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/* Copyright 2020 Remi Lehe
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#ifndef WARPX_FINITE_DIFFERENCE_ALGORITHM_CYLINDRICAL_YEE_H_
#define WARPX_FINITE_DIFFERENCE_ALGORITHM_CYLINDRICAL_YEE_H_
#include "Utils/WarpXConst.H"
#include <AMReX_REAL.H>
#include <AMReX_Array4.H>
#include <AMReX_Gpu.H>
#include <array>
#include <cmath>
/**
* This struct contains only static functions to initialize the stencil coefficients
* and to compute finite-difference derivatives for the Cartesian Yee algorithm.
*/
struct CylindricalYeeAlgorithm {
static void InitializeStencilCoefficients (
std::array<amrex::Real,3>& cell_size,
amrex::Gpu::ManagedVector<amrex::Real>& stencil_coefs_r,
amrex::Gpu::ManagedVector<amrex::Real>& stencil_coefs_z ) {
using namespace amrex;
// Store the inverse cell size along each direction in the coefficients
stencil_coefs_r.resize(1);
stencil_coefs_r[0] = 1._rt/cell_size[0]; // 1./dr
stencil_coefs_z.resize(1);
stencil_coefs_z[0] = 1._rt/cell_size[2]; // 1./dz
}
/** Compute the maximum, CFL-stable timestep
*
* Compute the maximum timestep, for which the scheme remains stable
* under the Courant-Friedrichs-Levy limit.
*/
static amrex::Real ComputeMaxDt ( amrex::Real const * const dx,
int const n_rz_azimuthal_modes ) {
using namespace amrex::literals;
// In the rz case, the Courant limit has been evaluated
// semi-analytically by R. Lehe, and resulted in the following
// coefficients.
std::array< amrex::Real, 6 > const multimode_coeffs = {{ 0.2105, 1.0, 3.5234, 8.5104, 15.5059, 24.5037 }};
amrex::Real multimode_alpha;
if (n_rz_azimuthal_modes < 7) {
// Use the table of the coefficients
multimode_alpha = multimode_coeffs[n_rz_azimuthal_modes-1];
} else {
// Use a realistic extrapolation
multimode_alpha = (n_rz_azimuthal_modes - 1._rt)*(n_rz_azimuthal_modes - 1._rt) - 0.4_rt;
}
amrex::Real delta_t = 1._rt / ( std::sqrt(
(1._rt + multimode_alpha) / (dx[0]*dx[0])
+ 1._rt / (dx[1]*dx[1])
) * PhysConst::c );
return delta_t;
}
/** Applies the differential operator `1/r * d(rF)/dr`,
* where `F` is on a *nodal* grid in `r`
* and the differential operator is evaluated on a *cell-centered* grid.
* The input parameter `r` is given at the cell-centered position */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real UpwardDrr_over_r (
amrex::Array4<amrex::Real> const& F,
amrex::Real const r, amrex::Real const dr,
amrex::Real const * const coefs_r, int const n_coefs_r,
int const i, int const j, int const k, int const comp ) {
using namespace amrex;
Real const inv_dr = coefs_r[0];
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) );
};
/** Applies the differential operator `1/r * d(rF)/dr`,
* where `F` is on a *cell-centered* grid in `r`
* and the differential operator is evaluated on a *nodal* grid.
* The input parameter `r` is given at the cell-centered position */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DownwardDrr_over_r (
amrex::Array4<amrex::Real> const& F,
amrex::Real const r, amrex::Real const dr,
amrex::Real const * const coefs_r, int const n_coefs_r,
int const i, int const j, int const k, int const comp ) {
using namespace amrex;
Real const inv_dr = coefs_r[0];
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) );
};
/**
* Perform derivative along r on a cell-centered grid, from a nodal field `F` */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real UpwardDr (
amrex::Array4<amrex::Real> const& F,
amrex::Real const * const coefs_r, int const n_coefs_r,
int const i, int const j, int const k, int const comp ) {
using namespace amrex;
Real const inv_dr = coefs_r[0];
return inv_dr*( F(i+1,j,k,comp) - F(i,j,k,comp) );
};
/**
* Perform derivative along r on a nodal grid, from a cell-centered field `F` */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
static amrex::Real DownwardDr (
amrex::Array4<amrex::Real> const& F,
amrex::Real const * const coefs_r, int const n_coefs_r,
int const i, int const j, int const k, int const comp ) {
using namespace amrex;
Real const inv_dr = coefs_r[0];
return inv_dr*( F(i,j,k,comp) - F(i-1,j,k,comp) );
};
/**
* 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 comp ) {
amrex::Real const inv_dz = coefs_z[0];
return inv_dz*( F(i,j+1,k,comp) - F(i,j,k,comp) );
};
/**
* 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 comp ) {
amrex::Real const inv_dz = coefs_z[0];
return inv_dz*( F(i,j,k,comp) - F(i,j-1,k,comp) );
};
};
#endif // WARPX_FINITE_DIFFERENCE_ALGORITHM_CYLINDRICAL_YEE_H_
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