|
| 1 | +/* Copyright 2020 Remi Lehe |
| 2 | + * |
| 3 | + * This file is part of WarpX. |
| 4 | + * |
| 5 | + * License: BSD-3-Clause-LBNL |
| 6 | + */ |
| 7 | + |
| 8 | +#ifndef WARPX_FINITE_DIFFERENCE_ALGORITHM_SPHERICAL_YEE_H_ |
| 9 | +#define WARPX_FINITE_DIFFERENCE_ALGORITHM_SPHERICAL_YEE_H_ |
| 10 | + |
| 11 | +#include "Utils/WarpXConst.H" |
| 12 | + |
| 13 | +#include <AMReX.H> |
| 14 | +#include <AMReX_Array4.H> |
| 15 | +#include <AMReX_Gpu.H> |
| 16 | +#include <AMReX_REAL.H> |
| 17 | + |
| 18 | +#include <array> |
| 19 | +#include <cmath> |
| 20 | + |
| 21 | + |
| 22 | +/** |
| 23 | + * This struct contains only static functions to initialize the stencil coefficients |
| 24 | + * and to compute finite-difference derivatives for the Spherical Yee algorithm. |
| 25 | + */ |
| 26 | +struct SphericalYeeAlgorithm { |
| 27 | + |
| 28 | + static void InitializeStencilCoefficients ( |
| 29 | + std::array<amrex::Real,3>& cell_size, |
| 30 | + amrex::Vector<amrex::Real>& stencil_coefs_r) { |
| 31 | + |
| 32 | + using namespace amrex; |
| 33 | + // Store the inverse cell size along each direction in the coefficients |
| 34 | + stencil_coefs_r.resize(1); |
| 35 | + stencil_coefs_r[0] = 1._rt/cell_size[0]; // 1./dr |
| 36 | + } |
| 37 | + |
| 38 | + /** Compute the maximum, CFL-stable timestep |
| 39 | + * |
| 40 | + * Compute the maximum timestep, for which the scheme remains stable |
| 41 | + * under the Courant-Friedrichs-Levy limit. |
| 42 | + */ |
| 43 | + static amrex::Real ComputeMaxDt (amrex::Real const * const dx) { |
| 44 | + using namespace amrex::literals; |
| 45 | + const amrex::Real alpha = 0.22_rt; // Check this value! |
| 46 | + const amrex::Real delta_t = 1._rt / ( std::sqrt( |
| 47 | + (1._rt + alpha) / (dx[0]*dx[0]) |
| 48 | + ) * PhysConst::c ); |
| 49 | + return delta_t; |
| 50 | + } |
| 51 | + |
| 52 | + /** |
| 53 | + * \brief Returns maximum number of guard cells required by the field-solve |
| 54 | + */ |
| 55 | + static amrex::IntVect GetMaxGuardCell () { |
| 56 | + // The spherical solver requires one guard cell in each dimension |
| 57 | + return amrex::IntVect{AMREX_D_DECL(1,1,1)}; |
| 58 | + } |
| 59 | + |
| 60 | + /** Applies the differential operator `1/r * d(rF)/dr`, |
| 61 | + * where `F` is on a *nodal* grid in `r` |
| 62 | + * and the differential operator is evaluated on a *cell-centered* grid. |
| 63 | + * The input parameter `r` is given at the cell-centered position */ |
| 64 | + AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE |
| 65 | + static amrex::Real UpwardDrr_over_r ( |
| 66 | + amrex::Array4<amrex::Real const> const& F, |
| 67 | + amrex::Real const r, amrex::Real const dr, |
| 68 | + amrex::Real const * const coefs_r, int const n_coefs_r, |
| 69 | + int const i, int const j, int const k, int const comp ) { |
| 70 | + |
| 71 | + using namespace amrex; |
| 72 | + ignore_unused(n_coefs_r); |
| 73 | + |
| 74 | + Real const inv_dr = coefs_r[0]; |
| 75 | + return 1._rt/r * inv_dr*( (r+0.5_rt*dr)*F(i+1,j,k,comp) - (r-0.5_rt*dr)*F(i,j,k,comp) ); |
| 76 | + } |
| 77 | + |
| 78 | + /** Applies the differential operator, the gradient, `1/r**2 * d(r**2F)/dr`, |
| 79 | + * where `F` is on a *cell-centered* grid in `r` |
| 80 | + * and the differential operator is evaluated on a *nodal* grid. |
| 81 | + * The input parameter `r` is given at the cell-centered position */ |
| 82 | + AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE |
| 83 | + static amrex::Real DownwardDrr2_over_r2 ( |
| 84 | + amrex::Array4<amrex::Real const> const& F, |
| 85 | + amrex::Real const r, amrex::Real const dr, |
| 86 | + amrex::Real const * const coefs_r, int const n_coefs_r, |
