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Add a dedicated linear WCNSFV page with links to the relevant sections in linearFV, NS and physics #31888

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Add a dedicated linear WCNSFV page with links to the relevant section…
GiudGiud Nov 10, 2025
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Address Alex's review
GiudGiud Nov 11, 2025
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1 change: 0 additions & 1 deletion framework/doc/content/finite_volumes/linear_fv_design.md
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# Linear Finite Volume Design Decisions in MOOSE

The main motivation for introducing a new approach for finite volume system
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16 changes: 9 additions & 7 deletions modules/navier_stokes/doc/content/modules/navier_stokes/index.md
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The MOOSE Navier-Stokes module is a library for the implementation of simulation tools that solve the
Navier-Stokes equations using either the continuous Galerkin finite element
(CGFE) or finite volume (FV) methods. The Navier-Stokes
equations are usually solved using either the pressure-based, incompressible formulation (assuming a
constant fluid density), or a density-based, compressible formulation, although
there are plans to add a finite volume weakly-compressible pressured-based implementation in
the not-too-distant future.
equations are usually solved using either the pressure-based, incompressible or weakly-compressible formulation (assuming a
constant or pressure-independent fluid density), or a density-based, compressible formulation.

For documentation specific to finite element or finite volume implementations,
please refer to the below pages:

- [Incompressible Finite Volume](insfv.md)
- [Weakly Compressible Finite Volume](wcnsfv.md)
- [Weakly compressible finite volume using a linear discretization and a segregated solvealgorithm (SIMPLE/PIMPLE)](linear_wcnsfv.md)
- [Porous media Incompressible Finite Volume](pinsfv.md)
- [Continuous Galerkin Finite Element](navier_stokes/cgfe.md)
- [Hybridized Discontinous Galerkin (HDG) Finite Element](NavierStokesLHDGKernel.md)
Expand All @@ -25,7 +24,7 @@ please refer to the below pages:
Here we give a brief tabular summary of the Navier-Stokes implementations:

!table id=navier_stokes_summary caption=Summary of Navier-Stokes implementations
| prefix | Jacobian | compressibility | turbulence support | friction support | method | advection strategy |
| prefix | Jacobian | compressibility | turbulence support | friction support | discretiz. | advection strategy |
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@lindsayad lindsayad Nov 11, 2025

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it might be more accurate/clearer to introduce an additional column called "solver" and then discretization would remain just "FV" for the linear FV implementation and solver would be "SIMPLE/PIMPLE"

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@GiudGiud GiudGiud Nov 11, 2025 •
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linearFV is kind of different though, not just the solver? like the base classes for the variables are similar but different
like some items that are "discretization"-related such as "two term expansions" are decided in a different place (variables & kernels) in nonlinearFV and linearFV

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Those are implementation details that are not relevant to a user. Real differences are things like lagging certain quantities in order to keep them linear. I don't know if that is really a difference in the spatial discretization though. More like a state difference

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@GiudGiud GiudGiud Nov 12, 2025

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well we do lag a ton more in linearFV than in Newton. In fact we try not to lag anything in Newton

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@GiudGiud GiudGiud Nov 12, 2025 •
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but that's all tied to the solver / discretization in time rather than in space

the gradients are lagged in linearFV and not FV that's a space-time discretization that is different

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well we do lag a ton more in linearFV than in Newton. In fact we try not to lag anything in Newton

I know that. That's why I said

Real differences are things like lagging certain quantities in order to keep them linear.

I wrote a very large share of the Newton code. I know how it works.

but that's all tied to the solver / discretization in time rather than in space

Agreed. That's why I said

I don't know if that is really a difference in the spatial discretization though. More like a state difference

If the spatial locations used to evaluate things like a Green-Gauss gradient or the non-orthogonal gradient are the same, then I believe the spatial discretization is the same. If the only difference is that you're indexing into different vectors (states), I don't think that equates to a difference in spatial discretization

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@GiudGiud GiudGiud Nov 12, 2025

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The iterative two term expansions are something that are unique to FV.
It is tied to not wanting to lag though

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@GiudGiud GiudGiud Nov 12, 2025

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If the spatial locations used to evaluate things like a Green-Gauss gradient or the non-orthogonal gradient are the same, then I believe the spatial discretization is the same.

