regionCoupledScalarFlux

Partitioned flux-side coupling BC for any scalar field: fixes the normal gradient so that the diffusive flux balances the flux of the value-side partner (zero flux jump), for use with any interface type.

Overview

regionCoupledScalarFlux is the concrete scalar flux side (Neumann side) of the partitioned DNA coupling. It derives from genericRegionCoupledFlux<scalar> (and so from fixedGradient). It fixes the patch-normal gradient so that the local diffusive flux is equal and opposite to the flux of the value-side partner, i.e. flux continuity without a source at the interface. It does not check the interface type and is normally used with defaultInterface. The partner on the neighbour patch must be a genericRegionCoupledJump<scalar>-derived BC, usually regionCoupledScalarJump.

Mathematical Formulation

Let $F$ be this patch and $J$ the neighbour (jump-side) patch:

$$ \Gamma_F \frac{\partial \phi_F}{\partial n_F} + \Gamma_J \frac{\partial \phi_J}{\partial n_J} = 0 \quad \text{on } \Gamma $$

imposed as the gradient

$$ \left.\frac{\partial \phi_F}{\partial n}\right|_b = -\frac{\mathcal{I}_{J\to F}\!\left(\Gamma_J\, \partial_n \phi_J\right)}{\Gamma_F} $$

followed by relaxation with the acceleration model. fluxJump() returns zero.

Symbol	Description	Unit
$\phi$	Coupled scalar field (same name in both regions)	field-dependent
$\Gamma_F$	Diffusivity named by this BC’s `diffusivity`	field-dependent
$\Gamma_J\,\partial_n\phi_J$	`flux()` of the jump-side partner, with the partner’s `diffusivity`	field-dependent
$\mathcal{I}_{J\to F}$	Interface-to-interface interpolation	–

Implementation

Everything except fluxJump() is inherited from genericRegionCoupledFlux<scalar>. In each DNA iteration updateCoeffs() updates the interface, refCasts the neighbour patch field to genericRegionCoupledJumpFvPatchField<scalar>, takes its flux(), interpolates and negates it, adds fluxJump() (= 0), divides by the local diffCoeff(), relaxes the gradient and fixes it. evaluate() sets the patch value from the gradient with optional non-orthogonal and second-order corrections. The flux residual $|\Gamma_F\,g_F + \mathcal{I}(q_J)|$ is checked against maxFluxRes.

Dictionary Entries

Keyword	Description	Required	Default
`type`	`regionCoupledScalarFlux`	yes	—
`interfaceType`	Interface type list, e.g. `(defaultInterface)`. Only the first entry is used; any type is accepted.	yes	—
`diffusivity`	Diffusivity name (`volScalarField` or `transportProperties` entry)	effectively yes	`word::null` (lookup fails)
`neighbourFieldName`	Read and written, not used	no	local field name
`accType`	`fixed`, `aitken` or `IQNILS`	no	`fixed` (with warning)
`relax`	Initial / fixed relaxation factor	no	`1.0`
`couplingReuse`	`IQNILS` only: reused time steps	no	`0`
`nonOrthCorr`	Non-orthogonal correction in `evaluate()`	no	`false`
`secondOrder`	Second-order value evaluation	no	`false`
`gradient`	Initial gradient; if given, the initial patch value is evaluated from it	no	zero
`value`	Not read (only written)	no	—

Usage

From tutorials/electrochemistry/NTGKBatteryWithTabs/0/negTabRegion/orig/partitioned/T (flux side on the tab):

toCellFromNeg
{
    type                    regionCoupledScalarFlux;
    interfaceType           (defaultInterface);
    diffusivity             "k";
    secondOrder             false;
    nonOrthCorr             false;
    value                   $internalField;
}

Partner in 0/batteryRegion/orig/partitioned/T:

toNegTab
{
    type                    regionCoupledScalarJump;
    interfaceType           (defaultInterface);
    diffusivity             "k";
    accType                 aitken;
    relax                   0.75;
    secondOrder             false;
    nonOrthCorr             false;
    value                   $internalField;
}

The regionInterfaceProperties (cellToNegTab, defaultInterface, coupledFields (phiPos phiNeg T)) and the DNA entries are shown in regionCoupledScalarJump. In this tutorial k is a uniform entry in the transportProperties of the NTGK and conductPotentialTemperature regions.

Known Limitations

Partner must be a jump BC of the same field (bad-cast error otherwise).
diffusivity must be set; the default word::null lookup fails.
No interfacial source. fluxJump() is always zero. Use a derived BC with its own fluxJump() (e.g. regionCoupledPhaseChangeHeatFlux) for a flux jump.
No consistency check between the diffusivities named on the two sides.
value is ignored on input and gradient is not written. On restart the coupled gradient starts from zero unless gradient is given.
First relaxation uses the patch values as reference (inherited; only matters with relax ≠ 1 or aitken/IQNILS on this side).
Inherited from genericRegionCoupledFlux: neighbourFieldName unused, nonOrthCorr/secondOrder only in the evaluated value, IQNILS not parallel-consistent, partitioned only.

Tutorials

Tutorial	Description
`tutorials/electrochemistry/NTGKBatteryWithTabs`	`phiPos`: flux side on the battery (`diffusivity sigmaPos`, initial `gradient uniform 0.1266`). `phiNeg`: flux side on the negative tab (`diffusivity sigma`). `T`: flux side on both tabs (`diffusivity k`). All with `defaultInterface` and `directMap`.

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