ForceFree::ComputeParallelTildeJ Struct Reference

Computes the stiff part ${\tilde{J}}_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{l}}^i$ of the generalized electric current density ${\tilde{J}}^i$. More...

#include <ElectricCurrentDensity.hpp>

Public Types
using	argument_tags = implementation defined
using	return_type = tnsr::I< DataVector, 3 >

Static Public Member Functions
static void	apply (gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > parallel_tilde_j, const Scalar< DataVector > &tilde_q, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_e, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b, double parallel_conductivity, const Scalar< DataVector > &lapse, const Scalar< DataVector > &sqrt_det_spatial_metric, const tnsr::ii< DataVector, 3, Frame::Inertial > &spatial_metric)

Detailed Description

Computes the stiff part ${\tilde{J}}_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{l}}^i$ of the generalized electric current density ${\tilde{J}}^i$.

$$\begin{array}{rl}{\tilde{J}}_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{l}}^i& =\alpha \sqrt{\gamma }\eta [\frac{(E_l{B}^l)B^i}{B^2}+\frac{\mathcal{R}(E^2-B^2)}{B^2}{E}^i]\end{array}$$

where $\alpha$ is lapse, $\gamma$ is the determinant of the spatial metric, $E^i$ is the electric field, $B^i$ is the magnetic field, $\eta$ is the parallel conductivity, and $\mathcal{R}(x)=max(x,0)$ is the rectifier function.

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

• src/Evolution/Systems/ForceFree/ElectricCurrentDensity.hpp