#include <srrmhd.h>
Public Member Functions | |
| SRRMHD () | |
| SRRMHD (Data *data) | |
| virtual | ~SRRMHD () |
| void | sourceTermSingleCell (double *cons, double *prims, double *aux, double *source, int i=-1, int j=-1, int k=-1) |
| void | sourceTerm (double *cons, double *prims, double *aux, double *source) |
| void | getPrimitiveVarsSingleCell (double *cons, double *prims, double *aux, int i=-1, int j=-1, int k=-1) |
| void | getPrimitiveVars (double *cons, double *prims, double *aux) |
| void | primsToAll (double *cons, double *prims, double *aux) |
| void | fluxVector (double *cons, double *prims, double *aux, double *f, const int dir) |
| void | finalise (double *cons, double *prims, double *aux) |
 Public Member Functions inherited from Model | |
| Model () | |
| Model (Data *data) | |
| virtual | ~Model () |
Additional Inherited Members | |
| Public Attributes inherited from Model | |
| Data * | data |
| int | Ncons |
| int | Nprims |
| int | Naux |
Detailed Description
Special Relativistic Resistive MagnetHydroDynamics
- The single fluid, special relativistic, resistive limit of the MHD equations.
- Note
- Model has 14 conserved variables:
\(\ \ \ D\), \(S_x\), \(S_y\), \(S_z\), \(\tau\), \(B_x\), \(B_y\), \(B_z\), \(E_x\), \(E_y\), \(E_z\), \(\psi\), \(\phi\), \(\varrho\)
11 primitive variables:
\(\ \ \ \rho\), \(v_x\), \(v_y\), \(v_z\), \(p\), \(B_x\), \(B_y\), \(B_z\), \(E_x\), \(E_y\), \(E_z\)
17 auxiliary variables:
\(\ \ \ h\), \(W\), \(e\), \(c\), \(J_x\), \(J_y\), \(J_z\), \(B^2\), \(E^2\), \(v^2\), \(\rho h W^2\), \(v \cdot E\), \(\overline{S}_x\), \(\overline{S}_y\), \(\overline{S}_z\), \(\overline{S}^2\), \(\overline{\tau}\)
The equations of motion are:
\begin{align} \partial_t \begin{pmatrix} D \\ S^i \\ \tau \\ B^i \\ E^i \\ \psi \\ \phi \\ \varrho \end{pmatrix} + \partial_k \begin{pmatrix} Dv^k \\ S^k_i\\ S^k - D v^k \\ - \epsilon^{ijk} E^j + \delta^k_i \phi \\ \epsilon^{ijk} B^j + \delta^k_i \psi \\ E^k \\ B^k \\ J^k \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ -J^i \\ \varrho -\psi / c_p^2 \\ -\phi / c_p^2 \\ 0 \end{pmatrix}. \end{align}
- Here, we sum over the \(k\) coordinate directions, and note the following relations:
\begin{align} D &= \rho W \\ S^i &= \rho h^* W^2 v^i + \epsilon^{ijk}E^j B^k \\ \tau &= \rho h^* W^2 - p^* + \frac{E^2 + B^2}{2} - D \\ W &= 1 / \sqrt(1 - v_i v^i) \\ J^i &= \varrho v^i + W \sigma \bigg[E^i + \epsilon^{ijk} v^j B^k - (v^kE^k)v^i\bigg] \\ S^{ij} &= \rho h W^2 v^i v^j + \delta^{ij}\bigg(P + \frac{E^2 + B^2}{2}\bigg) - E^i E^j - B^i B^j \\ c_p &= const. \end{align}
- We have also included the additional scalar fields \(\psi\) and \(\phi\) such that any errors in the evolution of the magnetic/electric fields that break the divergence constraint set by Maxwell's equations are driven to zero on a timescale set by the constant parameter \(c_p\). See Dedner et al. 2002.
- See also
- Model
Constructor & Destructor Documentation
◆ SRRMHD() [1/2]
| SRRMHD::SRRMHD | ( | ) |
Default constructor.
◆ SRRMHD() [2/2]
| SRRMHD::SRRMHD | ( | Data * | data | ) |
◆ ~SRRMHD()
Member Function Documentation
◆ finalise()
|
inlinevirtual |
◆ fluxVector()
|
virtual |
Flux vector.
