Compute the resistive MHD flux. More...

#include "pluto.h"

Functions
void	ResistiveFlux (Data_Arr V, double RF, double dcoeff, int beg, int end, Grid *grid)

Detailed Description

Compute the resistive fluxes for the induction and energy equations. In the induction equation, fluxes are computed by explicitly writing the curl operator in components. In Cartesian components, for instance, one has

$\pd{\vec{B}}{t} = - \nabla\times{\vec{E}_{\rm res}} = \pd{}{x}\left(\begin{array}{c} 0 \\ \noalign{\medskip} \eta_z J_z \\ \noalign{\medskip} - \eta_y J_y \end{array}\right) + \pd{}{y}\left(\begin{array}{c} - \eta_z J_z \\ \noalign{\medskip} 0 \\ \noalign{\medskip} \eta_x J_x \end{array}\right) + \pd{}{z}\left(\begin{array}{c} \eta_y J_y \\ \noalign{\medskip} -\eta_x J_x \\ \noalign{\medskip} 0 \end{array}\right) \,,\qquad \left(\vec{E}_{\rm res} = \tens{\eta}\cdot\vec{J}\right)$

where $\tens{\eta}$ is the resistive diagonal tensor and $J = \nabla\times\vec{B}$ is the current density. The corresponding contribution to the energy equation is

$\pd{E}{t} = -\nabla\cdot\Big[(\tens{\eta}\cdot\vec{J})\times\vec{B}\Big] = - \pd{}{x}\left(\eta_yJ_yB_z - \eta_zJ_zB_y\right) - \pd{}{y}\left(\eta_zJ_zB_x - \eta_xJ_xB_z\right) - \pd{}{z}\left(\eta_xJ_xB_y - \eta_yJ_yB_x\right)$

References

"The PLUTO Code for Adaptive Mesh Computations in Astrophysical Fluid Dynamics"
Mignone et al, ApJS (2012) 198, 7M

Authors: A. Mignone (migno.nosp@m.ne@p.nosp@m.h.uni.nosp@m.to.i.nosp@m.t)
T. Matsakos

Date: Nov 5, 2012

Function Documentation

void ResistiveFlux	(	Data_Arr	V,
		double **	RF,
		double **	dcoeff,
		int	beg,
		int	end,
		Grid *	grid
	)

Compute resistive fluxes for the induction and energy equations. Also, compute the diffusion coefficient. Called by either ParabolicFlux or ParabolicRHS.

Parameters

[in]	V	3D data array of primitive variables
[out]	RF	the resistive fluxes
[out]	dcoeff	the diffusion coefficients evaluated at cell interfaces
[in]	beg	initial index of computation
[in]	end	final index of computation
[in]	grid	pointer to an array of Grid structures.

Functions

Detailed Description

Function Documentation