1 // Copyright (c) 2017-2024, 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 #include <ceed/types.h> 15 #ifndef CEED_RUNNING_JIT_PASS 16 #include <math.h> 17 #endif 18 19 #include "newtonian_state.h" 20 #include "newtonian_types.h" 21 #include "utils.h" 22 23 typedef struct DensityCurrentContext_ *DensityCurrentContext; 24 struct DensityCurrentContext_ { 25 CeedScalar theta0; 26 CeedScalar thetaC; 27 CeedScalar P0; 28 CeedScalar N; 29 CeedScalar rc; 30 CeedScalar center[3]; 31 CeedScalar dc_axis[3]; 32 struct NewtonianIdealGasContext_ newtonian_ctx; 33 }; 34 35 // ***************************************************************************** 36 // This function sets the initial conditions and the boundary conditions 37 // 38 // These initial conditions are given in terms of potential temperature and Exner pressure and then converted to density and total energy. 39 // Initial momentum density is zero. 40 // 41 // Initial Conditions: 42 // Potential Temperature: 43 // theta = thetabar + delta_theta 44 // thetabar = theta0 exp( N**2 z / g ) 45 // delta_theta = r <= rc : thetaC(1 + cos(pi r/rc)) / 2 46 // r > rc : 0 47 // r = sqrt( (x - xc)**2 + (y - yc)**2 + (z - zc)**2 ) 48 // with (xc,yc,zc) center of domain, rc characteristic radius of thermal bubble 49 // Exner Pressure: 50 // Pi = Pibar + deltaPi 51 // Pibar = 1. + g**2 (exp( - N**2 z / g ) - 1) / (cp theta0 N**2) 52 // deltaPi = 0 (hydrostatic balance) 53 // Velocity/Momentum Density: 54 // Ui = ui = 0 55 // 56 // Conversion to Conserved Variables: 57 // rho = P0 Pi**(cv/Rd) / (Rd theta) 58 // E = rho (cv T + (u u)/2 + g z) 59 // 60 // Boundary Conditions: 61 // Mass Density: 62 // 0.0 flux 63 // Momentum Density: 64 // 0.0 65 // Energy Density: 66 // 0.0 flux 67 // 68 // Constants: 69 // theta0 , Potential temperature constant 70 // thetaC , Potential temperature perturbation 71 // P0 , Pressure at the surface 72 // N , Brunt-Vaisala frequency 73 // cv , Specific heat, constant volume 74 // cp , Specific heat, constant pressure 75 // Rd = cp - cv, Specific heat difference 76 // g , Gravity 77 // rc , Characteristic radius of thermal bubble 78 // center , Location of bubble center 79 // dc_axis , Axis of density current cylindrical anomaly, or {0,0,0} for spherically symmetric 80 // ***************************************************************************** 81 82 // ***************************************************************************** 83 // This helper function provides support for the exact, time-dependent solution 84 // (currently not implemented) and IC formulation for density current 85 // ***************************************************************************** 86 CEED_QFUNCTION_HELPER State Exact_DC(CeedInt dim, CeedScalar time, const CeedScalar X[], CeedInt Nf, void *ctx) { 87 // Context 88 const DensityCurrentContext context = (DensityCurrentContext)ctx; 89 const CeedScalar theta0 = context->theta0; 90 const CeedScalar thetaC = context->thetaC; 91 const CeedScalar P0 = context->P0; 92 const CeedScalar N = context->N; 93 const CeedScalar rc = context->rc; 94 const CeedScalar *center = context->center; 95 const CeedScalar *dc_axis = context->dc_axis; 96 NewtonianIdealGasContext gas = &context->newtonian_ctx; 97 const CeedScalar cp = gas->cp; 98 const CeedScalar cv = gas->cv; 99 const CeedScalar Rd = cp - cv; 100 const CeedScalar *g_vec = gas->g; 101 const CeedScalar g = -g_vec[2]; 102 103 // Setup 104 // -- Coordinates 105 const CeedScalar x = X[0]; 106 const CeedScalar y = X[1]; 107 const CeedScalar z = X[2]; 108 109 // -- Potential temperature, density current 110 CeedScalar rr[3] = {x - center[0], y - center[1], z - center[2]}; 111 // (I - q q^T) r: distance from dc_axis (or from center if dc_axis is the zero vector) 112 for (CeedInt i = 0; i < 3; i++) rr[i] -= dc_axis[i] * Dot3(dc_axis, rr); 113 const CeedScalar r = sqrt(Dot3(rr, rr)); 114 const CeedScalar delta_theta = r <= rc ? thetaC * (1. + cos(M_PI * r / rc)) / 2. : 0.; 115 const CeedScalar theta = theta0 * exp(Square(N) * z / g) + delta_theta; 116 117 // -- Exner pressure, hydrostatic balance 118 const CeedScalar Pi = 1. + Square(g) * (exp(-Square(N) * z / g) - 1.) / (cp * theta0 * Square(N)); 119 120 // Initial Conditions 121 CeedScalar Y[5] = {0.}; 122 Y[0] = P0 * pow(Pi, cp / Rd); 123 Y[1] = 0.0; 124 Y[2] = 0.0; 125 Y[3] = 0.0; 126 Y[4] = Pi * theta; 127 128 return StateFromY(gas, Y); 129 } 130 131 // ***************************************************************************** 132 // This QFunction sets the initial conditions for density current 133 // ***************************************************************************** 134 CEED_QFUNCTION(ICsDC)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 135 const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 136 CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 137 138 const DensityCurrentContext context = (DensityCurrentContext)ctx; 139 const NewtonianIdealGasContext gas = &context->newtonian_ctx; 140 141 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 142 const CeedScalar x[] = {X[0][i], X[1][i], X[2][i]}; 143 State s = Exact_DC(3, 0., x, 5, ctx); 144 CeedScalar q[5] = {0}; 145 StateToQ(gas, s, q, gas->state_var); 146 for (CeedInt j = 0; j < 5; j++) q0[j][i] = q[j]; 147 } 148 return 0; 149 } 150