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/* Copyright 2020 Remi Lehe
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#ifndef WARPX_FINITE_DIFFERENCE_ALGORITHM_CARTESIAN_CKC_H_
#define WARPX_FINITE_DIFFERENCE_ALGORITHM_CARTESIAN_CKC_H_
#include "Utils/WarpXConst.H"
#include <AMReX_REAL.H>
#include <AMReX_Array4.H>
#include <AMReX_Gpu.H>
#include <algorithm>
#include <array>
/**
* This struct contains only static functions to initialize the stencil coefficients
* and to compute finite-difference derivatives for the Cartesian CKC algorithm.
*/
struct CartesianCKCAlgorithm {
static void InitializeStencilCoefficients (
std::array<amrex::Real,3>& cell_size,
amrex::Gpu::ManagedVector<amrex::Real>& stencil_coefs_x,
amrex::Gpu::ManagedVector<amrex::Real>& stencil_coefs_y,
amrex::Gpu::ManagedVector<amrex::Real>& stencil_coefs_z ) {
using namespace amrex;
// Compute Cole-Karkkainen-Cowan coefficients according
// to Cowan - PRST-AB 16, 041303 (2013)
Real const inv_dx = 1._rt/cell_size[0];
Real const inv_dy = 1._rt/cell_size[1];
Real const inv_dz = 1._rt/cell_size[2];
#if defined WARPX_DIM_3D
Real const delta = std::max( { inv_dx,inv_dy,inv_dz } );
Real const rx = (inv_dx/delta)*(inv_dx/delta);
Real const ry = (inv_dy/delta)*(inv_dy/delta);
Real const rz = (inv_dz/delta)*(inv_dz/delta);
Real const beta = 0.125_rt*(1._rt - rx*ry*rz/(ry*rz + rz*rx + rx*ry));
Real const betaxy = ry*beta*inv_dx;
Real const betaxz = rz*beta*inv_dx;
Real const betayx = rx*beta*inv_dy;
Real const betayz = rz*beta*inv_dy;
Real const betazx = rx*beta*inv_dz;
Real const betazy = ry*beta*inv_dz;
Real const inv_r_fac = (1._rt/(ry*rz + rz*rx + rx*ry));
Real const gammax = ry*rz*(0.0625_rt - 0.125_rt*ry*rz*inv_r_fac);
Real const gammay = rx*rz*(0.0625_rt - 0.125_rt*rx*rz*inv_r_fac);
Real const gammaz = rx*ry*(0.0625_rt - 0.125_rt*rx*ry*inv_r_fac);
Real const alphax = (1._rt - 2._rt*ry*beta - 2._rt*rz*beta - 4._rt*gammax)*inv_dx;
Real const alphay = (1._rt - 2._rt*rx*beta - 2._rt*rz*beta - 4._rt*gammay)*inv_dy;
Real const alphaz = (1._rt - 2._rt*rx*beta - 2._rt*ry*beta - 4._rt*gammaz)*inv_dz;
#elif defined WARPX_DIM_XZ
Real const delta = std::max(inv_dx,inv_dz);
Real const rx = (inv_dx/delta)*(inv_dx/delta);
Real const rz = (inv_dz/delta)*(inv_dz/delta);
constexpr Real beta = 0.125_rt;
Real const betaxz = beta*rz*inv_dx;
Real const betazx = beta*rx*inv_dz;
Real const alphax = (1._rt - 2._rt*rz*beta)*inv_dx;
Real const alphaz = (1._rt - 2._rt*rx*beta)*inv_dz;
// Other coefficients are 0 in 2D Cartesian
// (and will actually not be used in the stencil)
constexpr Real gammax=0._rt, gammay=0._rt, gammaz=0._rt;
constexpr Real betaxy=0._rt, betazy=0._rt, betayx=0._rt, betayz=0._rt;
constexpr Real alphay=0._rt;
#endif
// Store the coefficients in array `stencil_coefs`, in prescribed order
stencil_coefs_x.resize(6);
stencil_coefs_x[0] = inv_dx;
stencil_coefs_x[1] = alphax;
stencil_coefs_x[2] = betaxy;
stencil_coefs_x[3] = betaxz;
