Cylindrical source for density diffusion in the MHD model.
Refer to DensityDiffusionFlux for details on the calculation of the diffusion coefficient.
Density diffusion in cartesian coordinates
\[
\frac{\partial \rho}{\partial t} + \nabla \cdot (-D \nabla \rho) = 0
\]
becomes in cylindrical coordinates
\[
\frac{\partial \rho}{ \partial t} + \nabla_{cart} (-D \nabla \rho) = D
\nabla_r(\rho) / r
\]
where \(\nabla_{cart} \cdot\) is the cartesian divergence operator and \(\nabla_r \) is the radial gradient operator.
- See also
- Warpy constructor: warpy.apps.mhd.rmhd.rmhd.density_diffusion_cyl_source_mhd
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| | DensityDiffusionCylSource () |
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| | ~DensityDiffusionCylSource () override |
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| void | setup (const WxCryptSet &wxc) override |
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| const std::vector< int > & | getInputVariableIndexes (int flag) const override |
| | Grab input variable indices.
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| const std::vector< int > & | getAuxiliaryVariableIndexes (int flag) const override |
| | Grab auxiliary variable indices.
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| const std::vector< int > & | getOutputVariableIndexes (int flag) const override |
| | Grab output variable indices.
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| real | source (const real *q, const real *aux, const elementGeometry_t *pEG, real *source) const override |
| | Redefinition of the source function.
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| | WmApplication () |
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| virtual | ~WmApplication ()=default |
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| virtual void | setup (const WxCryptSet &wxc) |
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| virtual const std::vector< int > & | getAuxiliaryVariableIndexes (int flag=WMAPPLICATIONFLAG_NONE) const |
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| virtual const std::vector< int > & | getCrossVariableIndexes (int flag=WMAPPLICATIONFLAG_NONE) const |
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| const std::vector< std::string > & | getBoundaryNames () const |
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| bool | isOnBoundary (const std::string &boundaryName) const |
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| bool | has (int flag) const |
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| virtual real | numerical_flux (const real *q_l, const real *q_r, const real *aux_l, const real *aux_r, const solverVariables_t *pFV, real *numericalFlux) const |
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| virtual real | internal_flux (const real *q, const real *aux, const solverVariables_t *pSV, std::vector< std::vector< real > > &internalFlux) const |
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| virtual real | source (const real *q, const real *aux, const elementGeometry_t *pEG, real *source) const |
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| virtual void | bc_q (const real *q_in, const real *aux_in, const real *aux_out, const solverVariables_t *pFV, real *q_out) const |
| | Boundary Condition Application which sets the boundary condition on ghost nodes.
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| virtual real | bcNumericalFlux (const real *q_l, const real *q_r, const real *aux_l, const real *aux_r, const solverVariables_t *pFV, real *numericalFlux) const |
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| virtual void | conserved_to_primitive (const real *q, const real *aux, real *w) const |
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| virtual void | primitive_to_conserved (const real *w, const real *aux, real *q) const |
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| virtual void | evaluate_function (const real *q, const real *aux, const solverVariables_t *pSV, real *result) const |
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| virtual void | bc_q_kinetic (const real *q_in, const real *aux_in, const solverVariables_t *pFV, real *q_out) const |
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| std::shared_ptr< std::string > | app_name () |
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| virtual const std::vector< int > & | getInputVariableIndexes (int flag=0) const |
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| virtual const std::vector< int > & | getOutputVariableIndexes (int flag=0) const |
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