1 // Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors. 2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details. 3 // 4 // SPDX-License-Identifier: BSD-2-Clause 5 // 6 // This file is part of CEED: http://github.com/ceed 7 8 /// @file 9 /// Density current initial condition and operator for Navier-Stokes example using PETSc 10 11 // Model from: 12 // Semi-Implicit Formulations of the Navier-Stokes Equations: Application to 13 // Nonhydrostatic Atmospheric Modeling, Giraldo, Restelli, and Lauter (2010). 14 15 #ifndef densitycurrent_h 16 #define densitycurrent_h 17 18 #include <ceed.h> 19 #include <math.h> 20 21 #include "newtonian_state.h" 22 #include "newtonian_types.h" 23 #include "utils.h" 24 25 typedef struct DensityCurrentContext_ *DensityCurrentContext; 26 struct DensityCurrentContext_ { 27 CeedScalar theta0; 28 CeedScalar thetaC; 29 CeedScalar P0; 30 CeedScalar N; 31 CeedScalar rc; 32 CeedScalar center[3]; 33 CeedScalar dc_axis[3]; 34 struct NewtonianIdealGasContext_ newtonian_ctx; 35 }; 36 37 // ***************************************************************************** 38 // This function sets the initial conditions and the boundary conditions 39 // 40 // These initial conditions are given in terms of potential temperature and 41 // Exner pressure and then converted to density and total energy. 42 // Initial momentum density is zero. 43 // 44 // Initial Conditions: 45 // Potential Temperature: 46 // theta = thetabar + delta_theta 47 // thetabar = theta0 exp( N**2 z / g ) 48 // delta_theta = r <= rc : thetaC(1 + cos(pi r/rc)) / 2 49 // r > rc : 0 50 // r = sqrt( (x - xc)**2 + (y - yc)**2 + (z - zc)**2 ) 51 // with (xc,yc,zc) center of domain, rc characteristic radius of thermal bubble 52 // Exner Pressure: 53 // Pi = Pibar + deltaPi 54 // Pibar = 1. + g**2 (exp( - N**2 z / g ) - 1) / (cp theta0 N**2) 55 // deltaPi = 0 (hydrostatic balance) 56 // Velocity/Momentum Density: 57 // Ui = ui = 0 58 // 59 // Conversion to Conserved Variables: 60 // rho = P0 Pi**(cv/Rd) / (Rd theta) 61 // E = rho (cv T + (u u)/2 + g z) 62 // 63 // Boundary Conditions: 64 // Mass Density: 65 // 0.0 flux 66 // Momentum Density: 67 // 0.0 68 // Energy Density: 69 // 0.0 flux 70 // 71 // Constants: 72 // theta0 , Potential temperature constant 73 // thetaC , Potential temperature perturbation 74 // P0 , Pressure at the surface 75 // N , Brunt-Vaisala frequency 76 // cv , Specific heat, constant volume 77 // cp , Specific heat, constant pressure 78 // Rd = cp - cv, Specific heat difference 79 // g , Gravity 80 // rc , Characteristic radius of thermal bubble 81 // center , Location of bubble center 82 // dc_axis , Axis of density current cylindrical anomaly, or {0,0,0} for spherically symmetric 83 // ***************************************************************************** 84 85 // ***************************************************************************** 86 // This helper function provides support for the exact, time-dependent solution 87 // (currently not implemented) and IC formulation for density current 88 // ***************************************************************************** 89 CEED_QFUNCTION_HELPER State Exact_DC(CeedInt dim, CeedScalar time, const CeedScalar X[], CeedInt Nf, void *ctx) { 90 // Context 91 const DensityCurrentContext context = (DensityCurrentContext)ctx; 92 const CeedScalar theta0 = context->theta0; 93 const CeedScalar thetaC = context->thetaC; 94 const CeedScalar P0 = context->P0; 95 const CeedScalar N = context->N; 96 const CeedScalar rc = context->rc; 97 const CeedScalar *center = context->center; 98 const CeedScalar *dc_axis = context->dc_axis; 99 NewtonianIdealGasContext gas = &context->newtonian_ctx; 100 const CeedScalar cp = gas->cp; 101 const CeedScalar cv = gas->cv; 102 const CeedScalar Rd = cp - cv; 103 const CeedScalar *g_vec = gas->g; 104 const CeedScalar g = -g_vec[2]; 105 106 // Setup 107 // -- Coordinates 108 const CeedScalar x = X[0]; 109 const CeedScalar y = X[1]; 110 const CeedScalar z = X[2]; 111 112 // -- Potential temperature, density current 113 CeedScalar rr[3] = {x - center[0], y - center[1], z - center[2]}; 114 // (I - q q^T) r: distance from dc_axis (or from center if dc_axis is the zero vector) 115 for (CeedInt i = 0; i < 3; i++) rr[i] -= dc_axis[i] * Dot3(dc_axis, rr); 116 const CeedScalar r = sqrt(Dot3(rr, rr)); 117 const CeedScalar delta_theta = r <= rc ? thetaC * (1. + cos(M_PI * r / rc)) / 2. : 0.; 118 const CeedScalar theta = theta0 * exp(Square(N) * z / g) + delta_theta; 119 120 // -- Exner pressure, hydrostatic balance 121 const CeedScalar Pi = 1. + Square(g) * (exp(-Square(N) * z / g) - 1.) / (cp * theta0 * Square(N)); 122 123 // Initial Conditions 124 CeedScalar Y[5] = {0.}; 125 Y[0] = P0 * pow(Pi, cp / Rd); 126 Y[1] = 0.0; 127 Y[2] = 0.0; 128 Y[3] = 0.0; 129 Y[4] = Pi * theta; 130 131 return StateFromY(gas, Y, X); 132 } 133 134 // ***************************************************************************** 135 // This QFunction sets the initial conditions for density current 136 // ***************************************************************************** 137 CEED_QFUNCTION(ICsDC)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 138 // Inputs 139 const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 140 141 // Outputs 142 CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 143 144 // Context 145 const DensityCurrentContext context = (DensityCurrentContext)ctx; 146 147 CeedPragmaSIMD 148 // Quadrature Point Loop 149 for (CeedInt i = 0; i < Q; i++) { 150 const CeedScalar x[] = {X[0][i], X[1][i], X[2][i]}; 151 State s = Exact_DC(3, 0., x, 5, ctx); 152 CeedScalar q[5] = {0}; 153 switch (context->newtonian_ctx.state_var) { 154 case STATEVAR_CONSERVATIVE: 155 UnpackState_U(s.U, q); 156 break; 157 case STATEVAR_PRIMITIVE: 158 UnpackState_Y(s.Y, q); 159 break; 160 } 161 162 for (CeedInt j = 0; j < 5; j++) q0[j][i] = q[j]; 163 164 } // End of Quadrature Point Loop 165 166 return 0; 167 } 168 169 // ***************************************************************************** 170 171 #endif // densitycurrent_h 172