1 // SPDX-FileCopyrightText: Copyright (c) 2017-2024, HONEE contributors. 2 // SPDX-License-Identifier: Apache-2.0 OR BSD-2-Clause 3 4 /// @file 5 /// Density current initial condition and operator for Navier-Stokes example using PETSc 6 7 // Model from: 8 // Semi-Implicit Formulations of the Navier-Stokes Equations: Application to 9 // Nonhydrostatic Atmospheric Modeling, Giraldo, Restelli, and Lauter (2010). 10 #include <ceed/types.h> 11 12 #include "newtonian_state.h" 13 #include "newtonian_types.h" 14 #include "utils.h" 15 16 typedef struct DensityCurrentContext_ *DensityCurrentContext; 17 struct DensityCurrentContext_ { 18 CeedScalar theta0; 19 CeedScalar thetaC; 20 CeedScalar P0; 21 CeedScalar N; 22 CeedScalar rc; 23 CeedScalar center[3]; 24 CeedScalar dc_axis[3]; 25 struct NewtonianIdealGasContext_ newtonian_ctx; 26 }; 27 28 // ***************************************************************************** 29 // This function sets the initial conditions and the boundary conditions 30 // 31 // These initial conditions are given in terms of potential temperature and Exner pressure and then converted to density and total energy. 32 // Initial momentum density is zero. 33 // 34 // Initial Conditions: 35 // Potential Temperature: 36 // theta = thetabar + delta_theta 37 // thetabar = theta0 exp( N**2 z / g ) 38 // delta_theta = r <= rc : thetaC(1 + cos(pi r/rc)) / 2 39 // r > rc : 0 40 // r = sqrt( (x - xc)**2 + (y - yc)**2 + (z - zc)**2 ) 41 // with (xc,yc,zc) center of domain, rc characteristic radius of thermal bubble 42 // Exner Pressure: 43 // Pi = Pibar + deltaPi 44 // Pibar = 1. + g**2 (exp( - N**2 z / g ) - 1) / (cp theta0 N**2) 45 // deltaPi = 0 (hydrostatic balance) 46 // Velocity/Momentum Density: 47 // Ui = ui = 0 48 // 49 // Conversion to Conserved Variables: 50 // rho = P0 Pi**(cv/Rd) / (Rd theta) 51 // E = rho (cv T + (u u)/2 + g z) 52 // 53 // Boundary Conditions: 54 // Mass Density: 55 // 0.0 flux 56 // Momentum Density: 57 // 0.0 58 // Energy Density: 59 // 0.0 flux 60 // 61 // Constants: 62 // theta0 , Potential temperature constant 63 // thetaC , Potential temperature perturbation 64 // P0 , Pressure at the surface 65 // N , Brunt-Vaisala frequency 66 // cv , Specific heat, constant volume 67 // cp , Specific heat, constant pressure 68 // Rd = cp - cv, Specific heat difference 69 // g , Gravity 70 // rc , Characteristic radius of thermal bubble 71 // center , Location of bubble center 72 // dc_axis , Axis of density current cylindrical anomaly, or {0,0,0} for spherically symmetric 73 // ***************************************************************************** 74 75 // ***************************************************************************** 76 // This helper function provides support for the exact, time-dependent solution 77 // (currently not implemented) and IC formulation for density current 78 // ***************************************************************************** 79 CEED_QFUNCTION_HELPER State Exact_DC(CeedInt dim, CeedScalar time, const CeedScalar X[], CeedInt Nf, void *ctx) { 80 // Context 81 const DensityCurrentContext context = (DensityCurrentContext)ctx; 82 const CeedScalar theta0 = context->theta0; 83 const CeedScalar thetaC = context->thetaC; 84 const CeedScalar P0 = context->P0; 85 const CeedScalar N = context->N; 86 const CeedScalar rc = context->rc; 87 const CeedScalar *center = context->center; 88 const CeedScalar *dc_axis = context->dc_axis; 89 NewtonianIdealGasContext gas = &context->newtonian_ctx; 90 const CeedScalar cp = gas->cp; 91 const CeedScalar cv = gas->cv; 92 const CeedScalar Rd = cp - cv; 93 const CeedScalar *g_vec = gas->g; 94 const CeedScalar g = -g_vec[2]; 95 96 // Setup 97 // -- Coordinates 98 const CeedScalar x = X[0]; 99 const CeedScalar y = X[1]; 100 const CeedScalar z = X[2]; 101 102 // -- Potential temperature, density current 103 CeedScalar rr[3] = {x - center[0], y - center[1], z - center[2]}; 104 // (I - q q^T) r: distance from dc_axis (or from center if dc_axis is the zero vector) 105 for (CeedInt i = 0; i < 3; i++) rr[i] -= dc_axis[i] * Dot3(dc_axis, rr); 106 const CeedScalar r = Norm3(rr); 107 const CeedScalar delta_theta = r <= rc ? thetaC * (1. + cos(M_PI * r / rc)) / 2. : 0.; 108 const CeedScalar theta = theta0 * exp(Square(N) * z / g) + delta_theta; 109 110 // -- Exner pressure, hydrostatic balance 111 const CeedScalar Pi = 1. + Square(g) * (exp(-Square(N) * z / g) - 1.) / (cp * theta0 * Square(N)); 112 113 // Initial Conditions 114 CeedScalar Y[5] = {0.}; 115 Y[0] = P0 * pow(Pi, cp / Rd); 116 Y[1] = 0.0; 117 Y[2] = 0.0; 118 Y[3] = 0.0; 119 Y[4] = Pi * theta; 120 121 return StateFromY(gas, Y); 122 } 123 124 // ***************************************************************************** 125 // This QFunction sets the initial conditions for density current 126 // ***************************************************************************** 127 CEED_QFUNCTION(ICsDC)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 128 const CeedScalar(*X)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 129 CeedScalar(*q0)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 130 131 const DensityCurrentContext context = (DensityCurrentContext)ctx; 132 const NewtonianIdealGasContext gas = &context->newtonian_ctx; 133 134 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 135 const CeedScalar x[] = {X[0][i], X[1][i], X[2][i]}; 136 State s = Exact_DC(3, 0., x, 5, ctx); 137 CeedScalar q[5]; 138 StateToQ(gas, s, q, gas->state_var); 139 for (CeedInt j = 0; j < 5; j++) q0[j][i] = q[j]; 140 } 141 return 0; 142 } 143