LinearFVRZViscousSource

Adds the axisymmetric viscous source term mu * u_r / r^2 to the FV momentum equations.

This kernel supplies the axisymmetric viscous source term $var element = document.getElementById("moose-equation-30f12bab-e97a-44ac-8fa9-2c1e617c06af");katex.render("\\mu u_r / r^2", element, {displayMode:false,throwOnError:false});$ that appears in the cylindrical vector Laplacian.

When "use_deviatoric_terms" is enabled, the axisymmetric contribution is modified to include the $var element = document.getElementById("moose-equation-e0076311-c614-4c44-bc92-d7dc8c6225cd");katex.render("-\\frac{2}{3} \\nabla\\cdot \\boldsymbol{u}", element, {displayMode:false,throwOnError:false});$ portion of the deviatoric stress. This doubles the implicit coefficient multiplying $var element = document.getElementById("moose-equation-0e87ad88-335e-41e2-b6dd-8e4f464037f9");katex.render("u_r / r^2", element, {displayMode:false,throwOnError:false});$ and adds a right-hand-side contribution of $var element = document.getElementById("moose-equation-9532f95d-b5b7-4960-970c-c97587d6766d");katex.render("\\frac{2}{3}\\mu \\nabla\\cdot \\boldsymbol{u}/r", element, {displayMode:false,throwOnError:false});$ . Because the divergence is evaluated from the velocity gradients, you must also provide the names of each velocity component through the "u" and "v" parameters whenever the deviatoric terms are requested.

This kernel must operate on the radial velocity component only; attempting to apply it to a non-radial component results in a parameter error. In coupled RZ simulations, enable this kernel's "use_deviatoric_terms" together with "use_deviatoric_terms" in LinearWCNSFVMomentumFlux so that the combination of these kernels reproduces the full cylindrical viscous operator (including the explicit hoop-stress contribution discussed in the latter's documentation).

RZ coordinate system

For axisymmetric, swirl-free flows we take $var element = document.getElementById("moose-equation-a162aacc-f3a1-4ce9-9609-6da2c76dd018");katex.render("\\vec{u} = (u_r, u_z)", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-548befca-d237-4d64-8cde-0fec4d237acd");katex.render("\\nabla \\cdot \\vec{u} = \\frac{\\partial u_r}{\\partial r} + \\frac{u_r}{r} + \\frac{\\partial u_z}{\\partial z}.", element, {displayMode:true,throwOnError:false});$ The Newtonian stress tensor with the Stokes approximation, $var element = document.getElementById("moose-equation-5674f5ce-7a09-4cbb-97bd-dbd759f82aef");katex.render("\\boldsymbol{\\tau} = \\mu \\nabla \\vec{u} + \\mu (\\nabla \\vec{u})^{\\top} - \\tfrac{2}{3}\\mu (\\nabla\\cdot\\vec{u})\\mathbf{I}", element, {displayMode:false,throwOnError:false});$ , then contains a hoop component $var element = document.getElementById("moose-equation-384d2e3b-5376-448c-bf82-fc9a402c1ada");katex.render("\\tau_{\\theta\\theta} = 2\\mu u_r / r - \\tfrac{2}{3}\\mu \\nabla\\cdot\\vec{u}", element, {displayMode:false,throwOnError:false});$ . Taking the divergence produces the volumetric contribution $var element = document.getElementById("moose-equation-cfda5615-cf56-4725-a82a-517f8cea08f8");katex.render("-(\\tau_{\\theta\\theta}/r)\\,\\mathbf{e}_r \\approx - 2\\mu u_r/r^2 + \\tfrac{2}{3}\\mu (\\nabla\\cdot\\vec{u})/r", element, {displayMode:false,throwOnError:false});$ that this kernel supplies, while the face terms are handled by LinearWCNSFVMomentumFlux.

For more information on the axisymmetric formulation we recommend visiting Peterson et al. (2018) and Hill and Stokes (2018).

Input Parameters

momentum_componentMomentum component this kernel contributes to.
C++ Type:MooseEnum
Options:x, y, z
Controllable:No
Description:Momentum component this kernel contributes to.
muDynamic viscosity functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Dynamic viscosity functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
variableThe name of the variable whose linear system this object contributes to
C++ Type:LinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable whose linear system this object contributes to

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
uThe velocity in the x direction.
C++ Type:SolverVariableName
Unit:(no unit assumed)
Controllable:No
Description:The velocity in the x direction.
use_deviatoric_termsFalseInclude the deviatoric correction (-2/3 div(u)) in the axisymmetric term.
Default:False
C++ Type:bool
Controllable:No
Description:Include the deviatoric correction (-2/3 div(u)) in the axisymmetric term.
vThe velocity in the y direction.
C++ Type:SolverVariableName
Unit:(no unit assumed)
Controllable:No
Description:The velocity in the y direction.

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>
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>
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>
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
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsrhsThe tag for the vectors this Kernel should fill
Default:rhs
C++ Type:MultiMooseEnum
Options:rhs, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
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
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
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
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
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_layers1The number of layers of elements to ghost.
Default:1
C++ Type:unsigned short
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
Controllable:No
Description:Whether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.

Parallel Ghosting Parameters

References

James M Hill and Yvonne Marie Stokes. A note on navier–stokes equations with nonorthogonal coordinates. The ANZIAM Journal, 59(3):335–348, 2018.

@article{hill2018note,
    author = "Hill, James M and Stokes, Yvonne Marie",
    title = "A note on Navier--Stokes equations with nonorthogonal coordinates",
    journal = "The ANZIAM Journal",
    volume = "59",
    number = "3",
    pages = "335--348",
    year = "2018",
    publisher = "Cambridge University Press"
}

John W. Peterson, Alexander D. Lindsay, and Fande Kong. Overview of the incompressible navier–stokes simulation capabilities in the moose framework. Advances in Engineering Software, 119:68–92, 2018.

@article{peterson2018overview,
    author = "Peterson, John W. and Lindsay, Alexander D. and Kong, Fande",
    title = "Overview of the incompressible Navier--Stokes simulation capabilities in the MOOSE framework",
    year = "2018",
    journal = "Advances in Engineering Software",
    volume = "119",
    pages = "68--92",
    publisher = "Elsevier"
}

RZ coordinate system
Input Parameters
References