_ij |
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| 92 | D_il(CELL) = R_il(CELL) * X_ij |
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| 93 | END_BLOCK |
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| 94 | BODY('2,llm') |
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| 95 | X_ij = 1./( B_il(CELL) + A_ik(DOWN(CELL))*C_ik(DOWN(CELL)) ) |
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| 96 | C_ik(CELL) = -A_ik(CELL) * X_ij |
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| 97 | D_il(CELL) = (R_il(CELL)+A_ik(DOWN(CELL))*D_il(DOWN(CELL))) * X_ij |
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| 98 | END_BLOCK |
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| 99 | EPILOGUE('llm+1') |
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| 100 | X_ij = 1./( B_il(CELL) + A_ik(DOWN(CELL))*C_ik(DOWN(CELL)) ) |
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| 101 | D_il(CELL) = (R_il(CELL)+A_ik(DOWN(CELL))*D_il(DOWN(CELL))) * X_ij |
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| 102 | ! Back substitution : |
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| 103 | ! x(i) = D(i)-C(i)x(i+1), x(llm+1)=0 |
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| 104 | ! + Newton-Raphson update |
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| 105 | ! top interface l=llm+1 |
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| 106 | x_il(CELL) = D_il(CELL) |
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| 107 | Phi_il(CELL) = Phi_il(CELL) - x_il(CELL) |
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| 108 | END_BLOCK |
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| 109 | BODY('llm,1,-1') |
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| 110 | ! Back substitution at lower interfaces |
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| 111 | x_il(CELL) = D_il(CELL) - C_ik(CELL)*x_il(UP(CELL)) |
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| 112 | Phi_il(CELL) = Phi_il(CELL) - x_il(CELL) |
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| 113 | END_BLOCK |
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| 114 | END_BLOCK |
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| 115 | |
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| 116 | IF(debug_hevi_solver) THEN |
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| 117 | PRINT *, '[hevi_solver] A,B', iter, MAXVAL(ABS(A_ik)),MAXVAL(ABS(B_il)) |
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| 118 | PRINT *, '[hevi_solver] C,D', iter, MAXVAL(ABS(C_ik)),MAXVAL(ABS(D_il)) |
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| 119 | DO l=1,llm+1 |
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| 120 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] x_il', iter,l, MAXVAL(ABS(x_il(l,:))) |
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| 121 | END DO |
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| 122 | DO l=1,llm+1 |
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| 123 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] R_il', iter,l, MAXVAL(ABS(R_il(l,:))) |
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| 124 | END DO |
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| 125 | END IF |
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| 126 | |
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| 127 | END DO ! Newton-Raphson |
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| 128 | |
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| 129 | BARRIER |
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| 130 | |
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| 131 | debug_hevi_solver=.FALSE. |
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| 132 | END_BLOCK |
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| 133 | |
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| 134 | #endif END_DYSL |
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| 135 | |
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| 136 | SUBROUTINE compute_NH_geopot_unst(tau, m_ik, m_il, theta, W_il, Phi_il) |
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| 137 | USE ISO_C_BINDING, only : C_DOUBLE, C_FLOAT |
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| 138 | USE disvert_mod, only : g,Treff,cpp,preff,kappa,caldyn_thermo,thermo_theta, & |
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| 139 | thermo_entropy |
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| 140 | USE disvert_mod, ONLY : ptop |
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[939] | 141 | USE data_unstructured_mod, ONLY : enter_trace, exit_trace, & |
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| 142 | id_NH_geopot,debug_hevi_solver_, & |
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| 143 | PHI_BOT,pbot,rho_bot |
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[878] | 144 | FIELD_MASS :: m_ik, theta ! IN*2 |
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| 145 | FIELD_GEOPOT :: m_il, W_il, Phi_il, Phi_star_il ! IN,INOUT*2, LOCAL |
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| 146 | NUM :: tau, gamma, tau2_g, tau2_g2, g2, gm2, vreff, Rd_preff |
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| 147 | INTEGER :: iter |
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| 148 | LOGICAL :: debug_hevi_solver |
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| 149 | DECLARE_INDICES |
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| 150 | NUM :: rho_ij, X_ij, Y_ij, wil, rho_c2_mik, c2_mik, ml_g2 |
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| 151 | #define COLUMN 0 |
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| 152 | #if COLUMN |
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| 153 | NUM1(llm) :: pk, Ak, Ck |
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| 154 | NUM1(llm+1):: Rl, Bl, Dl, xl |
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| 155 | #define p_ik(l,ij) pk(l) |
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| 156 | #define A_ik(l,ij) Ak(l) |
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| 157 | #define C_ik(l,ij) Ck(l) |
