From 1d26f1332f08f0db5887c5b64647f97412d19ae9 Mon Sep 17 00:00:00 2001 From: Allaun Silverfox <28494262+allaunthefox@users.noreply.github.com> Date: Tue, 19 May 2026 10:24:36 -0500 Subject: [PATCH] Add turbulence model atlas gate documentation --- .../famm/TURBULENCE_MODEL_ATLAS_GATE.md | 1421 +++++++++++++++++ 1 file changed, 1421 insertions(+) create mode 100644 6-Documentation/famm/TURBULENCE_MODEL_ATLAS_GATE.md diff --git a/6-Documentation/famm/TURBULENCE_MODEL_ATLAS_GATE.md b/6-Documentation/famm/TURBULENCE_MODEL_ATLAS_GATE.md new file mode 100644 index 00000000..35a368b7 --- /dev/null +++ b/6-Documentation/famm/TURBULENCE_MODEL_ATLAS_GATE.md @@ -0,0 +1,1421 @@ +# Turbulence Model Atlas Gate + +## Purpose + +Add the classical and modern turbulence-model family tree as an explicit model atlas for the FAMM / NUVMAP / 16D witness stack. + +This document imports turbulence models as **closure/witness gates**, not as solved proof objects. The goal is to let the Warden choose, compare, scar, or hybridize turbulence models by region rather than treating the turbulence-model hierarchy as a single fixed ladder. + +```text +flow region +→ model-family candidate +→ closure assumptions +→ physics retained +→ CPU / memory cost +→ unresolved residual +→ witness strength +→ FAMM scar or promotion +``` + +## Warden boundary + +Allowed claim: + +```text +The stack now has an explicit atlas of turbulence model families and can reason about their closure assumptions, cost/physics tradeoffs, residual risk, and 16D witness requirements. +``` + +Disallowed claim: + +```text +Adding the atlas proves a better turbulence closure, beats DNS/LES/RANS benchmarks, or solves Navier-Stokes regularity. +``` + +Hard rule: + +```text +A turbulence model is a witness projection, not the flow itself. +``` + +## Core taxonomy + +The old chart has a one-axis tradeoff: + +```text +more physics ↔ less CPU time +``` + +The project atlas expands it to: + +```text +physics retained +CPU / memory cost +closure assumption burden +wall treatment burden +unresolved residual +scar pressure +witness strength +region-of-validity guard +``` + +## Global packet + +```math +\Gamma_{\mathrm{turbulenceModel}} += +( +X_{\mathrm{flow}}, +\pi_{\mathrm{model}}, +W_{\mathrm{closure}}, +R_{\mathrm{residual}}, +I_{\mathrm{flow}}, +G_{\mathrm{validity}}, +K_{\mathrm{cost}}, +\epsilon +) +``` + +| Packet term | Meaning | +|---|---| +| `X_flow` | original turbulent flow region | +| `pi_model` | projection into DNS / LES / RANS / hybrid / algebraic model | +| `W_closure` | closure assumption or resolved-scale witness | +| `R_residual` | unresolved/subgrid/Reynolds-stress residual | +| `I_flow` | invariant/quantity to preserve: mass, momentum, energy, vorticity, wall shear, spectra, etc. | +| `G_validity` | assumptions: incompressible/compressible, wall-bounded/free shear, separated/attached, high/low Re, etc. | +| `K_cost` | CPU, memory, mesh, timestep, solver cost | +| `epsilon` | model error / closure gap / numerical residual | + +## 0. Exact / near-exact resolution family + +### DNS — Direct Numerical Simulation + +```text +DNS_EXACT_RESOLUTION_GATE +``` + +Purpose: + +```text +solve the Navier-Stokes equations while resolving all dynamically relevant scales down to dissipative scales +``` + +Project role: + +```text +highest-physics reference witness +brutal cost +benchmark / calibration source +not a practical everyday route for high-Re engineering flow +``` + +Warden checks: + +```text +mesh resolves Kolmogorov scale +proper timestep / CFL +numerical dissipation recorded +boundary conditions recorded +not called exact if discretization error is unbounded +``` + +### Filtered DNS / under-resolved DNS + +```text +FILTERED_DNS_WITNESS_GATE +``` + +Purpose: + +```text +DNS-like equations on a grid that may not fully resolve every scale; useful as data/witness but not full DNS +``` + +Project