Source term method for preferential diffusion

[joshkellyjak]

Proposed Changes

Adds the resolved Eq. (14) preferential diffusion flux formulation (model B2 of
Schepers & van Oijen, C&F 280 (2025) 114332) to the flamelet scalar transport,
alongside the existing beta correction, and fixes two defects that leave the
current preferential diffusion model not merely inert but actively wrong.

Two fixes that affect develop today. CSpeciesFlameletVariable sizes
AuxVar and Grad_AuxVar to the four beta terms but never sets nAuxVar, so
SetAuxVar_Gradient_GG/LS loop zero times and every beta gradient stays zero.
The FGM model drives the diffusive flux of the controlling variables by
grad(beta) rather than by their own gradient (Bunschoten, Eqs. 2.8-2.10); the
solver reaches that from the generic scalar base class by adding
div(D grad(beta - phi)) to the ordinary div(D grad phi), which sums to
div(D grad beta). With the beta gradients zero that sum is zero, so the
controlling variables are left with no diffusion at all. Separately,
LEAST_SQUARES falls through the auxiliary gradient switch, with the same
consequence for anyone not on Green-Gauss.

New model. PREFERENTIAL_DIFFUSION_METHOD selects BETA_CORRECTION
(default, unchanged) or SOURCE_TERM. PREFERENTIAL_DIFFUSION_MAJOR_SPECIES
names the species carrying the resolved flux; the manifold variables
(Res_<cv>, Y-<sp>, D_<cv>_<sp>, DT_<cv>) are composed from the
configured controlling variable and species names rather than hard-coded, so one
set of strings describes the table on both sides. The Eq. (14) fluxes are a new
branch of CScalarFlux_Flamelet, driven by the CFD-resolved gradients of the
major species and of temperature — the point of tabulating a coefficient per
species instead of pre-contracting them against the one-dimensional flamelet
gradients. They are applied explicitly, with a stabilising self-diffusion added
to the Jacobian alone so the converged solution is untouched. The Eq. (16)
closure sources are gated on manifold validity only.

Also fixed. Soret coefficients are zeroed on viscous walls, where the
manifold carries no quench-layer data. A collective in the volume output ran
behind an iPoint == 0 test inside the per-point loop, so a rank owning no
points would have hung every other rank; it moves to a new per-write
COutput::PrepareVolumeData hook, where an empty partition contributes the
MIN/MAX identity elements instead of not participating. The cached preferential
diffusion source is cleared at off-manifold nodes, and the Newton
non-convergence message is rank-guarded.

Diagnostics. FLAME_QUALITY volume group (C+, chi_C, Da), hull-miss
deviations, FLAMELET_VERBOSE_MISSES, and per-location probe history files.

Validation

Laminar premixed H2 burner against an OpenFOAM FGM reference, on a manifold
whose progress variable is defined on the major species only.

• Reproduces the reference: converged residuals agree to ~3 decimals across all
  four equations; Temperature and Density agree with the reference
  implementation to 5-6 significant figures.
• Manifold misses drop from 592 to 1-2.
• Stabiliser: converged answer unchanged (residuals agree to 5-7 significant
  figures at CFL 1); CFL ceiling moves from (1, 2) without it to (2, 3) with it;
  misses hold at 1-2 across that range, against 1 -> 7 -> 49 without.

A chemical-activity gate on the closure sources was removed:
fmax(0, .) clipping meant it only closed where the tabulated source was
negative, so it closed at 320 preheat-zone nodes (304-567 K) while staying open
across 21k gradient-free bulk nodes — the inverse of its stated purpose.