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| 158 | #define R_il(l,ij) Rl(l) |
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| 159 | #define B_il(l,ij) Bl(l) |
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| 160 | #define D_il(l,ij) Dl(l) |
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| 161 | #define x_il(l,ij) xl(l) |
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| 162 | #else |
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| 163 | FIELD_MASS :: p_ik, A_ik, C_ik |
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| 164 | FIELD_GEOPOT :: R_il, B_il, D_il, x_il |
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| 165 | #endif |
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| 166 | |
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| 167 | debug_hevi_solver=.FALSE. |
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| 168 | !$OMP MASTER |
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| 169 | debug_hevi_solver = debug_hevi_solver_ |
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| 170 | !$OMP END MASTER |
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| 171 | |
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| 172 | #define PHI_BOT(ij) Phi_bot |
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| 173 | START_TRACE(id_NH_geopot, 7,0,0) |
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| 174 | #include "../kernels_unst/compute_NH_geopot.k90" |
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| 175 | STOP_TRACE |
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| 176 | |
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| 177 | !$OMP MASTER |
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| 178 | debug_hevi_solver_ = debug_hevi_solver |
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| 179 | !$OMP END MASTER |
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| 180 | #undef PHI_BOT |
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| 181 | |
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| 182 | #if COLUMN |
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| 183 | #undef p_ik |
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| 184 | #undef A_ik |
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| 185 | #undef C_ik |
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| 186 | #undef R_il |
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| 187 | #undef B_il |
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| 188 | #undef D_il |
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| 189 | #undef x_il |
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| 190 | #endif |
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| 191 | #undef COLUMN |
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| 192 | END SUBROUTINE compute_NH_geopot_unst |
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| 193 | |
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[859] | 194 | SUBROUTINE compute_NH_geopot(tau, phis, m_ik, m_il, theta, W_il, Phi_il) |
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| 195 | USE disvert_mod |
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| 196 | USE caldyn_vars_mod |
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| 197 | USE omp_para |
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| 198 | REAL(rstd),INTENT(IN) :: tau ! solve Phi-tau*dPhi/dt = Phi_rhs |
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| 199 | REAL(rstd),INTENT(IN) :: phis(iim*jjm) |
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| 200 | REAL(rstd),INTENT(IN) :: m_ik(iim*jjm,llm) |
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| 201 | REAL(rstd),INTENT(IN) :: m_il(iim*jjm,llm+1) |
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| 202 | REAL(rstd),INTENT(IN) :: theta(iim*jjm,llm) |
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| 203 | REAL(rstd),INTENT(IN) :: W_il(iim*jjm,llm+1) ! vertical momentum |
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| 204 | REAL(rstd),INTENT(INOUT) :: Phi_il(iim*jjm,llm+1) ! geopotential |
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| 205 | |
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| 206 | REAL(rstd) :: Phi_star_il(iim*jjm,llm+1) |
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| 207 | REAL(rstd) :: p_ik(iim*jjm,llm) ! pressure |
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| 208 | REAL(rstd) :: R_il(iim*jjm,llm+1) ! rhs of tridiag problem |
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| 209 | REAL(rstd) :: x_il(iim*jjm,llm+1) ! solution of tridiag problem |
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| 210 | REAL(rstd) :: A_ik(iim*jjm,llm) ! off-diagonal coefficients of tridiag problem |
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| 211 | REAL(rstd) :: B_il(iim*jjm,llm+1) ! diagonal coefficients of tridiag problem |
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| 212 | REAL(rstd) :: C_ik(iim*jjm,llm) ! Thomas algorithm |
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| 213 | REAL(rstd) :: D_il(iim*jjm,llm+1) ! Thomas algorithm |
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| 214 | REAL(rstd) :: gamma, rho_ij, X_ij, Y_ij |
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| 215 | REAL(rstd) :: wil, tau2_g, g2, gm2, ml_g2, c2_mik, vreff |
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| 216 | |
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| 217 | INTEGER :: iter, ij, l, ij_omp_begin_ext, ij_omp_end_ext |
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| 218 | |
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| 219 | CALL distrib_level(ij_begin_ext,ij_end_ext, ij_omp_begin_ext,ij_omp_end_ext) |
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| 220 | |
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| 221 | IF(dysl) THEN |
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| 222 | #define PHI_BOT(ij) phis(ij) |
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| 223 | #include "../kernels_hex/compute_NH_geopot.k90" |
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| 224 | #undef PHI_BOT |
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| 225 | ELSE |
