1 | {% macro compute_p_and_Aik() %} |
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2 | {% set p_and_c2_from_theta=caller %} |
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3 | SEQUENCE_C1 |
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4 | BODY('1,llm') |
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5 | rho_ij = (g*m_ik(CELL))/(Phi_il(UP(CELL))-Phi_il(CELL)) |
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6 | {{ p_and_c2_from_theta() }} |
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7 | A_ik(CELL) = c2_mik*(tau/g*rho_ij)**2 |
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8 | END_BLOCK |
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9 | END_BLOCK |
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10 | {%- endmacro %} |
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11 | |
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12 | KERNEL(compute_NH_geopot) |
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13 | tau2_g=tau*tau/g |
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14 | g2=g*g |
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15 | gm2 = 1./g2 |
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16 | vreff = Treff*cpp/preff*kappa |
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17 | gamma = 1./(1.-kappa) |
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18 | |
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19 | BARRIER |
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20 | |
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21 | ! compute Phi_star |
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22 | SEQUENCE_C1 |
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23 | BODY('1,llm+1') |
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24 | Phi_star_il(CELL) = Phi_il(CELL) + tau*g2*(W_il(CELL)/m_il(CELL)-tau) |
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25 | END_BLOCK |
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26 | END_BLOCK |
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27 | |
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28 | ! Newton-Raphson iteration : Phi_il contains current guess value |
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29 | DO iter=1,2 ! 2 iterations should be enough |
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30 | ! Compute pressure, A_ik |
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31 | SELECT CASE(caldyn_thermo) |
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32 | CASE(thermo_theta) |
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33 | {% call() compute_p_and_Aik() %} |
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34 | X_ij = (cpp/preff)*kappa*theta(CELL)*rho_ij |
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35 | p_ik(CELL) = preff*(X_ij**gamma) |
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36 | c2_mik = gamma*p_ik(CELL)/(rho_ij*m_ik(CELL)) ! c^2 = gamma*R*T = gamma*p/rho |
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37 | {% endcall %} |
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38 | CASE(thermo_entropy) |
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39 | {% call() compute_p_and_Aik() %} |
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40 | X_ij = log(vreff*rho_ij) + theta(CELL)/cpp |
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41 | p_ik(CELL) = preff*exp(X_ij*gamma) |
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42 | c2_mik = gamma*p_ik(CELL)/(rho_ij*m_ik(CELL)) ! c^2 = gamma*R*T = gamma*p/rho |
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43 | {% endcall %} |
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44 | CASE DEFAULT |
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45 | PRINT *, 'caldyn_thermo not supported by compute_NH_geopot', caldyn_thermo |
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46 | STOP |
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47 | END SELECT |
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48 | |
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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 | |
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52 | SEQUENCE_C1 |
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53 | ! Compute residual R_il and B_il |
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54 | PROLOGUE(1) |
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55 | ! bottom interface l=1 |
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56 | ml_g2 = gm2*m_il(CELL) |
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57 | B_il(CELL) = A_ik(CELL) + ml_g2 + tau2_g*rho_bot |
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58 | R_il(CELL) = ml_g2*( Phi_il(CELL)-Phi_star_il(CELL)) & |
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59 | + tau2_g*( p_ik(CELL)-pbot+rho_bot*(Phi_il(CELL)-PHI_BOT(HIDX(CELL))) ) |
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60 | END_BLOCK |
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61 | BODY('2,llm') |
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62 | ! inner interfaces |
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63 | ml_g2 = gm2*m_il(CELL) |
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64 | B_il(CELL) = A_ik(CELL)+A_ik(DOWN(CELL)) + ml_g2 |
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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)-p_ik(DOWN(CELL))) |
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67 | ! consistency check : if Wil=0 and initial state is in hydrostatic balance |
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68 | ! then Phi_star_il(CELL) = Phi_il(CELL) - tau^2*g^2 |
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69 | ! and residual = tau^2*(ml+(1/g)dl_pi)=0 |
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70 | END_BLOCK |
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71 | EPILOGUE('llm+1') |
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72 | ! top interface l=llm+1 |
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73 | ml_g2 = gm2*m_il(CELL) |
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74 | B_il(CELL) = A_ik(DOWN(CELL)) + ml_g2 |
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75 | R_il(CELL) = ml_g2*( Phi_il(CELL)-Phi_star_il(CELL)) & |
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76 | + tau2_g*( ptop-p_ik(DOWN(CELL)) ) |
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77 | END_BLOCK |
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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 | PROLOGUE(1) |
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83 | X_ij = 1./B_il(CELL) |
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84 | C_ik(CELL) = -A_ik(CELL) * X_ij |