stencil_coefs_x[4] = gammax*inv_dx;
stencil_coefs_y.resize(6);
stencil_coefs_y[0] = inv_dy;
stencil_coefs_y[1] = alphay;
stencil_coefs_y[2] = betayz;
stencil_coefs_y[3] = betayx;
stencil_coefs_y[4] = gammay*inv_dy;
stencil_coefs_z.resize(6);
stencil_coefs_z[0] = inv_dz;
stencil_coefs_z[1] = alphaz;
stencil_coefs_z[2] = betazx;
stencil_coefs_z[3] = betazy;
stencil_coefs_z[4] = gammaz*inv_dz;
}
/**
* Compute the maximum timestep, for which the scheme remains stable
* (Courant-Friedrichs-Levy limit) */
static amrex::Real ComputeMaxDt ( amrex::Real const * const dx ) {
#if (defined WARPX_DIM_XZ)
// - In Cartesian 2D geometry: determined by the minimum cell size in all direction
amrex::Real const delta_t = std::min( dx[0], dx[1] )/PhysConst::c;
#else
// - In Cartesian 3D geometry: determined by the minimum cell size in all direction
amrex::Real const delta_t = std::min( dx[0], std::min( dx[1], dx[2] ) ) / PhysConst::c;
#endif
return delta_t;
}
/**
* Perform derivative along x on a cell-centered grid, from a nodal field `F` */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real UpwardDx (
amrex::Array4<amrex::Real> const& F,
amrex::Real const * const coefs_x, int const n_coefs_x,
int const i, int const j, int const k, int const ncomp=0 ) {
amrex::Real const alphax = coefs_x[1];
#if defined WARPX_DIM_3D
amrex::Real const betaxy = coefs_x[2];
#endif
amrex::Real const betaxz = coefs_x[3];
#if defined WARPX_DIM_3D
amrex::Real const gammax = coefs_x[4];
#endif
#if defined WARPX_DIM_3D
return alphax * (F(i+1,j ,k ,ncomp) - F(i, j, k ,ncomp))
+ betaxy * (F(i+1,j+1,k ,ncomp) - F(i ,j+1,k ,ncomp)
+ F(i+1,j-1,k ,ncomp) - F(i ,j-1,k ,ncomp))
+ betaxz * (F(i+1,j ,k+1,ncomp) - F(i ,j ,k+1,ncomp)
+ F(i+1,j ,k-1,ncomp) - F(i ,j ,k-1,ncomp))
+ gammax * (F(i+1,j+1,k+1,ncomp) - F(i ,j+1,k+1,ncomp)
+ F(i+1,j-1,k+1,ncomp) - F(i ,j-1,k+1,ncomp)
+ F(i+1,j+1,k-1,ncomp) - F(i ,j+1,k-1,ncomp)
+ F(i+1,j-1,k-1,ncomp) - F(i ,j-1,k-1,ncomp));
#elif (defined WARPX_DIM_XZ)
return alphax * (F(i+1,j ,k ,ncomp) - F(i, j, k ,ncomp))
+ betaxz * (F(i+1,j+1,k ,ncomp) - F(i ,j+1,k ,ncomp)
+ F(i+1,j-1,k ,ncomp) - F(i ,j-1,k ,ncomp));
#endif
}
/**
* Perform derivative along x on a nodal grid, from a cell-centered field `F` */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DownwardDx (
amrex::Array4<amrex::Real> const& F,
amrex::Real const * const coefs_x, int const n_coefs_x,
int const i, int const j, int const k, int const ncomp=0 ) {
amrex::Real const inv_dx = coefs_x[0];
return inv_dx*( F(i,j,k,ncomp) - F(i-1,j,k,ncomp) );
}
/**
* Perform derivative along y on a cell-centered grid, from a nodal field `F` */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real UpwardDy (
amrex::Array4<amrex::Real> const& F,
amrex::Real const * const coefs_y, int const n_coefs_y,
int const i, int const j, int const k, int const ncomp=0 ) {
using namespace amrex;
#if defined WARPX_DIM_3D
Real const alphay = coefs_y[1];