role: + +```text +calibration source with explicit resolution scar +``` + +## 1. LES family — spatially filtered turbulence + +### LES — Large Eddy Simulation + +```text +LES_FILTERED_SUBGRID_GATE +``` + +Purpose: + +```text +resolve large eddies, model subgrid-scale stresses +``` + +Canonical filtered form: + +```math +\partial_t \bar u_i + \bar u_j\partial_j\bar u_i += +-\frac{1}{\rho}\partial_i\bar p ++\nu\partial_{jj}\bar u_i +-\partial_j\tau_{ij}^{\mathrm{sgs}} +``` + +Subgrid stress: + +```math +\tau_{ij}^{\mathrm{sgs}} += +\overline{u_i u_j}-\bar u_i\bar u_j +``` + +Project role: + +```text +resolved-scale witness + subgrid residual channel +``` + +### Smagorinsky SGS model + +```text +SMAGORINSKY_SGS_GATE +``` + +```math +\nu_t=(C_s\Delta)^2|\bar S| +``` + +Role: + +```text +baseline eddy-viscosity subgrid closure +``` + +Scar risks: + +```text +over-dissipation +near-wall damping needed +poor transitional/backscatter behavior +``` + +### Dynamic Smagorinsky / Germano dynamic model + +```text +DYNAMIC_SMAGORINSKY_SGS_GATE +``` + +Role: + +```text +computes local coefficient from test filtering rather than fixed coefficient +``` + +Scar risks: + +```text +coefficient noise +averaging choices +negative eddy viscosity / stability handling +``` + +### WALE — Wall-Adapting Local Eddy-viscosity + +```text +WALE_SGS_GATE +``` + +Role: + +```text +near-wall LES subgrid model using local velocity-gradient invariants +``` + +Good for: + +```text +wall-bounded LES without ad-hoc damping in many cases +``` + +### Vreman SGS model + +```text +VREMAN_SGS_GATE +``` + +Role: + +```text +algebraic SGS closure designed to vanish in certain laminar/shear cases and behave robustly near walls +``` + +### Sigma SGS model + +```text +SIGMA_SGS_GATE +``` + +Role: + +```text +SGS model based on singular values of velocity-gradient tensor +``` + +### One-equation SGS kinetic-energy model + +```text +ONE_EQUATION_SGS_K_GATE +``` + +Role: + +```text +transport subgrid kinetic energy and derive eddy viscosity from it +``` + +### Mixed / similarity / Bardina model + +```text +BARDINA_SIMILARITY_SGS_GATE +MIXED_SGS_GATE +``` + +Role: + +```text +use scale similarity and/or combine similarity with eddy viscosity +``` + +Scar risks: + +```text +stability +backscatter control +need explicit residual/witness monitoring +``` + +### Clark gradient model + +```text +CLARK_GRADIENT_SGS_GATE +``` + +Role: + +```text +Taylor/gradient expansion of subgrid stress +``` + +### Approximate deconvolution model + +```text +APPROXIMATE_DECONVOLUTION_SGS_GATE +``` + +Role: + +```text +approximate unfiltered field from filtered field, then model SGS contribution +``` + +### Coherent Structure / Structure-function SGS models + +```text +COHERENT_STRUCTURE_SGS_GATE +STRUCTURE_FUNCTION_SGS_GATE +``` + +Role: + +```text +subgrid closure based on coherent vortical structures or local structure functions +``` + +### ILES / MILES — implicit LES + +```text +IMPLICIT_LES_NUMERICAL_SGS_GATE +MILES_GATE +``` + +Role: + +```text +use numerical dissipation of the scheme as implicit SGS model +``` + +Warden check: + +```text +numerical viscosity is the model; it must be measured, not ignored +``` + +## 2. Hybrid RANS / LES and scale-resolving simulation + +### DES — Detached Eddy Simulation + +```text +DES_HYBRID_RANS_LES_GATE +``` + +Purpose: + +```text +RANS near attached boundary layers, LES in separated regions +``` + +Role: + +```text +region-router between modeled and resolved turbulence +``` + +Scar risks: + +```text +grid-induced separation +gray-area behavior +incorrect shielding of boundary layer +``` + +### DDES — Delayed Detached Eddy Simulation + +```text +DDES_HYBRID_GATE +``` + +Role: + +```text +DES with shielding to delay LES activation in attached boundary layers +``` + +### IDDES — Improved Delayed Detached Eddy Simulation + +```text +IDDES_HYBRID_GATE +``` + +Role: + +```text +improved near-wall / wall-modeled LES and RANS-LES blending behavior +``` + +### ZDES — Zonal DES + +```text +ZONAL_DES_GATE +``` + +Role: + +```text +explicitly prescribe RANS/LES zones by region +``` + +### SAS — Scale-Adaptive Simulation + +```text +SAS_SCALE_ADAPTIVE_GATE +``` + +Role: + +```text +allows resolved unsteadiness based on local flow scale, often from RANS base model +``` + +### PANS — Partially Averaged Navier-Stokes + +```text +PANS_PARTIALLY_AVERAGED_GATE +``` + +Role: + +```text +continuous bridge between RANS and DNS/LES by choosing unresolved kinetic-energy fraction +``` + +### PITM — Partially Integrated Transport Model + +```text +PITM_PARTIALLY_INTEGRATED_GATE +``` + +Role: + +```text +scale-resolving hybrid based on partial integration of turbulence spectrum/transport +``` + +### VLES — Very Large Eddy Simulation + +```text +VLES_GATE +``` + +Role: + +```text +resolve very-large structures, model more of the spectrum than LES +``` + +### XLES / X-RANS variants + +```text +XLES_GATE +X_RANS_GATE +``` + +Role: + +```text +hybrid scale-resolving variants between RANS and LES +``` + +### WMLES — Wall-Modeled LES + +```text +WALL_MODELED_LES_GATE +``` + +Role: + +```text +LES in outer layer plus wall model to avoid resolving viscous sublayer +``` + +## 3. RANS family — Reynolds averaging closures + +RANS decomposes velocity into mean plus fluctuation: + +```math +u_i = \overline{u_i}+u_i' +``` + +and produces Reynolds stress: + +```math +R_{ij}=\overline{u_i'u_j'} +``` + +Mean equation: + +```math +\partial_t\overline{u_i} ++ +\overline{u_j}\partial_j\overline{u_i} += +-\frac{1}{\rho}\partial_i\overline p ++\nu\partial_{jj}\overline{u_i} +-\partial_j R_{ij} +``` + +Closure problem: + +```text +model R_ij +``` + +### Linear eddy-viscosity / Boussinesq assumption + +```text +BOUSSINESQ_EDDY_VISCOSITY_GATE +``` + +```math +-R_{ij} += +2\nu_t\overline S_{ij} +- +\frac{2}{3}k\delta_{ij} +``` + +Role: + +```text +assume turbulent stresses align with mean strain +``` + +Scar risks: + +```text +anisotropy +curvature +rotation +separation +secondary flows +strong strain history +``` + +## 4. Zero-equation / algebraic closures + +### Prandtl mixing-length model + +```text +PRANDTL_MIXING_LENGTH_GATE +``` + +```math +\nu_t=l_m^2\left|\frac{dU}{dy}\right| +``` + +Role: + +```text +simple wall/shear eddy-viscosity estimate +``` + +### Cebeci-Smith algebraic model + +```text +CEBECI_SMITH_ALGEBRAIC_GATE +``` + +Role: + +```text +algebraic boundary-layer eddy-viscosity model with inner/outer formulation +``` + +### Baldwin-Lomax algebraic model + +```text +BALDWIN_LOMAX_ALGEBRAIC_GATE +``` + +Role: + +```text +classic algebraic model for attached aerodynamic boundary layers +``` + +### Van Driest damping / wall damping functions + +```text +VAN_DRIEST_DAMPING_GATE +``` + +Role: + +```text +near-wall damping correction for mixing-length/eddy-viscosity models +``` + +## 5. One-equation RANS closures + +### Spalart-Allmaras model + +```text +SPALART_ALLMARAS_ONE_EQUATION_GATE +``` + +Role: + +```text +transport a modified turbulent viscosity variable; common for external aerodynamic boundary layers +``` + +Project role: + +```text +cheap RANS closure with better physical content than algebraic models +``` + +Scar risks: + +```text +massive separation +complex recirculation +strong anisotropy +non-equilibrium turbulence +``` + +### Baldwin-Barth one-equation model + +```text +BALDWIN_BARTH_ONE_EQUATION_GATE +``` + +Role: + +```text +older one-equation eddy-viscosity model for aerodynamic applications +``` + +## 6. Two-equation RANS closures + +### Standard k-epsilon + +```text +K_EPSILON_STANDARD_GATE +``` + +Variables: + +```text +k = turbulent kinetic energy +ε = dissipation rate +``` + +Eddy viscosity: + +```math +\nu_t=C_\mu\frac{k^2}{\epsilon} +``` + +Role: + +```text +robust industrial free-shear / many engineering