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85 | D_il(CELL) = R_il(CELL) * X_ij |
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86 | END_BLOCK |
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87 | BODY('2,llm') |
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88 | X_ij = 1./( B_il(CELL) + A_ik(DOWN(CELL))*C_ik(DOWN(CELL)) ) |
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89 | C_ik(CELL) = -A_ik(CELL) * X_ij |
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90 | D_il(CELL) = (R_il(CELL)+A_ik(DOWN(CELL))*D_il(DOWN(CELL))) * X_ij |
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91 | END_BLOCK |
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92 | EPILOGUE('llm+1') |
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93 | X_ij = 1./( B_il(CELL) + A_ik(DOWN(CELL))*C_ik(DOWN(CELL)) ) |
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94 | D_il(CELL) = (R_il(CELL)+A_ik(DOWN(CELL))*D_il(DOWN(CELL))) * X_ij |
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95 | ! Back substitution : |
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96 | ! x(i) = D(i)-C(i)x(i+1), x(llm+1)=0 |
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97 | ! + Newton-Raphson update |
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98 | ! top interface l=llm+1 |
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99 | x_il(CELL) = D_il(CELL) |
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100 | Phi_il(CELL) = Phi_il(CELL) - x_il(CELL) |
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101 | END_BLOCK |
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102 | BODY('llm,1,-1') |
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103 | ! Back substitution at lower interfaces |
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104 | x_il(CELL) = D_il(CELL) - C_ik(CELL)*x_il(UP(CELL)) |
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105 | Phi_il(CELL) = Phi_il(CELL) - x_il(CELL) |
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106 | END_BLOCK |
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107 | END_BLOCK |
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108 | |
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109 | IF(debug_hevi_solver) THEN |
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110 | PRINT *, '[hevi_solver] A,B', iter, MAXVAL(ABS(A_ik)),MAXVAL(ABS(B_il)) |
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111 | PRINT *, '[hevi_solver] C,D', iter, MAXVAL(ABS(C_ik)),MAXVAL(ABS(D_il)) |
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112 | DO l=1,llm+1 |
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113 | WRITE(*,'(A,I2.1,I3.2,E9.2)'), '[hevi_solver] x_il', iter,l, MAXVAL(ABS(x_il(l,:))) |
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114 | END DO |
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115 | DO l=1,llm+1 |
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116 | WRITE(*,'(A,I2.1,I3.2,E9.2)'), '[hevi_solver] R_il', iter,l, MAXVAL(ABS(R_il(l,:))) |
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117 | END DO |
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118 | END IF |
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119 | |
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120 | END DO ! Newton-Raphson |
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121 | |
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122 | BARRIER |
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123 | |
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124 | debug_hevi_solver=.FALSE. |
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125 | END_BLOCK |
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126 | |
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127 | KERNEL(caldyn_mil) |
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128 | FORALL_CELLS_EXT('1', 'llm+1') |
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129 | ON_PRIMAL |
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130 | CST_IF(IS_BOTTOM_LEVEL, m_il(CELL) = .5*rhodz(CELL) ) |
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131 | CST_IF(IS_INNER_INTERFACE, m_il(CELL) = .5*(rhodz(CELL)+rhodz(DOWN(CELL))) ) |
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132 | CST_IF(IS_TOP_INTERFACE, m_il(CELL) = .5*rhodz(DOWN(CELL)) ) |
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133 | END_BLOCK |
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134 | END_BLOCK |
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135 | END_BLOCK |
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136 | |
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137 | KERNEL(caldyn_solver) |
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138 | ! |
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139 | ! Compute pressure (pres) and Exner function (pk) |
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140 | ! kappa = R/Cp |
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141 | ! 1-kappa = Cv/Cp |
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142 | ! Cp/Cv = 1/(1-kappa) |
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143 | gamma = 1./(1.-kappa) |
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144 | vreff = Rd*Treff/preff ! reference specific volume |
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145 | Cvd = 1./(cpp-Rd) |
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146 | Rd_preff = kappa*cpp/preff |
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147 | FORALL_CELLS_EXT() |
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148 | SELECT CASE(caldyn_thermo) |
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149 | CASE(thermo_theta) |
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150 | ON_PRIMAL |
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151 | rho_ij = 1./(geopot(UP(CELL))-geopot(CELL)) |
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152 | rho_ij = rho_ij*g*rhodz(CELL) |
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153 | X_ij = Rd_preff*theta(CELL,1)*rho_ij |
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154 | ! kappa.theta.rho = p/exner |
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155 | ! => X = (p/p0)/(exner/Cp) |
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156 | ! = (p/p0)^(1-kappa) |
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157 | pres(CELL) = preff*(X_ij**gamma) ! pressure |
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158 | ! Compute Exner function (needed by compute_caldyn_fast) |
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159 | ! other formulae possible if exponentiation is slow |
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160 | pk(CELL) = cpp*((pres(CELL)/preff)**kappa) ! Exner |