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| 226 | ! FIXME : vertical OpenMP parallelism will not work |
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| 227 | |
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| 228 | tau2_g=tau*tau/g |
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| 229 | g2=g*g |
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[1026] | 230 | gm2 = g**(-2) |
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[859] | 231 | gamma = 1./(1.-kappa) |
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| 232 | |
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| 233 | ! compute Phi_star |
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| 234 | DO l=1,llm+1 |
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| 235 | !DIR$ SIMD |
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| 236 | DO ij=ij_begin_ext,ij_end_ext |
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| 237 | Phi_star_il(ij,l) = Phi_il(ij,l) + tau*g2*(W_il(ij,l)/m_il(ij,l)-tau) |
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| 238 | ENDDO |
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| 239 | ENDDO |
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| 240 | |
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| 241 | ! Newton-Raphson iteration : Phi_il contains current guess value |
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| 242 | DO iter=1,5 ! 2 iterations should be enough |
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| 243 | |
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| 244 | ! Compute pressure, A_ik |
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| 245 | DO l=1,llm |
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| 246 | !DIR$ SIMD |
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| 247 | DO ij=ij_begin_ext,ij_end_ext |
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| 248 | rho_ij = (g*m_ik(ij,l))/(Phi_il(ij,l+1)-Phi_il(ij,l)) |
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| 249 | X_ij = (cpp/preff)*kappa*theta(ij,l)*rho_ij |
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| 250 | p_ik(ij,l) = preff*(X_ij**gamma) |
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| 251 | 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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| 252 | A_ik(ij,l) = c2_mik*(tau/g*rho_ij)**2 |
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| 253 | ENDDO |
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| 254 | ENDDO |
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| 255 | |
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| 256 | ! Compute residual, B_il |
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| 257 | ! bottom interface l=1 |
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| 258 | !DIR$ SIMD |
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| 259 | DO ij=ij_begin_ext,ij_end_ext |
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| 260 | ml_g2 = gm2*m_il(ij,1) |
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| 261 | B_il(ij,1) = A_ik(ij,1) + ml_g2 + tau2_g*rho_bot |
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| 262 | R_il(ij,1) = ml_g2*( Phi_il(ij,1)-Phi_star_il(ij,1)) & |
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| 263 | + tau2_g*( p_ik(ij,1)-pbot+rho_bot*(Phi_il(ij,1)-phis(ij)) ) |
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| 264 | ENDDO |
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| 265 | ! inner interfaces |
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| 266 | DO l=2,llm |
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| 267 | !DIR$ SIMD |
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| 268 | DO ij=ij_begin_ext,ij_end_ext |
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| 269 | ml_g2 = gm2*m_il(ij,l) |
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| 270 | B_il(ij,l) = A_ik(ij,l)+A_ik(ij,l-1) + ml_g2 |
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| 271 | R_il(ij,l) = ml_g2*( Phi_il(ij,l)-Phi_star_il(ij,l)) & |
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| 272 | + tau2_g*(p_ik(ij,l)-p_ik(ij,l-1)) |
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| 273 | ! consistency check : if Wil=0 and initial state is in hydrostatic balance |
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| 274 | ! then Phi_star_il(ij,l) = Phi_il(ij,l) - tau^2*g^2 |
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| 275 | ! and residual = tau^2*(ml+(1/g)dl_pi)=0 |
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| 276 | ENDDO |
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| 277 | ENDDO |
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| 278 | ! top interface l=llm+1 |
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| 279 | !DIR$ SIMD |
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| 280 | DO ij=ij_begin_ext,ij_end_ext |
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| 281 | ml_g2 = gm2*m_il(ij,llm+1) |
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| 282 | B_il(ij,llm+1) = A_ik(ij,llm) + ml_g2 |
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| 283 | R_il(ij,llm+1) = ml_g2*( Phi_il(ij,llm+1)-Phi_star_il(ij,llm+1)) & |
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| 284 | + tau2_g*( ptop-p_ik(ij,llm) ) |
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| 285 | ENDDO |
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| 286 | |
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| 287 | ! FIXME later |
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| 288 | ! the lines below modify the tridiag problem |
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| 289 | ! for flat, rigid boundary conditions at top and bottom : |
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| 290 | ! zero out A(1), A(llm), R(1), R(llm+1) |
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| 291 | ! => x(l)=0 at l=1,llm+1 |
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| 292 | DO ij=ij_begin_ext,ij_end_ext |
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| 293 | A_ik(ij,1) = 0. |
