Docs: pimpleFluid

Mon, 01 Jan 0001 00:00:00 +0000

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

$$ \nabla \cdot \mathbf{U} = 0 $$

Momentum

$$ \frac{\partial \mathbf{U}}{\partial t} + \nabla\cdot\left(\mathbf{U}\mathbf{U}\right) - \nabla\cdot\mathbf{R} = -\nabla p_\text{kin} + \mathbf{S}_U $$

Symbol	Description	Unit
$\mathbf{U}$	Velocity	m/s
$p_\text{kin} = p/\rho$	Kinematic pressure	m²/s²
$\mathbf{R}$	Effective stress tensor (viscous + turbulent)	m²/s²
$\mathbf{S}_U$	Momentum source (from `fvOptions`)	m/s²

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:

$$ \boldsymbol{\sigma} = \rho \left( -p_\text{kin}\,\mathbf{I} - \mathbf{R}^\text{dev} \right) $$

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:

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

$$ \nabla \cdot \left( r_{AU}\,\nabla p_\text{kin} \right) = \nabla \cdot \hat{\mathbf{U}} $$

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

$$ \mathbf{U} = \hat{\mathbf{U}} - r_{AU}\,\nabla p_\text{kin} $$

Non-orthogonal corrector sub-loop — improves accuracy on non-orthogonal meshes (controlled by nNonOrthogonalCorrectors).
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

Sub-model	Selection mechanism	Notes
Turbulence (laminar / RANS / LES)	`constant/turbulenceProperties`	Uses `incompressible::turbulenceModel`
Transport properties	`constant/transportProperties`	Kinematic viscosity $\nu$ via `singlePhaseTransportModel`
Moving Reference Frame (MRF)	`constant/MRFProperties`	`IOMRFZoneList`; multiple zones supported
`fvOptions`	`system/fvOptions`	Explicit/implicit source terms, porosity, momentum sources

Required Fields

Field	Type	Description	Unit
`U`	`volVectorField`	Velocity	m/s
`pKin`	`volScalarField`	Kinematic pressure $p/\rho$	m²/s²
Turbulence fields	—	As required by selected model (e.g. `k`, `epsilon`, `omega`, `nut`)	—

Additionally created at runtime:

Field	Type	Description	Condition
`phi`	`surfaceScalarField`	Face-normal flux	always
`Uf`	`surfaceVectorField`	Face velocity	moving mesh only
`sigma`	`volSymmTensorField`	Cauchy stress tensor	always (FSI)

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:

Interface type	Exchanged fields	Coupling modes
`heatTransferInterface`	Temperature `T`, heat flux `q`	partitioned (DNA), monolithic
`fsiInterface`	Displacement `D`, traction `sigma·n`	partitioned (DNA)
`defaultInterface`	Any scalar/vector	partitioned (DNA)

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

Tutorial path	Description
`tutorials/singleRegion/pimpleFluid/pitzDaily`	Backward-facing step flow (single-region, adjustable time-step)
`tutorials/singleRegion/pimpleFluid/mixerVesselAMI2D`	Rotating mixer with AMI interface (MRF / sliding mesh)
`tutorials/conjugateHeatTransfer/flowOverHeatedPlate`	Flow over a heated plate (pimpleFluid + conductTemperature)
`tutorials/conjugateHeatTransfer/ShellAndTubeHeatExchanger`	Shell-and-tube heat exchanger (pimpleFluid + conductTemperature)
`tutorials/fluidStructureInteraction/beamInCrossFlow`	Beam in cross-flow FSI (pimpleFluid + solidStVK)
`tutorials/fluidStructureInteraction/HronTurekFsi3`	Hron-Turek FSI benchmark (pimpleFluid + solidStVK)

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

multiPhysicsFoam – Incompressible