multiPhysicsFoam – Scalar-Transport

Docs: regionCoupledScalarFlux

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

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

Docs: regionCoupledScalarJump

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

Overview

regionCoupledScalarJump is the concrete scalar value side (Dirichlet side) of the partitioned DNA coupling. It derives from genericRegionCoupledJump<scalar> (and so from fixedValue). It fixes the patch value to the neighbour value interpolated onto this patch, scaled by a jump (partition) coefficient $c$, which defaults to 1, i.e. continuity. It does not check the interface type, so it works with any interface, in practice defaultInterface. It is the generic choice for potentials, temperatures and concentrations that need no interface physics. The partner on the neighbour patch is regionCoupledScalarFlux (or any other genericRegionCoupledFlux<scalar>-derived BC, e.g. regionCoupledPhaseChangeHeatFlux).

Mathematical Formulation

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

$$ \phi_J = c\;\mathcal{I}_{F\to J}(\phi_F) \quad \text{on } \Gamma $$

implemented as $\phi_J = \mathcal{I}_{F\to J}(\phi_F) + j$ with the value jump

$$ j = \mathcal{I}_{F\to J}(\phi_F)\,(c - 1). $$

The value is then relaxed by the acceleration model. The flux handed to the partner is

$$ q_J = \Gamma_J \left.\frac{\partial \phi_J}{\partial n}\right|_b $$

with the coupled snGrad of genericRegionCoupledJump (optional non-orthogonal and second-order corrections).

Symbol	Description	Unit
$\phi$	Coupled scalar field (same name in both regions)	field-dependent
$c$	Jump (partition) coefficient, keyword `jumpCoefficient`	–
$\mathcal{I}_{F\to J}$	Interface-to-interface interpolation	–
$\Gamma_J$	Diffusivity named by `diffusivity`	field-dependent

Implementation

All run-time work (interface lookup, updateCoeffs(), relaxation, snGrad, flux(), diffCoeff(), residuals) is inherited from genericRegionCoupledJump<scalar>. The class only implements valueJump():

Looks up the neighbour field under the local field name and interpolates its neighbour patch values onto this patch.
Determines $c$ per face:
- if a volScalarField named jumpCoefficient is registered on the local region, its local patch values are used;
- else, if jumpCoefficient is set, a uniform dimensionedScalar of that name is read from the local region’s transportProperties;
- else $c = 1$.
Returns $\mathcal{I}_{F\to J}(\phi_F)\,(c - 1)$.

valueJump() is evaluated in updateCoeffs() and again in each residual evaluation (jump residual $|\phi_J - \mathcal{I}(\phi_F) - j|$, checked against maxJumpRes).

Dictionary Entries

Keyword	Description	Required	Default
`type`	`regionCoupledScalarJump`	yes	—
`interfaceType`	Interface type list, e.g. `(defaultInterface)`. Only the first entry is used to find the interface; any type is accepted.	yes	—
`diffusivity`	Diffusivity name (`volScalarField` or `transportProperties` entry) used by `flux()` for the partner	effectively yes	`word::null` (lookup fails)
`jumpCoefficient`	Name of the partition-coefficient field / `transportProperties` entry	no	`word::null` → $c = 1$
`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 of `snGrad`	no	`false`
`secondOrder`	Second-order `snGrad`	no	`false`
`value`	Initial patch value (read if present, otherwise uninitialised)	effectively yes	—

Usage

From tutorials/electrochemistry/NTGKBatteryWithTabs/0/posTabRegion/orig/partitioned/phiPos (jump side on the tab):

toCellFromPos
{
 type regionCoupledScalarJump;
 interfaceType (defaultInterface);
 diffusivity "sigma";
 accType aitken;
 relax 0.1;
 secondOrder false;
 nonOrthCorr false;
 value $internalField;
}

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

toPosTab
{
 type regionCoupledScalarFlux;
 interfaceType (defaultInterface);
 diffusivity "sigmaPos";
 secondOrder false;
 nonOrthCorr false;
 value $internalField;
 gradient uniform 0.1266;
}

Interface entry in constant/regionInterfaceProperties:

cellToPosTab
{
 interfaceType (defaultInterface);
 coupledPatchPair
 (
 (batteryRegion toPosTab)
 (posTabRegion toCellFromPos)
 );
 coupledFields
 (
 phiPos
 phiNeg
 T
 );
 defaultInterfaceCoeffs
 {}
}

and a DNA entry per coupled field in constant/multiRegionProperties:

DNA
{
 phiPos
 {
 maxCoupleIter 50;
 residualControl
 {
 maxJumpRes 1e-05;
 outputJumpResField no;
 maxFluxRes 1e-05;
 outputFluxResField no;
 }
 }
}

For a partition coefficient (e.g. Henry’s law $C_A = H\,C_B$), add jumpCoefficient H; and provide H either as a volScalarField on the jump-side region or as H H [0 0 0 0 0 0 0] 0.5; in its transportProperties.

Known Limitations

No interface-type check. Any interface type listed first in interfaceType is accepted. The interface’s own physics, if any, is not used, except that its correct() is called through update().
diffusivity must be set. The default word::null makes the diffCoeff() lookup in transportProperties fail as soon as the partner asks for flux().
Diffusivities are not checked for consistency. Each side uses whatever its diffusivity names (in NTGK, sigmaPos on the battery and sigma on the tab). Flux conservation requires the same units on both sides.
Jump coefficient is taken from the jump side only (local field or local transportProperties). With a volScalarField, the local patch values are used and not interpolated.
jumpCoefficient is not written by write(), so it disappears from written time directories and after decomposePar.
Inherited limitations of genericRegionCoupledJump: neighbourFieldName unused, side detection by patch name only, IQNILS not parallel-consistent, partitioned only.

Tutorials

Tutorial	Description
`tutorials/electrochemistry/NTGKBatteryWithTabs`	`batteryRegion (NTGK)` coupled to two `conductPotentialTemperature` tabs through `defaultInterface`. `phiPos`: jump side on the positive tab (`diffusivity sigma`, Aitken 0.1). `phiNeg`: jump side on the battery (`diffusivity sigmaNeg`, Aitken 0.75). `T`: jump side on the battery at both tabs (`diffusivity k`, Aitken 0.75). `directMap` transfer.

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