Viscous face spectral radius (model 3)

Purpose

Model 3 is the cheapest viscous spectral placeholder:

\[\lambda_{\mathrm{vis}}=\frac{A^{2}}{\mathrm{Re}\,\rho}\]

Family overview: Viscous face spectral radius (overview).

Formula and rationale

Only geometry (\(A\)), density, and Reynolds number enter. Dynamic viscosity is not explicit: viscous magnitude is assumed absorbed into the non-dimensional (mathrm{Re}) scaling. This is useful as a robust fallback or when a full (mu,mathrm{Pr}) field is unavailable.

It still scales as :math:`A^{2}), consistent with a (ksim A/V) diffusion argument, but without the (max(c_1,c_2)) structure of model 1.

Source map

  • ViscousFaceSpectralRadiusModel3 in TimeStepPolicy

  • Existing unit test: TimeStepPolicy.ViscousFaceSpectralRadiusModel3IsArea2OverReRho

  • Theory table: tools/verification/data/viscous_spectral_radius_model3_theory.csv

  • Contract Workbench id: viscous_spectral_radius_model3

Viscous spectral radius model3 vs area

What this proves / does not prove

Proves: (A^{2}/(mathrm{Re}rho)) algebra matches the pure API.

Does not prove: adequacy for high-(mu_t) boundary layers (model 1 is preferred when viscosities are known).

References

  • Degenerate limit of area-squared viscous estimates when the diffusivity prefactor is absorbed into (mathrm{Re}) (engineering simplification; not a separate classical theorem).

  • Blazek (same time-step chapters) motivates including viscous spectral radii; model 3 is OneFLOW’s minimal realization of that requirement.

  • Family overview: Viscous face spectral radius (overview).