The StationaryCylindricalHyperdiffusionBump is the stationary solution to.
\begin{align*}
0 = \frac{\partial T}{\partial t} = -\nabla^{4}T
\end{align*}
in 1D polar radial coordinates, so the equation becomes
\begin{align*}
0 = \nabla^{4}T = \frac{1}{r}\frac{d}{dr} r \frac{d}{dr} \frac{1}{r} \frac{d}{dr}
r\frac{dT}{dr}
\end{align*}
This leads to a solution of the form
\begin{align*}
T = c_{1}r^{2} \ln(r/e) + c_{2} \ln(r)
\end{align*}
- See also
- Warpy constructor: warpy::apps::functions::arbitrary::stationary_cylindrical_hyperdiffusion_bump
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| StationaryCylindricalHyperdiffusionBump () |
| Constructor.
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| ~StationaryCylindricalHyperdiffusionBump () override |
| Destructor.
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void | setup (const WxCryptSet &wxc) override |
| Setup.
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const std::vector< int > & | getOutputVariableIndexes (int flag) const override |
| Grab output variable indices.
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void | evaluate_function (const real *q, const real *aux, const solverVariables_t *pSV, real *result) const override |
| Redefinition of the function evaluator.
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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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