PCNSFVKT

Computes the residual of advective term using finite volume method.

Overview

This object implements the Kurganov-Tadmor (Kurganov and Tadmor, 2000) (KT) scheme for computing inter-cell advective fluxes for the Euler equations. We will outline some of the important equations below, drawing from (Greenshields et al., 2010). The KT flux is a second-order generalization of the Lax-Friedrichs flux. For a given face ff it can be written as

F=αϕf+Ψf++(1α)ϕfΨf+ωf(ΨfΨf+) \bm{F} = \alpha \phi_{f+}\bm{\Psi}_{f+} + \left(1 - \alpha\right)\phi_{f-}\bm{\Psi}_{f-} + \omega_f\left(\bm{\Psi}_{f-} - \bm{\Psi}_{f+}\right)(1)

where Ψf±\bm{\Psi}_{f\pm} represents the vector of advected quantities, and

ϕf±=ϵf±af±n^\phi_{f\pm} = \epsilon_{f\pm}\bm{a}_{f\pm}\cdot\hat{n}

where ϵ\epsilon is the porosity, a={u,v,w}\bm{a} = \lbrace u,v,w\rbrace where uu, vv, and ww are the component particle velocities, and n^\hat{n} is the normal vector pointing from ++ to -. This definition of ϕ\phi is slightly different from that in (Greenshields et al., 2010) in that it does not contain the face area. This is because here we are essentially describing the implementation in PCNSFVKT while area multiplication happens in the base class FVFluxKernel. α\alpha is defined as

α={12for Kurganov-Tadmorψf+ψf++ψffor Kurganov, Noelle, Petrova\alpha= \begin{cases} \frac{1}{2} &\text{for Kurganov-Tadmor}\\ \frac{\psi{_f+}}{\psi_{f+} + \psi_{f-}} &\text{for Kurganov, Noelle, Petrova} \end{cases}

where

ψf+=max(cf++ϕf+, cf+ϕf, 0)ψf=max(cf+ϕf+, cfϕf, 0)\psi_{f+} = \text{max}\left(c_{f+} + \phi_{f+},\ c_{f-} + \phi_{f-},\ 0\right)\\ \psi_{f-} = \text{max}\left(c_{f+} - \phi_{f+},\ c_{f-} - \phi_{f-},\ 0\right)

where cc is the locally computed speed of sound. The default method when computing α\alpha and ω\omega is Kurganov, Noelle, Petrova (Kurganov et al., 2001) (KNP) since it's reported (Greenshields et al., 2010) as being less diffusive (enabling sharper front capturing) than the KT method of computing α\alpha and ω\omega. ω\omega is given by

ωf={αmax(ψf+, ψf)for KTα(1α)(ψf++ψf)for KNP\omega_f= \begin{cases} \alpha \text{max}\left(\psi_{f+},\ \psi_{f-}\right) &\text{for KT}\\ \alpha\left(1 - \alpha\right)\left(\psi_{f+} + \psi_{f-}\right) &\text{for KNP} \end{cases}

Interpolation of Ψf±\bm{\Psi}_{f\pm} is described in Limiters.

Input Parameters

  • eqnThe equation you're solving.

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:mass, momentum, energy, scalar

    Controllable:No

    Description:The equation you're solving.

  • fpFluid userobject

    C++ Type:UserObjectName

    Unit:(no unit assumed)

    Controllable:No

    Description:Fluid userobject

  • variableThe name of the variable that this residual object operates on

    C++ Type:NonlinearVariableName

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the variable that this residual object operates on

Required Parameters

  • blockThe list of blocks (ids or names) that this object will be applied

    C++ Type:std::vector<SubdomainName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • knp_for_omegaTrueWhether to use the Kurganov, Noelle, and Petrova method to compute the omega parameter for stabilization. If false, then the Kurganov-Tadmor method will be used.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether to use the Kurganov, Noelle, and Petrova method to compute the omega parameter for stabilization. If false, then the Kurganov-Tadmor method will be used.

  • limiterupwindThe limiter to apply during interpolation.

    Default:upwind

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:vanLeer, upwind, central_difference, min_mod, sou, quick

    Controllable:No

    Description:The limiter to apply during interpolation.

  • momentum_componentThe component of the momentum equation that this kernel applies to.

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:x, y, z

    Controllable:No

    Description:The component of the momentum equation that this kernel applies to.

  • prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

  • use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional Parameters

  • absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution

  • extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The extra tags for the matrices this Kernel should fill

  • extra_vector_tagsThe extra tags for the vectors this Kernel should fill

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The extra tags for the vectors this Kernel should fill

  • matrix_tagssystemThe tag for the matrices this Kernel should fill

    Default:system

    C++ Type:MultiMooseEnum

    Unit:(no unit assumed)

    Options:nontime, system

    Controllable:No

    Description:The tag for the matrices this Kernel should fill

  • vector_tagsnontimeThe tag for the vectors this Kernel should fill

    Default:nontime

    C++ Type:MultiMooseEnum

    Unit:(no unit assumed)

    Options:nontime, time

    Controllable:No

    Description:The tag for the vectors this Kernel should fill

Tagging Parameters

  • boundaries_to_avoidThe set of sidesets to not execute this FVFluxKernel on. This takes precedence over force_boundary_execution to restrict to less external boundaries. By default flux kernels are executed on all internal boundaries and Dirichlet boundary conditions.

    C++ Type:std::vector<BoundaryName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The set of sidesets to not execute this FVFluxKernel on. This takes precedence over force_boundary_execution to restrict to less external boundaries. By default flux kernels are executed on all internal boundaries and Dirichlet boundary conditions.

  • boundaries_to_forceThe set of sidesets to force execution of this FVFluxKernel on. Setting force_boundary_execution to true is equivalent to listing all external mesh boundaries in this parameter.

    C++ Type:std::vector<BoundaryName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The set of sidesets to force execution of this FVFluxKernel on. Setting force_boundary_execution to true is equivalent to listing all external mesh boundaries in this parameter.

  • force_boundary_executionFalseWhether to force execution of this object on all external boundaries.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether to force execution of this object on all external boundaries.

Boundary Execution Modification Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

  • implicitTrueDetermines whether this object is calculated using an implicit or explicit form

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Determines whether this object is calculated using an implicit or explicit form

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:The seed for the master random number generator

  • use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

  • ghost_layers2The number of layers of elements to ghost.

    Default:2

    C++ Type:unsigned short

    Unit:(no unit assumed)

    Controllable:No

    Description:The number of layers of elements to ghost.

  • use_point_neighborsFalseWhether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.

Parallel Ghosting Parameters

References

  1. Christopher J Greenshields, Henry G Weller, Luca Gasparini, and Jason M Reese. Implementation of semi-discrete, non-staggered central schemes in a colocated, polyhedral, finite volume framework, for high-speed viscous flows. International journal for numerical methods in fluids, 63(1):1–21, 2010.[BibTeX]
  2. Alexander Kurganov, Sebastian Noelle, and Guergana Petrova. Semidiscrete central-upwind schemes for hyperbolic conservation laws and hamilton–jacobi equations. SIAM Journal on Scientific Computing, 23(3):707–740, 2001.[BibTeX]
  3. Alexander Kurganov and Eitan Tadmor. New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations. Journal of Computational Physics, 160(1):241–282, 2000.[BibTeX]