regionCoupledMassTransferVelocityFlux

Overview

regionCoupledMassTransferVelocityFlux is the Neumann (flux) half of the partitioned velocity coupling across a sharp liquid-vapour interface with phase change. It acts on a volVectorField (U) and derives from genericRegionCoupledFlux<vector>, i.e. from fixedGradient. It uses the same stress balance as regionCoupledVelocityFlux and adds the momentum flux $\dot m\,[\![\mathbf{u}_\text{rel}]\!]$ that the mass flux carries across the interface. The partner condition on the other side is regionCoupledMassTransferVelocityValue. The BC needs a capillaryInterface as the first interfaceType entry and a massTransferInterface on the same patch pair.

Mathematical Formulation

“own” is the side the BC sits on (side A, which carries the faMesh) and “nbr” the other side. $\mathbf{n}$ is the faMesh face normal, $\mathbf{n}_\varepsilon = \mathbf{n}$ if the local region is meshA of the capillaryInterface (otherwise $-\mathbf{n}$). $\tilde{\mathbf{F}}$ is the interpolated diffusive flux of the partner BC ($\mu_\text{nbr}$ times the tangential face-normal gradient) and $\tilde{\dot m} = \mathcal{I}_{\text{nbr}\to\text{own}}(\dot m)$.

with the tangential surface-tension force

$\mathbf{U}_\text{own}$ are the current patch values (previous iteration) and $\mathbf{U}_\text{nbr}$ the neighbour patch values without interpolation (see Known Limitations). The gradient is relaxed, $g^{k} = g^{k-1} + \omega\,(g^{*} - g^{k-1})$, and the patch value is reconstructed from it in evaluate() as described for regionCoupledVelocityFlux.

Implementation

updateCoeffs() is the generic one of genericRegionCoupledFlux: return if updated or coupled no; call update() on the first interfaceType (the capillaryInterface); interpolate and negate the neighbour flux() (the neighbour patch field is refCast to genericRegionCoupledJump<vector>); add fluxJump(); divide by diffCoeff() (hardcoded name mu: registered volScalarField mu, else transportProperties); relax; call fixedGradient::updateCoeffs().

fluxJump():

• aborts unless the first interfaceType is capillaryInterface; finds the massTransferInterface by type name;
• computes $\nabla_s\cdot\mathbf{u}_s$, $\nabla_s\mathbf{u}_s$ and the edge-integrated surface-tension force on the faMesh;
• reads mu and rho of both regions from transportProperties; if a region has a pKin field, its mu must equal rho*nu exactly, otherwise the run stops;
• interpolates mDotS() from the neighbour side.

Because only the first interface is update()d, $\dot m$ is not recomputed by this BC. It changes only when a BC that lists massTransferInterface first (e.g. regionCoupledPhaseChangeHeatFlux on T) is updated.

The U flux residual of the pUPimple DNA loop is taken from this BC if it sits on side A: $\lVert\mu_\text{own}\partial_n\mathbf{U}_\text{own} + \tilde{\mathbf{F}} - \text{fluxJump}\rVert_2$, normalised as in genericRegionCoupledFlux.

Dictionary Entries

write() does not write gradient.

Usage

No tutorial uses this BC. Untested entry on side A, following massTransferInterface:

// 0/fluidA/U
interface
{
    type                    regionCoupledMassTransferVelocityFlux;
    interfaceType           (capillaryInterface massTransferInterface);
    secondOrder             false;
    nonOrthCorr             false;
    value                   uniform (0 0 0);
}

Partner on side B:

// 0/fluidB/U
interfaceShadow
{
    type                    regionCoupledMassTransferVelocityValue;
    interfaceType           (capillaryInterface massTransferInterface);
    value                   uniform (0 0 0);
}

The regionInterfaceProperties entry is shown on the regionCoupledMassTransferVelocityValue page and in massTransferInterface.

Known Limitations

• Neighbour velocity is not interpolated (bug). $\mathbf{U}_\text{nbr}$ in the mass-flux term is the raw neighbour patch field, combined index by index with local fields. This is only correct for conformal patches with identical face order; otherwise the sizes may not even match.
• mDotS() is interpolated from the neighbour although it is defined on side A (inferred), where this BC sits. Harmless only for identical conformal patches.
• Must sit on side A (inferred): faMesh normals, $\mathbf{u}_s$, $\sigma$, $\kappa$ are used without interpolation.
• $\dot m$ is only updated through another BC. See Implementation.
• Exact mu == rho*nu check for regions with pKin.
• Relaxation history starts from the patch value (inferred). The base class initialises the acceleration model with the patch values but relaxes the gradient; harmless with relax 1.
• Untested, no tutorial; interTrackFluid is disabled.

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