Caveats

• The nAuxVar fix changes results for every existing BETA_CORRECTION
  user, including regression case 07, which runs the default method.
  Baselines will move. The fix is correct, but the new behaviour still needs
  validating on a manifold built for the beta formulation — on the
  SOURCE_TERM-oriented manifold used here, BETA_CORRECTION diverges.
• Wall Soret zeroing is a modelling choice, not a bug fix. It changes wall
  heat flux by up to 1.2% and wall temperature by 0.4 K, decaying to nothing
  within 0.5 mm. Justified by manifold support, not impermeability: the wall
  face carries no Eq. (14) flux in any case, since only interior edges are
  visited. What it changes is the near-wall interior edges, through the
  coefficient averaging.
• The CFL figures are case-specific — 100 iterations from a converged
  restart on this burner, with a coarse ladder (1, 2, 3). Treat ~1.5x as
  indicative, not a precise factor.
• The three manifold-miss gates were inert in every test (<= 1e-5 K on two
  different manifolds and two different flux discretizations). Retained as
  insurance against a poorly matched table, but unexercised.

Related Work

This work was developed on a branch that predates the rewrite of the flamelet
scalar transport into CScalarFlux_Flamelet / EdgeFluxResidual, and the flux
assembly was ported onto that framework rather than carried over. The port is
validated by reproducing the pre-port implementation's residuals to the digit
with the stabiliser disabled.

PR Checklist

• I am submitting my contribution to the develop branch.
• My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
• My contribution is commented and consistent with SU2 style (https://su2code.github.io/docs_v7/Style-Guide/).
• I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
• I have added a test case that demonstrates my contribution, if necessary.
• I have updated appropriate documentation (Tutorials, Docs Page, config_template.cpp), if necessary.

[bigfooted]

CScalarFlux_Flamelet::extraDiffusionTerms then evaluates grad(beta) - grad(phi) as -grad(phi), and res.flux_i -= D * projGrad adds back
+D*grad(phi) — cancelling the ordinary diffusion of the controlling variables
rather than correcting it

This is the correct behavior as described in Everts thesis, the ordinary diffusion should be cancelled, leaving only the beta correction term.
You could choose not to add the diffusion term in the first place.

[joshkellyjak]

CScalarFlux_Flamelet::extraDiffusionTerms then evaluates grad(beta) - grad(phi) as -grad(phi), and res.flux_i -= D * projGrad adds back
+D*grad(phi) — cancelling the ordinary diffusion of the controlling variables
rather than correcting it

This is the correct behavior as described in Everts thesis, the ordinary diffusion should be cancelled, leaving only the beta correction term. You could choose not to add the diffusion term in the first place.

This description is wrong the beta correction side is unchanged from develop other than the nAuxVar fix

[bigfooted]

OK, I checked what was really going on with the nAuxvar fix. This bug actually puts the cross-diffusion term of the gradient of beta to zero. On orthogonal meshes this nAuxvar contribution is zero.
So the preferential diffusion results on the testcases that we have in the regression tests are correct. I was a bit worried there... In any case it's a good fix.

[bigfooted]

OK, so I checked the paper of Stijn. So it's an extension of Nithin's paper for mixture averaged diffusion (instead of constant Lewis per species) and he adds Soret diffusion. And Stijn uses only major species and then has some truncation source term.
Can you also make Soret optional, it is usually neglected - and negligible.

[joshkellyjak]

OK, so I checked the paper of Stijn. So it's an extension of Nithin's paper for mixture averaged diffusion (instead of constant Lewis per species) and he adds Soret diffusion. And Stijn uses only major species and then has some truncation source term. Can you also make Soret optional, it is usually neglected - and negligible.

Yes, as the forthcoming PR to DataMiner will show, when you have a PV definition with non-major species you end up with some additional conservation term, relatively small to all other contributions but necessary for conservation

[bigfooted]

btw soret effect:
https://www.researchgate.net/publication/382507670_The_importance_of_Soret_effect_preferential_diffusion_and_conjugate_heat_transfer_for_flashback_limits_of_hydrogen-fueled_perforated_burners

https://eprints.soton.ac.uk/id/eprint/494934/1/1-s2.0-S1540748924003894-main.pdf

From Heinz's group

also good for validation study