Real const betayz = coefs_y[2];
Real const betayx = coefs_y[3];
Real const gammay = coefs_y[4];
return alphay * (F(i ,j+1,k ,ncomp) - F(i ,j ,k ,ncomp))
+ betayx * (F(i+1,j+1,k ,ncomp) - F(i+1,j ,k ,ncomp)
+ F(i-1,j+1,k ,ncomp) - F(i-1,j ,k ,ncomp))
+ betayz * (F(i ,j+1,k+1,ncomp) - F(i ,j ,k+1,ncomp)
+ F(i ,j+1,k-1,ncomp) - F(i ,j ,k-1,ncomp))
+ gammay * (F(i+1,j+1,k+1,ncomp) - F(i+1,j ,k+1,ncomp)
+ F(i-1,j+1,k+1,ncomp) - F(i-1,j ,k+1,ncomp)
+ F(i+1,j+1,k-1,ncomp) - F(i+1,j ,k-1,ncomp)
+ F(i-1,j+1,k-1,ncomp) - F(i-1,j ,k-1,ncomp));
#elif (defined WARPX_DIM_XZ)
return 0._rt; // 2D Cartesian: derivative along y is 0
#endif
}
/**
* Perform derivative along y on a nodal grid, from a cell-centered field `F` */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DownwardDy (
amrex::Array4<amrex::Real> const& F,
amrex::Real const * const coefs_y, int const n_coefs_y,
int const i, int const j, int const k, int const ncomp=0 ) {
using namespace amrex;
#if defined WARPX_DIM_3D
Real const inv_dy = coefs_y[0];
return inv_dy*( F(i,j,k,ncomp) - F(i,j-1,k,ncomp) );
#elif (defined WARPX_DIM_XZ)
return 0._rt; // 2D Cartesian: derivative along y is 0
#endif
}
/**
* Perform derivative along z on a cell-centered grid, from a nodal field `F` */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real UpwardDz (
amrex::Array4<amrex::Real> const& F,
amrex::Real const * const coefs_z, int const n_coefs_z,
int const i, int const j, int const k, int const ncomp=0 ) {
using namespace amrex;
Real const alphaz = coefs_z[1];
Real const betazx = coefs_z[2];
#if defined WARPX_DIM_3D
Real const betazy = coefs_z[3];
Real const gammaz = coefs_z[4];
#endif
#if defined WARPX_DIM_3D
return alphaz * (F(i ,j ,k+1,ncomp) - F(i ,j ,k ,ncomp))
+ betazx * (F(i+1,j ,k+1,ncomp) - F(i+1,j ,k ,ncomp)
+ F(i-1,j ,k+1,ncomp) - F(i-1,j ,k ,ncomp))
+ betazy * (F(i ,j+1,k+1,ncomp) - F(i ,j+1,k ,ncomp)
+ F(i ,j-1,k+1,ncomp) - F(i ,j-1,k ,ncomp))
+ gammaz * (F(i+1,j+1,k+1,ncomp) - F(i+1,j+1,k ,ncomp)
+ F(i-1,j+1,k+1,ncomp) - F(i-1,j+1,k ,ncomp)
+ F(i+1,j-1,k+1,ncomp) - F(i+1,j-1,k ,ncomp)
+ F(i-1,j-1,k+1,ncomp) - F(i-1,j-1,k ,ncomp));
#elif (defined WARPX_DIM_XZ)
return alphaz * (F(i ,j+1,k ,ncomp) - F(i ,j ,k ,ncomp))
+ betazx * (F(i+1,j+1,k ,ncomp) - F(i+1,j ,k ,ncomp)
+ F(i-1,j+1,k ,ncomp) - F(i-1,j ,k ,ncomp));
#endif
}
/**
* Perform derivative along z on a nodal grid, from a cell-centered field `F` */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DownwardDz (
amrex::Array4<amrex::Real> const& F,
amrex::Real const * const coefs_z, int const n_coefs_z,
int const i, int const j, int const k, int const ncomp=0 ) {
amrex::Real const inv_dz = coefs_z[0];
#if defined WARPX_DIM_3D
return inv_dz*( F(i,j,k,ncomp) - F(i,j,k-1,ncomp) );
#elif (defined WARPX_DIM_XZ)
return inv_dz*( F(i,j,k,ncomp) - F(i,j-1,k,ncomp) );
#endif
}
};
#endif // WARPX_FINITE_DIFFERENCE_ALGORITHM_CARTESIAN_CKC_H_
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