@grmnptr any differences on that aspect?

| ------ | -------- | ----------------------------- | --------------------------- | ---------------- | ------ | --------------------------------- |
| INS | Hand-coded | incompressible | None | Not porous | CGFE | SUPG |
| INSAD | AD | incompressible | Smagorinsky | Not porous | CGFE | SUPG |
Expand All @@ -35,7 +34,9 @@ Here we give a brief tabular summary of the Navier-Stokes implementations:
| INSChorin | Hand-coded | incompressible | None | Not porous | CGFE | Chorin predictor-corrector |
| INSFV | AD | incompressible | mixing length; $k-\epsilon$ | Not porous | FV | RC, CD velocity; limited advected |
| WCNSFV | AD | weakly compressible | mixing length | Not porous | FV | RC, CD velocity; limited advected |
| Linear(WCNS)FV | N/A | weakly compressible | $k-\epsilon$ | Not porous | LinearFV | RC velocity; limited advected |
| WCNSFV2P | AD | weakly compressible; 2-phase | mixing length | Not porous | FV | RC, CD velocity; limited advected |
| LinearWCNSFV2P | N/A | weakly compressible; 2-phase | None | Not porous | LinearFV | RC velocity; limited advected |
| PINSFV | AD | incompressible | mixing length | Darcy, Forcheimer | FV | RC, CD velocity; limited advected |
| CNSFVHLLC | AD | compressible | None | Not porous | FV | HLLC, piecewise constant data |
| PCNSFVHLLC | AD | compressible | None | Darcy, Forcheimer | FV | HLLC, piecewise constant data |
Expand All @@ -49,6 +50,7 @@ Table definitions:
- WCNS2P: weakly-compressible Navier-Stokes 2-phase
- CNS: compressible Navier-Stokes
- PINS or PCNS: porous incompressible Navier-Stokes or porous compressible Navier-Stokes
- LinearFV: the [linear finite volume discretization](linear_fv_design.md)
- SUPG: Streamline-Upwind Petrov-Galerkin
- RC: Rhie-Chow interpolation
- CD: central differencing interpolation; equivalent to average interpolation
Expand Down Expand Up @@ -78,7 +80,7 @@ As Navier-Stokes Finite Volume solvers continue to evolve in MOOSE, many new sol
| Turbulence | Mixing length | Yes | Yes | Yes | |
| | $k-\epsilon$ | | Yes | Yes | Yes |
| | $k-\omega$ SST | | | in [PR #28151](https://github.com/idaholab/moose/pull/28151) | |
| Two-phase | Mixture model | Yes | Yes | Yes | in [PR #29614](https://github.com/idaholab/moose/pull/29614) |
| Two-phase | Mixture model | Yes | Yes | Yes | Yes |
| | Eulerian-Eulerian | | | Yes | |
| Porous Flow | -- | Yes | Yes | Yes | |
| Compressibility | Incompressible | Yes | Yes | Yes | Yes |
Expand All @@ -91,7 +93,7 @@ As Navier-Stokes Finite Volume solvers continue to evolve in MOOSE, many new sol
| Physics Syntax | Flow | | Yes | | Yes |
| | Fluid heat transfer | | Yes | | Yes |
| | Solid phase heat transfer | | Yes | | |
| | Two phase | | Yes | | in [PR #29614](https://github.com/idaholab/moose/pull/29614) |
| | Two phase | | Yes | | Yes |
| | Turbulence | | Yes | | |
| | Scalar transport | | Yes | | Yes |

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# 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.md])
- 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 [linear_wcnsfv.md#syntax], for the strong form of the equations.

## Solver algorithm(s)

For steady state simulations, you may use the [SIMPLE.md] executioner which implements the SIMPLE algorithm [!citep](patankar1983calculation).

For transient simulations, you may use the [PIMPLE.md] executioner which implements the PIMPLE algorithm [!citep](greenshieldsweller2022).

## Discretization

### General

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

!alert note
Triangular and tetrahedral meshes currently only achieve first order convergence rates at the moment.

!alert 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](linear_fv_design.md).

### Advection term

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

## Syntax id=syntax

These equations can be created in MOOSE using the [LinearFVKernels](syntax/LinearFVKernels/index.md) and [LinearFVBCs](syntax/LinearFVBCs/index.md)
classes, or using the [Physics](syntax/Physics/index.md) classes.
For `LinearWCNSFV`, the relevant `Physics` classes are:

- [WCNSLinearFVFlowPhysics.md] for the velocity-pressure coupling.
- [WCNSLinearFVFluidHeatTransferPhysics.md] for the fluid energy conservation equation.
- [WCNSLinearFVScalarTransportPhysics.md] for the advection of passive scalars.

For `LinearWCNSFV2P`, the relevant `Physics` classes are:

- [WCNSLinearFVTwoPhaseMixturePhysics.md] 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](https://mooseframework.inl.gov/open_pronghorn/) for this ongoing effort.

## Gallery

!alert construction
The gallery has not been created for this discretization yet.
Please refer to [OpenPronghorn](https://mooseframework.inl.gov/open_pronghorn/) for example simulations.