regionCoupledTraction

Overview

regionCoupledTraction applies the fluid load to the solid in a partitioned fluid-structure interaction. It acts on the solid displacement D (volVectorField) and derives from genericRegionCoupledFlux<vector>, i.e. from fixedGradient. It uses the “direct flux” path of the base class: the gradient is computed entirely from the fluid traction and the solid stress state, with no flux matching against a partner BC. There is no partner coupled BC on the fluid side, because the fluid has no D field. The fluid side follows the solid through the interfaceTrackingFvMesh mesh motion, and its velocity usually uses movingWallVelocity. The BC belongs to fsiInterface and aborts if the first entry of its interfaceType list is not fsiInterface. The solid region must be solidStVK.

Mathematical Formulation

The fluid traction is evaluated on the fluid patch, mapped to the solid patch and its sign is flipped:

The normal displacement gradient is then

This is the usual segregated traction condition: the explicit stress $\mathbf{n}\cdot\boldsymbol{\sigma}_s$ is replaced by the implicit $K\,\partial\mathbf{D}/\partial n$ part. At convergence of the solid Picard loop $\mathbf{n}\cdot\boldsymbol{\sigma}_s = \mathbf{t}$ holds in the deformed configuration. The gradient is relaxed by the acceleration model, $g^{k} = g^{k-1} + \omega\,(g^{*} - g^{k-1})$, and the patch value is reconstructed as $\mathbf{D}_b = \mathbf{D}_P + \mathbf{k}\cdot\nabla\mathbf{D}_P + g/\Delta_f$ (first order) or $\mathbf{D}_P + \mathbf{k}\cdot\nabla\mathbf{D}_P + (g + \mathbf{n}_0\cdot\nabla\mathbf{D}_P)/(2\Delta_f)$ (secondOrder yes); the $\mathbf{k}$ term only with nonOrthCorr yes.

Implementation

updateCoeffs() is the generic one of genericRegionCoupledFlux with useDirectFlux() returning true:

1. Return if updated or if the interface has coupled no. The gradient is then frozen at its last value. With couplingStartTime, the coupling is switched on once that time is reached.
2. Call update() on the first interfaceType, i.e. the fsiInterface.
3. Set gradient() = flux(), relax it, call fixedGradient::updateCoeffs().

flux():

• checks that the first interfaceType is fsiInterface;
• looks up the fluid field named sigma (hardcoded) in the neighbour region, takes its patch values on the neighbour patch, dots them with the neighbour patch normals, interpolates the result to the solid patch and negates it;
• looks up impK, rImpK, gradD, sigma and Finv on the solid patch (all provided by solidStVK);
• calls fsiInterface::setTotalForce() with $\sum \mathbf{t}\,\lvert\mathbf{S}_0\rvert$ (undeformed face areas). The interface logs this value in info().

evaluate() uses the registered grad(D) if one exists. solidStVK registers its gradient as gradD, so in practice fvc::grad(D) is computed on every evaluation.

In the DNA loop for D (multiRegionSystem::solve()), each iteration runs solvePIMPLE() on the fluid (updating the fluid sigma), then assembles and solves D with this BC, then meshMotionCorrector() and interfaces_->update(). Convergence is judged by the fsiInterface interface residual (maxIntRes). The jump and flux residuals of the generic base classes cannot be used: rawResidual()/normResidual() abort for a direct-flux BC, and the fluid has no D field anyway.

Dictionary Entries

write() writes diffusivity only if it was set, and does not write gradient.

Usage

Solid 0/solid/D from tutorials/fluidStructureInteraction/HronTurekFsi3/0/solid/orig/partitioned/D:

interface
{
    type                    regionCoupledTraction;
    neighbourFieldName      sigma;          // ignored, sigma is hardcoded
    interfaceType           (fsiInterface);
    secondOrder             false;
    nonOrthCorr             false;
    value                   uniform (0 0 0); // not read
}

The matching fluid patch has no coupled BC. In the tutorials it uses movingWallVelocity for U, zeroGradient for pKin, and fixedValue for pointMotionU (driven by interfaceTrackingFvMesh with fsiInterface yes).

constant/regionInterfaceProperties:

partitionedCoupledPatches
(
    fluidsolid
    {
        interfaceType (fsiInterface);

        coupledPatchPair
        (
            (fluid interfaceShadow)
            (solid interface)
        );

        coupledFields
        (
            D
        );

        fsiInterfaceCoeffs
        {}
    }
);

constant/multiRegionProperties:

DNA
{
    D
    {
        maxCoupleIter 100;

        residualControl
        {
            maxIntRes 1e-7;
        }
    }
}

The full setup (dynamic mesh, transfer method, coupling start time) is described in fsiInterface.

Known Limitations

• fsiInterface and solidStVK only. The interface type is checked; the solid fields impK, rImpK, gradD, sigma and Finv are only provided by solidStVK.
• The fluid stress must be called sigma. neighbourFieldName is read but not used.
• No generic residuals. Use the fsiInterface interface residual (maxIntRes); jump/flux residuals abort for this BC.
• Relaxation history starts from the patch value (inferred). The base class initialises the acceleration model with the patch values of D but relaxes the gradient. With relax 1 (the default, used in all tutorials) this has no effect.
• Total force uses the undeformed area and is set on every call of flux(). It is a diagnostic only.
• gradient is not written to the time directories, so a restart starts from zero gradient until the first update.
• Partitioned only. There is no monolithic FSI path.

Tutorials

The BC is set in the 0/solid/orig/partitioned/D variant of each tutorial (./Allrun -p).

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