Roe average state

Roe-type inviscid fluxes evaluate dissipation at an intermediate state. The density is a geometric mean; other scalars use the Roe density-weighted average.

Formulas

\[r = \sqrt{\frac{\rho_R}{\rho_L}},\qquad c = \frac{1}{1+r}\]
\[\rho_m = \sqrt{\rho_L\rho_R},\qquad \phi_m = (\phi_L + \phi_R\, r)\, c \quad (\phi \in \{u,v,w,p,h,\gamma\})\]

Pipeline role

left/right primitives + total enthalpies
     |
     +--> RoeAverageState -> (rho,u,v,w,p,h,gamma)_m
     +--> sound speed / eigenvalues at mid state
     +--> physical flux + Roe dissipation
     +--> residual deposit

Pure APIs: RoeAverageWeights, RoeAverageComponent, RoeAverageState (NsInvFluxPolicy.h). Tests: inv_flux_policy_test.

LUSGS face-state closure

The face state prepared by UNsLusgs::PrepareDataFacePrim() has a solver-specific use. In NsLusgs::GetStandardFluxIncrement(), the prepared face state is consumed by CalcFaceEigenValue() to estimate the face spectral radius. It is not used there to recompute the steady physical flux residual. The resulting eigenvalue participates in the implicit LUSGS correction. The current PrepareData() path subsequently assigns nslu.gama from the right cell, and CalcFaceEigenValue() uses that value for the face sound speed. Thus the pressure closure uses left-cell gamma while this eigenvalue calculation uses right-cell gamma. This is existing behavior worth preserving in compatibility tests and auditing separately for variable-gamma flows; it should not be silently normalized as part of an unrelated refactor.

The current compressible unstructured LUSGS implementation first computes the Roe-weighted total enthalpy and velocity, then closes pressure using the left-cell heat-capacity ratio:

\[p_m^{H} = \rho_m \left(H_m - \frac{1}{2}|\mathbf{u}_m|^2\right) \frac{\gamma_L-1}{\gamma_L}\]

A weighted static-pressure alternative is:

\[p_m^{p} = \frac{p_L + r p_R}{1+r}\]

These expressions are not algebraically equivalent in general. For example, with left state (rho=1, p=1, u=0), right state (rho=4, p=4, u=3), and gamma=1.4, the current enthalpy closure gives 18/7, while the weighted static pressure gives 3.

The difference changes the face sound speed and therefore the implicit spectral-radius estimate. Since this face state is used in the LUSGS linearization/preconditioning path, a different intermediate residual history does not by itself prove that the underlying steady discretization has changed or that one closure is mathematically wrong. If both iterations converge to the same root of the same residual equations, their final solutions may agree even when their iteration paths differ.

This is a hypothesis to verify, not an assertion that both choices are equally robust. A meaningful A/B study should keep the mesh, physical residual, boundary conditions, initialization, and convergence criteria fixed, then compare:

  • residual histories and convergence rates, not just one intermediate file;

  • whether both runs reach the same converged residual level;

  • conservative variables and derived quantities such as lift and drag;

  • conservation balance and sensitivity to CFL, initialization, and mesh.

The compressible unstructured LUSGS closure can be selected with the optional integer parameter lusgsFacePressureMode in cfd.txt:

  • 0 (default): reconstruct pressure from Roe-averaged total enthalpy, preserving the established behavior. Older case files that omit the key also use this mode.

  • 1: use the Roe density-weighted average of the left and right static pressures.

Only the mean-flow UNsLusgs face-state preparation reads this switch. The separate turbulence-equation LUSGS implementation and the incompressible solver are not changed by this option. An invalid value or a non-scalar/non-integer entry is reported as a configuration error. The database storage and case-file grammar are unchanged; the key is optional at runtime.

Regression result files serve a different purpose: they pin the established numerical behavior for compatibility. The unit test for RoePressureFromTotalEnthalpy verifies the selected algebraic closure; it does not establish that a weighted-static-pressure closure is universally invalid. Any intentional change of closure should therefore be evaluated as a numerical-method change, with convergence and solution comparisons, rather than silently redefining the compatibility baseline.