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161 | END_BLOCK |
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162 | CASE(thermo_entropy) |
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163 | ON_PRIMAL |
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164 | rho_ij = 1./(geopot(UP(CELL))-geopot(CELL)) |
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165 | rho_ij = rho_ij*g*rhodz(CELL) |
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166 | T_ij = Treff*exp( (theta(CELL,1)+Rd*log(vreff*rho_ij))*Cvd ) |
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167 | pres(CELL) = rho_ij*Rd*T_ij |
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168 | pk(CELL) = T_ij |
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169 | END_BLOCK |
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170 | CASE DEFAULT |
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171 | STOP |
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172 | END SELECT |
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173 | END_BLOCK |
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174 | |
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175 | ! We need a barrier here because we compute pres above and do a vertical difference below |
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176 | BARRIER |
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177 | |
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178 | FORALL_CELLS_EXT('1', 'llm+1') |
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179 | ON_PRIMAL |
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180 | CST_IFTHEN(IS_BOTTOM_LEVEL) |
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181 | ! Lower BC |
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182 | dW(CELL) = (1./g)*(pbot-rho_bot*(geopot(CELL)-PHI_BOT(HIDX(CELL)))-pres(CELL)) - m_il(CELL) |
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183 | CST_ELSEIF(IS_TOP_INTERFACE) |
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184 | ! Top BC |
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185 | dW(CELL) = (1./g)*(pres(DOWN(CELL))-ptop) - m_il(CELL) |
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186 | CST_ELSE |
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187 | dW(CELL) = (1./g)*(pres(DOWN(CELL))-pres(CELL)) - m_il(CELL) |
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188 | CST_ENDIF |
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189 | W(CELL) = W(CELL)+tau*dW(CELL) ! update W |
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190 | dPhi(CELL) = g*g*W(CELL)/m_il(CELL) |
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191 | END_BLOCK |
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192 | END_BLOCK |
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193 | |
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194 | ! We need a barrier here because we update W above and do a vertical average below |
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195 | BARRIER |
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196 | |
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197 | FORALL_CELLS_EXT() |
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198 | ON_PRIMAL |
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199 | ! compute du = -0.5*g^2.grad(w^2) |
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200 | berni(CELL) = (-.25*g*g)*((W(CELL)/m_il(CELL))**2 + (W(UP(CELL))/m_il(UP(CELL)))**2 ) |
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201 | END_BLOCK |
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202 | END_BLOCK |
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203 | FORALL_CELLS_EXT() |
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204 | ON_EDGES |
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205 | du(EDGE) = SIGN*(berni(CELL1)-berni(CELL2)) |
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206 | END_BLOCK |
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207 | END_BLOCK |
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208 | END_BLOCK |
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209 | |
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210 | KERNEL(caldyn_vert_NH) |
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211 | FORALL_CELLS_EXT() |
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212 | ON_PRIMAL |
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213 | CST_IF(IS_BOTTOM_LEVEL, w_ij = ( W(CELL)+.5*W(UP(CELL)) )/mass(CELL) ) |
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214 | CST_IF(IS_INNER_LAYER , w_ij = .5*( W(CELL)+W(UP(CELL)) )/mass(CELL) ) |
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215 | CST_IF(IS_TOP_LAYER, w_ij = ( .5*W(CELL)+W(UP(CELL)) )/mass(CELL) ) |
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216 | wflux_ij = .5*(wflux(CELL)+wflux(UP(CELL))) |
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217 | W_etadot(CELL) = wflux_ij*w_ij |
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218 | eta_dot(CELL) = wflux_ij / mass(CELL) |
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219 | wcov(CELL) = w_ij*(geopot(UP(CELL))-geopot(CELL)) |
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220 | END_BLOCK |
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221 | END_BLOCK |
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222 | ! add NH term to du |
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223 | FORALL_CELLS() |
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224 | ON_EDGES |
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225 | du(EDGE) = du(EDGE) - .5*(wcov(CELL1)+wcov(CELL2))*SIGN*(eta_dot(CELL2)-eta_dot(CELL1)) |
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226 | END_BLOCK |
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227 | END_BLOCK |
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228 | ! add NH terms to dW, dPhi |
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229 | ! FIXME : TODO top and bottom |
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230 | FORALL_CELLS('2','llm') |
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231 | ON_PRIMAL |
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232 | dPhi(CELL)=dPhi(CELL)-wflux(CELL)*(geopot(UP(CELL))-geopot(DOWN(CELL)))/(mass(DOWN(CELL))+mass(CELL)) |
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233 | END_BLOCK |
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234 | END_BLOCK |
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235 | |
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236 | ! We need a barrier here because we compute W_etadot above and do a vertical difference below |
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237 | BARRIER |
