pimpleFluid

Overview

pimpleFluid solves the transient, incompressible Navier-Stokes equations for a Newtonian single-phase fluid using the PIMPLE (merged PISO–SIMPLE) pressure-velocity coupling algorithm. It supports turbulence modelling (laminar, RANS, LES), arbitrary moving meshes (ALE formulation), multiple reference frames (MRF), and run-time selectable source terms via fvOptions. It is the most general-purpose fluid region type in multiPhysicsFoam and is suitable as the fluid side in conjugate heat transfer, fluid-structure interaction, and standalone flow problems.

Governing Equations

Continuity

Momentum

The effective stress tensor $\mathbf{R}$ is computed by the selected turbulence model via turbulence::divDevReff(U). For laminar flow this reduces to the viscous stress $2\nu\,\text{dev}(\mathbf{D})$ where $\mathbf{D}$ is the rate-of-strain tensor.

Stress tensor (for FSI coupling)

After each pressure-correction step the Cauchy stress tensor is updated:

This field (sigma) is used when pimpleFluid is coupled to a solid region via fsiInterface.

Numerical Algorithm

The PIMPLE loop consists of an outer iteration (SIMPLE-like relaxation) wrapping an inner PISO loop:

1. Pre-predictor — mesh motion update (ALE); flux correction after mesh deformation (correctPhi); MRF zone update.
2. Momentum predictor — assemble and (optionally) solve the momentum equation to obtain a predicted velocity $\mathbf{U}^*$.
3. Pressure correction (PISO inner loop) — solve the pressure Poisson equation:

where $r_{AU} = (A_U)^{-1}$ and $\hat{\mathbf{U}} = \mathbf{H}(U)/A_U$. Velocity is then explicitly corrected:

4. Non-orthogonal corrector sub-loop — improves accuracy on non-orthogonal meshes (controlled by nNonOrthogonalCorrectors).
5. Turbulence correction — transport equations for the selected turbulence model are solved once per outer PIMPLE iteration (controlled by turbOnFinalIterOnly / turbCorr).

Steps 2–5 are repeated for nOuterCorrectors outer iterations; steps 3–4 are repeated for nCorrectors inner iterations.

Sub-Models

Required Fields

Additionally created at runtime:

Case Setup

Required dictionaries

constant/transportProperties    – kinematic viscosity (nu)
constant/turbulenceProperties   – turbulence model selection
system/fvSolution               – PIMPLE sub-dict and linear solver settings
system/fvSchemes                – discretisation schemes

multiRegionProperties entry

regions
(
    ( fluid (pimpleFluid) )
);

For combined fluid + passive scalar transport add further region types:

regions
(
    ( fluid (pimpleFluid transportTemperature) )
);

controlDict (singleRegionMode)

When running as a standalone single-region case via singleRegionMode:

singleRegionMode    yes;
regionType          pimpleFluid;

Key fvSolution settings

PIMPLE
{
    momentumPredictor       yes;
    nOuterCorrectors        1;      // outer SIMPLE-like iterations
    nCorrectors             2;      // inner PISO iterations
    nNonOrthogonalCorrectors 1;

    // Moving mesh
    correctPhi              yes;    // defaults to yes if mesh is dynamic
    checkMeshCourantNo      no;
    moveMeshOuterCorrectors no;

    // Pressure reference (closed domains)
    pKinRefCell             0;
    pKinRefValue            0.0;
}

Adjustable time stepping (controlDict)

adjustTimeStep  yes;
maxCo           0.5;        // maximum Courant number
maxDeltaT       1e-3;       // upper bound on time-step size

Coupling

pimpleFluid participates in the following multi-region interfaces:

The stress tensor sigma is automatically maintained and made available to fsiInterface for computing the traction boundary condition on the solid side.

Known Limitations

• Incompressible only — density is constant (read from transportProperties). Compressibility, variable density, or buoyancy-driven flows are not supported; use buoyantPimpleFluid for the latter.
• Newtonian fluid — viscosity is treated as constant or temperature- independent. Non-Newtonian rheology is not supported via this region type.
• Single phase — two-phase or interface-tracking flows are not supported; use interTrackFluid instead.
• No energy equation — the fluid energy/temperature equation is not solved here. Pair with transportTemperature or turbulentTransportTemperature for heat transfer in the fluid.
• Monolithic p-U coupling not implemented — setCoupledEqns is a no-op. For monolithic pressure-velocity coupling use pUCoupledIcoFluid.

Tutorials

References

• Alkfri, A., Habes, C., Marschall, H., *multiRegionFoam: A Unified Multiphysics Framework for Multi-Region Coupled Continuum-Physical Problems, Engineering with Computers, 2023. DOI: 10.1007/s00366-024-01974-4