Weakly Compressible Navier Stokes using the Linear Finite Volume discretization

Equations

The linear finite volume discretization of the weakly compressible Navier Stokes equations is used to solve the following equations:

conservation of momentum
pressure-correction (see SIMPLE)
turbulence equations
conservation of energy
conservation of advected passive scalars
conservation of an advected phase in a homogeneous mixture

We refer the reader to the respective Physics pages, listed in Syntax, for the strong form of the equations.

Solver algorithm(s)

For steady state simulations, you may use the SIMPLE executioner which implements the SIMPLE algorithm (Patankar and Spalding, 1983).

For transient simulations, you may use the PIMPLE executioner which implements the PIMPLE algorithm (Greenshields and Weller, 2022).

Discretization

General

We use the linear finite volume discretization, a face-centered finite volume discretization. We have implemented orthogonal gradient correction for face values, and thus can reach second-order accuracy in many cases.

note

Triangular and tetrahedral meshes currently only achieve first order convergence rates in most cases at the moment, notably for the pressure variable.

note

This implementation does not require forming a Jacobian because it is solving using the SIMPLE/PIMPLE algorithm, which involve segregated linear equation solved nested in a fixed point iteration loop, rather than a Newton method-based solver. The discretization of the equation is optimized to form a right hand side (RHS) and sparse matrices. Additional details about the linear finite volume discretization can be found on this page.

Advection term

The advection term is discretized using the Rhie Chow interpolation for the face fluxes. Additional details may be found in the documentation for the object handling the computation of the Rhie Chow velocities: the RhieChowMassFlux.

Syntax

These equations can be created in MOOSE using the LinearFVKernels and LinearFVBCs classes, or using the Physics classes. For LinearWCNSFV, the relevant Physics classes are:

Navier Stokes Flow Segregated / WCNSLinearFVFlowPhysics for the velocity-pressure coupling.
Navier Stokes Fluid Heat Transfer / WCNSLinearFVFluidHeatTransferPhysics for the fluid energy conservation equation.
Navier Stokes Scalar Transport Segregated / WCNSLinearFVScalarTransportPhysics for the advection of passive scalars.

For LinearWCNSFV2P, the relevant Physics classes are:

Navier Stokes Two Phase Mixture using a Linear Finite Volume discretization / WCNSLinearFVTwoPhaseMixturePhysics for a basic implementation of a mixture model.

Validation

The linear finite volume discretization is being verified and validated as part of the OpenPronghorn open-source software. Please refer to OpenPronghorn for this ongoing effort.

Gallery

construction

The gallery has not been created for this discretization yet. Please refer to OpenPronghorn for example simulations.

References

Christopher Greenshields and Henry Weller. Notes on Computational Fluid Dynamics: General Principles. CFD Direct Ltd, Reading, UK, 2022.

@book{greenshieldsweller2022,
    author = "Greenshields, Christopher and Weller, Henry",
    title = "Notes on Computational Fluid Dynamics: General Principles",
    year = "2022",
    publisher = "CFD Direct Ltd",
    address = "Reading, UK"
}

Suhas V Patankar and D Brian Spalding. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. In Numerical prediction of flow, heat transfer, turbulence and combustion, pages 54–73. Elsevier, 1983.

@incollection{patankar1983calculation,
    author = "Patankar, Suhas V and Spalding, D Brian",
    title = "A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows",
    booktitle = "Numerical prediction of flow, heat transfer, turbulence and combustion",
    pages = "54--73",
    year = "1983",
    publisher = "Elsevier"
}

Equations
Solver algorithm ( s )
Discretization
Syntax
Validation
Gallery
References