Method determines the value of the conserved vector in the specified direction. For the form of the fluxes see Dionysopoulou 2016 with the inclusion of divergence cleaning from Muddle 2015.
- Note
- We are assuming that all primitive and auxiliary variables are up-to-date at the time of this function execution.
- Parameters
-
*cons pointer to conserved vector work array. Size is Ncons*Nx*Ny*Nz *prims pointer to primitive vector work array. Size is Nprims*Nx*Ny*Nz *aux pointer to auxiliary vector work array. Size is Naux*Nx*Ny*Nz *f pointer to flux vector work array. Size is Ncons*Nx*Ny*Nz dir direction in which to generate flux vector. (x, y, z) = (0, 1, 2)
- See also
- Model::fluxVector
Implements Model.
◆ getPrimitiveVars()
|
virtual |
Spectral decomposition.
Generates the values of the primitive and auxiliary variables consistent with the conservative vector given. Method first subtracts the EM fields from the conserved quantities, reducing the problem to the hydrodynamic properties only before determining their values via a newton method. Function calls single celled version (below) for each compute cell.
- Parameters
-
*cons pointer to conserved vector work array. Size is Ncons*Nx*Ny*Nz *prims pointer to primitive vector work array. Size is Nprims*Nx*Ny*Nz *aux pointer to auxiliary vector work array. Size is Naux*Nx*Ny*Nz
- See also
- Model::getPrimitiveVars
Implements Model.
◆ getPrimitiveVarsSingleCell()
|
virtual |
Single cell spectral decomposition.
Generates the values for aux and prims for the given cons vector for only a single cell (i, j, k). Note : pointers to arrays are the (Ncons,) conservative array, (Nprims,) prim array and (Naux,) aux array, NOT the (Ncons, Nx, Ny, Nz) arrays as in most other functions. Single celled version required for the inside of the residual functions for the (semi) implicit time integrators.
- Parameters
-
*cons pointer to conserved vector work array. Size is Ncons *prims pointer to primitive vector work array. Size is Nprims *aux pointer to auxiliary vector work array. Size is Naux i cell number in x-direction (optional) j cell number in y-direction (optional) k cell number in z-direction (optional)
Implements Model.
◆ primsToAll()
|
virtual |
Primitive-to-all transformation.
Transforms the initial state given in primitive form in to the conserved vector state. Relations have been taken from Dionysopoulou 2016.
- Parameters
-
*cons pointer to conserved vector work array. Size is Ncons*Nx*Ny*Nz *prims pointer to primitive vector work array. Size is Nprims*Nx*Ny*Nz *aux pointer to auxiliary vector work array. Size is Naux*Nx*Ny*Nz
- See also
- Model::primsToAll
Implements Model.
◆ sourceTerm()
|
virtual |
Source term contribution.
Source terms arise from the evolution of the electric fields and from implementing the divergence cleaning method. This function determines the source contribution to the change in the conserved vector for all cells. This function calls sourceTermSingleCell for every compute cell.
- Parameters
-
*cons pointer to conserved vector work array. Size is Ncons*Nx*Ny*Nz *prims pointer to primitive vector work array. Size is Nprims*Nx*Ny*Nz *aux pointer to auxiliary vector work array. Size is Naux*Nx*Ny*Nz *source pointer to source vector work array. Size is Ncons*Nx*Ny*Nz
- See also
- Model::sourceTerm
Implements Model.
◆ sourceTermSingleCell()
|
virtual |
Destructor.
Single cell source term contribution
Determines the source vector due the the cond prims and aux vector of a single compute cell. Note : pointers to arrays are the (Ncons,) conservative array, (Nprims,) prim array and (Naux,) aux array, NOT the (Ncons, Nx, Ny, Nz) arrays as in most other functions.
- Parameters
-
*cons pointer to conserved vector work array. Size is Ncons *prims pointer to primitive vector work array. Size is Nprims *aux pointer to auxiliary vector work array. Size is Naux *source pointer to source vector work array. Size is Ncons i cell number in x-direction (optional) j cell number in y-direction (optional) k cell number in z-direction (optional)
- See also
- Model::sourceTermSingleCell
Implements Model.
The documentation for this class was generated from the following file:
