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

refs #31887

Author: GiudGiud

framework/doc/content/finite_volumes/linear_fv_design.md

@@ -1,4 +1,3 @@
-
 # Linear Finite Volume Design Decisions in MOOSE
 
 The main motivation for introducing a new approach for finite volume system

modules/navier_stokes/doc/content/modules/navier_stokes/index.md

@@ -3,16 +3,15 @@
 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)
@@ -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            |
 | ------     | --------   | ----------------------------- | --------------------------- | ----------------  | ------ | --------------------------------- |
 | INS        | Hand-coded | incompressible                | None                        | Not porous        | CGFE   | SUPG                              |
 | INSAD      | AD         | incompressible                | Smagorinsky                 | Not porous        | CGFE   | SUPG                              |
@@ -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     |
@@ -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
@@ -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                    |
@@ -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                    |
 

modules/navier_stokes/doc/content/modules/navier_stokes/linear_wcnsfv.md

@@ -0,0 +1,67 @@
+# 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.