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238 | |
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239 | FORALL_CELLS('1','llm+1') |
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240 | ON_PRIMAL |
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241 | CST_IFTHEN(IS_BOTTOM_LEVEL) |
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242 | dW(CELL) = dW(CELL) - W_etadot(CELL) |
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243 | CST_ELSEIF(IS_TOP_INTERFACE) |
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244 | dW(CELL) = dW(CELL) + W_etadot(DOWN(CELL)) |
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245 | CST_ELSE |
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246 | dW(CELL) = dW(CELL) + W_etadot(DOWN(CELL)) - W_etadot(CELL) |
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247 | CST_ENDIF |
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248 | END_BLOCK |
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249 | END_BLOCK |
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250 | END_BLOCK |
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251 | |
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252 | KERNEL(caldyn_slow_NH) |
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253 | FORALL_CELLS_EXT('1', 'llm+1') |
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254 | ON_PRIMAL |
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255 | CST_IF(IS_INNER_INTERFACE, w_il(CELL) = 2.*W(CELL)/(rhodz(KDOWN(CELL))+rhodz(KUP(CELL))) ) |
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256 | CST_IF(IS_BOTTOM_LEVEL, w_il(CELL) = 2.*W(CELL)/rhodz(KUP(CELL)) ) |
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257 | CST_IF(IS_TOP_INTERFACE, w_il(CELL) = 2.*W(CELL)/rhodz(KDOWN(CELL)) ) |
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258 | END_BLOCK |
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259 | END_BLOCK |
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260 | FORALL_CELLS_EXT('1', 'llm+1') |
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261 | ON_EDGES |
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262 | ! compute DePhi, v_el, G_el, F_el |
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263 | ! v_el, W2_el and therefore G_el incorporate metric factor le_de |
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264 | ! while DePhil, W_el and F_el do not |
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265 | W_el = .5*( W(CELL2)+W(CELL1) ) |
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266 | DePhil(EDGE) = SIGN*(Phi(CELL2)-Phi(CELL1)) |
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267 | F_el(EDGE) = DePhil(EDGE)*W_el |
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268 | W2_el = .5*LE_DE * ( W(CELL1)*w_il(CELL1) + W(CELL2)*w_il(CELL2) ) |
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269 | v_el(EDGE) = .5*LE_DE*(u(KUP(EDGE))+u(KDOWN(EDGE))) ! checked |
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270 | G_el(EDGE) = v_el(EDGE)*W_el - DePhil(EDGE)*W2_el |
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271 | END_BLOCK |
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272 | END_BLOCK |
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273 | |
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274 | FORALL_CELLS_EXT('1', 'llm+1') |
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275 | ! compute GradPhi2, dPhi, dW |
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276 | ON_PRIMAL |
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277 | gPhi2=0. |
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278 | dP=0. |
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279 | divG=0 |
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280 | FORALL_EDGES |
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281 | gPhi2 = gPhi2 + LE_DE*DePhil(EDGE)**2 |
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282 | dP = dP + LE_DE*DePhil(EDGE)*v_el(EDGE) |
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283 | divG = divG + SIGN*G_el(EDGE) ! -div(G_el), G_el already has le_de |
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284 | END_BLOCK |
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285 | gradPhi2(CELL) = 1./(2.*AI) * gPhi2 |
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286 | dPhi(CELL) = gradPhi2(CELL)*w_il(CELL) - 1./(2.*AI)*dP |
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287 | dW(CELL) = (-1./AI)*divG |
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288 | END_BLOCK |
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289 | END_BLOCK |
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290 | |
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291 | ! We need a barrier here because we compute gradPhi2, F_el and w_il above and do a vertical average below |
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292 | BARRIER |
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293 | |
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294 | FORALL_CELLS_EXT() |
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295 | ! Compute berni at scalar points |
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296 | ON_PRIMAL |
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297 | u2=0. |
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298 | FORALL_EDGES |
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299 | u2 = u2 + LE_DE*u(EDGE)**2 |
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300 | END_BLOCK |
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301 | berni(CELL) = 1./(4.*AI) * u2 - .25*( gradPhi2(CELL)*w_il(CELL)**2 + gradPhi2(UP(CELL))*w_il(UP(CELL))**2 ) |
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302 | END_BLOCK |
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303 | END_BLOCK |
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304 | |
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305 | FORALL_CELLS_EXT() |
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306 | ON_EDGES |
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307 | ! Compute mass flux and grad(berni) |
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308 | uu = .5*(rhodz(CELL1)+rhodz(CELL2))*u(EDGE) - .5*( F_el(EDGE)+F_el(UP(EDGE)) ) |
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309 | hflux(EDGE) = LE_DE*uu |
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310 | du(EDGE) = SIGN*(berni(CELL1)-berni(CELL2)) |
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311 | END_BLOCK |
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312 | END_BLOCK |
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313 | |
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314 | END_BLOCK |
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