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| 294 | A_ik(ij,llm) = 0. |
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| 295 | R_il(ij,1) = 0. |
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| 296 | R_il(ij,llm+1) = 0. |
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| 297 | ENDDO |
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| 298 | |
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| 299 | IF(debug_hevi_solver) THEN ! print Linf(residual) |
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| 300 | PRINT *, '[hevi_solver] R,p', iter, MAXVAL(ABS(R_il)), MAXVAL(p_ik) |
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| 301 | END IF |
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| 302 | |
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| 303 | ! 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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| 304 | ! Forward sweep : |
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| 305 | ! C(0)=0, C(l) = -A(l) / (B(l)+A(l-1)C(l-1)), |
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| 306 | ! 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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| 307 | ! bottom interface l=1 |
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| 308 | !DIR$ SIMD |
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| 309 | DO ij=ij_begin_ext,ij_end_ext |
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| 310 | X_ij = 1./B_il(ij,1) |
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| 311 | C_ik(ij,1) = -A_ik(ij,1) * X_ij |
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| 312 | D_il(ij,1) = R_il(ij,1) * X_ij |
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| 313 | ENDDO |
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| 314 | ! inner interfaces/layers |
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| 315 | DO l=2,llm |
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| 316 | !DIR$ SIMD |
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| 317 | DO ij=ij_begin_ext,ij_end_ext |
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| 318 | X_ij = 1./(B_il(ij,l) + A_ik(ij,l-1)*C_ik(ij,l-1)) |
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| 319 | C_ik(ij,l) = -A_ik(ij,l) * X_ij |
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| 320 | D_il(ij,l) = (R_il(ij,l)+A_ik(ij,l-1)*D_il(ij,l-1)) * X_ij |
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| 321 | ENDDO |
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| 322 | ENDDO |
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| 323 | ! top interface l=llm+1 |
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| 324 | !DIR$ SIMD |
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| 325 | DO ij=ij_begin_ext,ij_end_ext |
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| 326 | X_ij = 1./(B_il(ij,llm+1) + A_ik(ij,llm)*C_ik(ij,llm)) |
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| 327 | D_il(ij,llm+1) = (R_il(ij,llm+1)+A_ik(ij,llm)*D_il(ij,llm)) * X_ij |
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| 328 | ENDDO |
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| 329 | |
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| 330 | ! Back substitution : |
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| 331 | ! x(i) = D(i)-C(i)x(i+1), x(N+1)=0 |
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| 332 | ! + Newton-Raphson update |
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| 333 | x_il=0. ! FIXME |
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| 334 | ! top interface l=llm+1 |
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| 335 | !DIR$ SIMD |
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| 336 | DO ij=ij_begin_ext,ij_end_ext |
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| 337 | x_il(ij,llm+1) = D_il(ij,llm+1) |
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| 338 | Phi_il(ij,llm+1) = Phi_il(ij,llm+1) - x_il(ij,llm+1) |
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| 339 | ENDDO |
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| 340 | ! lower interfaces |
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| 341 | DO l=llm,1,-1 |
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| 342 | !DIR$ SIMD |
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| 343 | DO ij=ij_begin_ext,ij_end_ext |
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| 344 | x_il(ij,l) = D_il(ij,l) - C_ik(ij,l)*x_il(ij,l+1) |
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| 345 | Phi_il(ij,l) = Phi_il(ij,l) - x_il(ij,l) |
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| 346 | ENDDO |
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| 347 | ENDDO |
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| 348 | |
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| 349 | IF(debug_hevi_solver) THEN |
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| 350 | PRINT *, '[hevi_solver] A,B', iter, MAXVAL(ABS(A_ik)),MAXVAL(ABS(B_il)) |
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| 351 | PRINT *, '[hevi_solver] C,D', iter, MAXVAL(ABS(C_ik)),MAXVAL(ABS(D_il)) |
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| 352 | DO l=1,llm+1 |
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| 353 | WRITE(*,'(A,I2.1,I3.2,E9.2)') '[hevi_solver] x', iter,l, MAXVAL(ABS(x_il(:,l))) |
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| 354 | END DO |
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| 355 | END IF |
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| 356 | |
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| 357 | END DO ! Newton-Raphson |
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| 358 | |
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| 359 | END IF ! dysl |
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| 360 | |
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| 361 | END SUBROUTINE compute_NH_geopot |
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| 362 | |
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| 363 | END MODULE compute_NH_geopot_mod |
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