| 87 | + int const i, int const j, int const k, int const comp ) { |
| 88 | + |
| 89 | + using namespace amrex; |
| 90 | + ignore_unused(n_coefs_r); |
| 91 | + |
| 92 | + Real const inv_dr = coefs_r[0]; |
| 93 | + Real const rph = r + 0.5_rt*dr; |
| 94 | + Real const rmh = r - 0.5_rt*dr; |
| 95 | + return 1._rt/(r*r) * inv_dr*( rph*rph*F(i,j,k,comp) - rmh*rmh*F(i-1,j,k,comp) ); |
| 96 | + } |
| 97 | + |
| 98 | + /** Applies the differential operator `1/r * d(rF)/dr`, |
| 99 | + * where `F` is on a *cell-centered* grid in `r` |
| 100 | + * and the differential operator is evaluated on a *nodal* grid. |
| 101 | + * The input parameter `r` is given at the cell-centered position */ |
| 102 | + AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE |
| 103 | + static amrex::Real DownwardDrr_over_r ( |
| 104 | + amrex::Array4<amrex::Real const> const& F, |
| 105 | + amrex::Real const r, amrex::Real const dr, |
| 106 | + amrex::Real const * const coefs_r, int const n_coefs_r, |
| 107 | + int const i, int const j, int const k, int const comp ) { |
| 108 | + |
| 109 | + using namespace amrex; |
| 110 | + ignore_unused(n_coefs_r); |
| 111 | + |
| 112 | + Real const inv_dr = coefs_r[0]; |
| 113 | + return 1._rt/r * inv_dr*( (r+0.5_rt*dr)*F(i,j,k,comp) - (r-0.5_rt*dr)*F(i-1,j,k,comp) ); |
| 114 | + } |
| 115 | + |
| 116 | + /** |
| 117 | + * Perform derivative along r on a cell-centered grid, from a nodal field `F` */ |
| 118 | + AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE |
| 119 | + static amrex::Real UpwardDr ( |
| 120 | + amrex::Array4<amrex::Real const> const& F, |
| 121 | + amrex::Real const * const coefs_r, int const n_coefs_r, |
| 122 | + int const i, int const j, int const k, int const comp ) { |
| 123 | + |
| 124 | + using namespace amrex; |
| 125 | + ignore_unused(n_coefs_r); |
| 126 | + |
| 127 | + Real const inv_dr = coefs_r[0]; |
| 128 | + return inv_dr*( F(i+1,j,k,comp) - F(i,j,k,comp) ); |
| 129 | + } |
| 130 | + |
| 131 | + /** |
| 132 | + * Perform derivative along r on a nodal grid, from a cell-centered field `F` */ |
| 133 | + AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE |
| 134 | + static amrex::Real DownwardDr ( |
| 135 | + amrex::Array4<amrex::Real const> const& F, |
| 136 | + amrex::Real const * const coefs_r, int const n_coefs_r, |
| 137 | + int const i, int const j, int const k, int const comp ) { |
| 138 | + |
| 139 | + using namespace amrex; |
| 140 | + ignore_unused(n_coefs_r); |
| 141 | + |
| 142 | + Real const inv_dr = coefs_r[0]; |
| 143 | + return inv_dr*( F(i,j,k,comp) - F(i-1,j,k,comp) ); |
| 144 | + } |
| 145 | + |
| 146 | + /** Applies the differential operator `1/r * d(r * dF/dr)/dr`, |
| 147 | + * where `F` is on a *cell-centered* or a nodal grid in `r` |
| 148 | + * The input parameter `r` is given at the cell-centered position */ |
| 149 | + template< typename T_Field> |
| 150 | + AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE |
| 151 | + static amrex::Real Dr_rDr_over_r ( |
| 152 | + T_Field const& F, |
| 153 | + amrex::Real const r, amrex::Real const dr, |
| 154 | + amrex::Real const * const coefs_r, int const /*n_coefs_r*/, |
| 155 | + int const i, int const j, int const k, int const comp ) { |
| 156 | + |
| 157 | + using namespace amrex; |
| 158 | + |
| 159 | + Real const inv_dr2 = coefs_r[0]*coefs_r[0]; |
| 160 | + return 1._rt/r * inv_dr2*( (r+0.5_rt*dr)*(F(i+1,j,k,comp) - F(i,j,k,comp)) |
| 161 | + - (r-0.5_rt*dr)*(F(i,j,k,comp) - F(i-1,j,k,comp)) ); |
| 162 | + } |
| 163 | + |
| 164 | +}; |
| 165 | + |
| 166 | +#endif // WARPX_FINITE_DIFFERENCE_ALGORITHM_SPHERICAL_YEE_H_ |
0 commit comments