Compute the source terms for the flux-conservative Valencia formulation of GRMHD with divergence cleaning, coupled with electron fraction. More...

#include <Sources.hpp>

Public Types
using	return_tags = implementation defined

using	argument_tags = implementation defined

Static Public Member Functions
static void	apply (gsl::not_null< Scalar< DataVector > * > source_tilde_tau, gsl::not_null< tnsr::i< DataVector, 3, Frame::Inertial > * > source_tilde_s, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > source_tilde_b, gsl::not_null< Scalar< DataVector > * > source_tilde_phi, const Scalar< DataVector > &tilde_d, const Scalar< DataVector > &tilde_ye, const Scalar< DataVector > &tilde_tau, const tnsr::i< DataVector, 3, Frame::Inertial > &tilde_s, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b, const Scalar< DataVector > &tilde_phi, const tnsr::I< DataVector, 3, Frame::Inertial > &spatial_velocity, const tnsr::I< DataVector, 3, Frame::Inertial > &magnetic_field, const Scalar< DataVector > &rest_mass_density, const Scalar< DataVector > &electron_fraction, const Scalar< DataVector > &specific_internal_energy, const Scalar< DataVector > &lorentz_factor, const Scalar< DataVector > &pressure, const Scalar< DataVector > &lapse, const tnsr::i< DataVector, 3, Frame::Inertial > &d_lapse, const tnsr::iJ< DataVector, 3, Frame::Inertial > &d_shift, const tnsr::ii< DataVector, 3, Frame::Inertial > &spatial_metric, const tnsr::ijj< DataVector, 3, Frame::Inertial > &d_spatial_metric, const tnsr::II< DataVector, 3, Frame::Inertial > &inv_spatial_metric, const Scalar< DataVector > &sqrt_det_spatial_metric, const tnsr::ii< DataVector, 3, Frame::Inertial > &extrinsic_curvature, double constraint_damping_parameter)

Detailed Description

Compute the source terms for the flux-conservative Valencia formulation of GRMHD with divergence cleaning, coupled with electron fraction.

A flux-conservative system has the generic form:

$\partial_{t} U_{i} + \partial_{m} F^{m} (U_{i}) = S (U_{i})$

where $F^{a} ()$ denotes the flux of a conserved variable $U_{i}$ and $S ()$ denotes the source term for the conserved variable.

For the Valencia formulation:

$\begin{aligned} S (\tilde{D}) = & 0 \\ S ({\tilde{S}}_{i}) = & \frac{1}{2} α {\tilde{S}}^{m n} \partial_{i} γ_{m n} + {\tilde{S}}_{m} \partial_{i} β^{m} - (\tilde{D} + \tilde{τ}) \partial_{i} α \\ S (\tilde{τ}) = & α {\tilde{S}}^{m n} K_{m n} - {\tilde{S}}^{m} \partial_{m} α \\ S ({\tilde{B}}^{i}) = & \tilde{Φ} γ^{i m} \partial_{m} α + α \tilde{Φ} (\frac{1}{2} γ^{i l} γ^{j k} - γ^{i j} γ^{l k}) \partial_{l} γ_{j k} \\ S (\tilde{Φ}) = & {\tilde{B}}^{k} \partial_{k} α - α K \tilde{Φ} - α κ \tilde{Φ} \end{aligned}$

where

$\begin{aligned} {\tilde{S}}^{i} = & {\tilde{S}}_{m} γ^{i m} \\ {\tilde{S}}^{i j} = & \sqrt{γ} [(h ρ W^{2} + B^{n} B_{n}) v^{i} v^{j} + (p + p_{m}) γ^{i j} - B^{n} v_{n} (B^{i} v^{j} + B^{j} v^{i}) - \frac{B^{i} B^{j}}{W^{2}}] \end{aligned}$

where $\tilde{D}$ , ${\tilde{S}}_{i}$ , $\tilde{τ}$ , ${\tilde{B}}^{i}$ , and $\tilde{Φ}$ are a generalized mass-energy density, momentum density, specific internal energy density, magnetic field, and divergence cleaning field. Furthermore, $γ$ is the determinant of the spatial metric $γ_{i j}$ , $ρ$ is the rest mass density, $W$ is the Lorentz factor, $h$ is the specific enthalpy, $v^{i}$ is the spatial velocity, $B^{k}$ is the magnetic field, $p$ is the pressure, $p_{m} = \frac{1}{2} [{(B^{n} v_{n})}^{2} + B^{n} B_{n} / W^{2}]$ is the magnetic pressure, $α$ is the lapse, $β^{i}$ is the shift, $K$ is the trace of the extrinsic curvature $K_{i j}$ , and $κ$ is a damping parameter that damps violations of the divergence-free (no-monopole) condition $Φ = \partial_{i} {\tilde{B}}^{i} = 0$ .

Note: For the electron fraction side, the source term is currently set to $S ({\tilde{Y}}_{e}) = 0$ where the conserved variable ${\tilde{Y}}_{e}$ is a generalized electron fraction. Implementing the source term using neutrino scheme is in progress (Last update : Oct 2022).

The documentation for this struct was generated from the following file:

src/Evolution/Systems/GrMhd/ValenciaDivClean/Sources.hpp

Public Types

Static Public Member Functions

Detailed Description