flows +``` + +Scar risks: + +```text +near-wall treatment +adverse pressure gradient +strong separation +curvature/rotation +``` + +### RNG k-epsilon + +```text +K_EPSILON_RNG_GATE +``` + +Role: + +```text +renormalization-group motivated k-epsilon variant with improved strain/curvature behavior in some regimes +``` + +### Realizable k-epsilon + +```text +K_EPSILON_REALIZABLE_GATE +``` + +Role: + +```text +variant designed to satisfy certain mathematical realizability constraints on Reynolds stresses +``` + +### Low-Re k-epsilon variants + +```text +LOW_RE_K_EPSILON_GATE +``` + +Role: + +```text +resolve near-wall region with damping functions / low-Re corrections +``` + +### Standard k-omega / Wilcox k-omega + +```text +K_OMEGA_STANDARD_GATE +``` + +Variables: + +```text +k = turbulent kinetic energy +ω = specific dissipation rate +``` + +Eddy viscosity: + +```math +\nu_t=\frac{k}{\omega} +``` + +Role: + +```text +strong near-wall behavior; sensitive to free-stream ω +``` + +### SST k-omega — Menter Shear-Stress Transport + +```text +K_OMEGA_SST_GATE +``` + +Role: + +```text +blends k-omega near wall with k-epsilon-like behavior away from wall; includes shear-stress limiter +``` + +Project role: + +```text +industrial default candidate for adverse-pressure-gradient and separated aerodynamic flows +``` + +### Baseline k-omega / BSL + +```text +K_OMEGA_BSL_GATE +``` + +Role: + +```text +blended k-omega/k-epsilon baseline without full SST limiter behavior +``` + +### k-kl-omega transition model + +```text +K_KL_OMEGA_TRANSITION_GATE +``` + +Role: + +```text +three-equation transition-sensitive model using laminar kinetic energy plus k/omega variables +``` + +### k-tau / k-zeta / related two-equation variants + +```text +K_TAU_VARIANT_GATE +K_ZETA_VARIANT_GATE +``` + +Role: + +```text +alternative time-scale or variable transformations of two-equation turbulence closures +``` + +## 7. Three-/four-equation and transition closures + +### v2-f model + +```text +V2_F_GATE +``` + +Role: + +```text +near-wall turbulence anisotropy and wall-normal velocity scale model, often four-equation +``` + +### ζ-f / zeta-f model + +```text +ZETA_F_GATE +``` + +Role: + +```text +elliptic relaxation / wall-blocking inspired variant using velocity-scale ratio +``` + +### Intermittency / gamma-Re-theta transition model + +```text +GAMMA_RE_THETA_TRANSITION_GATE +``` + +Role: + +```text +transition model with intermittency and transition momentum-thickness Reynolds number variables +``` + +### e^N / boundary-layer transition method + +```text +E_N_TRANSITION_GATE +``` + +Role: + +```text +linear stability / amplification-factor transition prediction, often coupled to boundary-layer/RANS methods +``` + +### Langtry-Menter transition model + +```text +LANGTRY_MENTER_TRANSITION_GATE +``` + +Role: + +```text +correlation-based transition model often used with SST +``` + +## 8. Reynolds Stress Transport Models + +### RSM / RSTM — Reynolds Stress Model + +```text +REYNOLDS_STRESS_MODEL_GATE +``` + +Purpose: + +```text +solve transport equations for individual Reynolds stress tensor components plus scale equation +``` + +Role: + +```text +higher-physics RANS closure; avoids simple Boussinesq alignment assumption +``` + +Classic chart note: + +```text +roughly 7 additional PDEs in common formulations +``` + +Scar risks: + +```text +pressure-strain closure +wall reflection terms +numerical stiffness +boundary conditions +model constants +``` + +### LRR Reynolds stress model + +```text +LRR_REYNOLDS_STRESS_GATE +``` + +Role: + +```text +Launder-Reece-Rodi style pressure-strain closure family +``` + +### SSG Reynolds stress model + +```text +SSG_REYNOLDS_STRESS_GATE +``` + +Role: + +```text +Speziale-Sarkar-Gatski nonlinear pressure-strain closure family +``` + +### Elliptic blending Reynolds stress models + +```text +ELLIPTIC_BLEND_RSM_GATE +``` + +Role: + +```text +near-wall anisotropy and wall-blocking behavior using elliptic blending/relaxation ideas +``` + +## 9. Nonlinear eddy-viscosity / algebraic stress models + +### Nonlinear Eddy Viscosity Models + +```text +NONLINEAR_EDDY_VISCOSITY_GATE +``` + +Role: + +```text +extend Boussinesq model with nonlinear strain/rotation tensor terms +``` + +### Explicit Algebraic Reynolds Stress Models — EARSM + +```text +EARSM_GATE +``` + +Role: + +```text +approximate Reynolds stress anisotropy algebraically from strain/rotation invariants, often derived from RSM equilibrium assumptions +``` + +### Quadratic / cubic constitutive relation models + +```text +QUADRATIC_CUBIC_STRESS_CLOSURE_GATE +``` + +Role: + +```text +higher-order tensor polynomial stress-strain closures +``` + +## 10. Compressible / high-speed turbulence additions + +### Compressibility corrections + +```text +COMPRESSIBILITY_CORRECTION_GATE +``` + +Role: + +```text +modify RANS/LES closures for dilatation, turbulent Mach number, shock interaction +``` + +### Shock-unsteadiness / shock-capturing scar gate + +```text +SHOCK_TURBULENCE_INTERACTION_GATE +``` + +Role: + +```text +flag regions where shock/turbulence coupling makes closure assumptions fragile +``` + +### Morkovin-hypothesis guard + +```text +MORKOVIN_GUARD_GATE +``` + +Role: + +```text +records whether compressible boundary layer assumptions are expected to be valid +``` + +## 11. Multiphase / reacting / MHD turbulence closures + +These are not one universal closure; they are model families layered on top of turbulence closures. + +### Scalar flux / turbulent Prandtl-Schmidt closures + +```text +TURBULENT_PRANDTL_SCHMIDT_GATE +``` + +Role: + +```text +model turbulent transport of heat/species/scalars +``` + +### Combustion turbulence closures + +```text +TURBULENCE_CHEMISTRY_INTERACTION_GATE +EDC_COMBUSTION_GATE +FLAMELET_TURBULENCE_GATE +PDF_COMBUSTION_TURBULENCE_GATE +``` + +Role: + +```text +model turbulence-chemistry interaction; separate Warden guard from pure flow closure +``` + +### Multiphase turbulence closures + +```text +MULTIPHASE_TURBULENCE_GATE +TWO_FLUID_TURBULENCE_GATE +DISPERSED_PHASE_TURBULENCE_GATE +``` + +Role: + +```text +turbulence modulation by particles/bubbles/droplets and interphase coupling +``` + +### MHD turbulence closures + +```text +MHD_TURBULENCE_GATE +ALFVENIC_TURBULENCE_WITNESS_GATE +``` + +Role: + +```text +magnetohydrodynamic turbulence; links to plasma chiral drag and Alfvén-wave witness channels +``` + +## 12. Reduced-order / data-driven turbulence models + +These must be treated as model-augmentation gates, not automatic truth. + +### POD / Galerkin reduced-order models + +```text +POD_GALERKIN_ROM_GATE +``` + +Role: + +```text +low-dimensional basis for flow reconstruction/control +``` + +### DMD / Koopman models + +```text +DMD_KOOPMAN_TURBULENCE_GATE +``` + +Role: + +```text +modal time-evolution and recurrence witness +``` + +### Neural turbulence closures + +```text +NEURAL_TURBULENCE_CLOSURE_GATE +``` + +Role: + +```text +learn subgrid, RANS closure, correction, or wall model from data +``` + +Warden checks: + +```text +training distribution +generalization regime +physical constraints +invariance +stability +uncertainty +out-of-distribution flags +``` + +### Symbolic-regression closures + +```text +SYMBOLIC_REGRESSION_CLOSURE_GATE +``` + +Role: + +```text +learn explicit algebraic/tensor closure forms that can be inspected and receipted +``` + +### Bayesian / UQ turbulence model calibration + +```text +BAYESIAN_TURBULENCE_CALIBRATION_GATE +UQ_TURBULENCE_MODEL_GATE +``` + +Role: + +```text +parameter uncertainty, model-form uncertainty, posterior closure calibration +``` + +## 13. Wall-treatment atlas + +Wall models are often as important as the turbulence model itself. + +```text +WALL_FUNCTION_GATE +ENHANCED_WALL_TREATMENT_GATE +LOW_RE_WALL_RESOLVED_GATE +TWO_LAYER_WALL_MODEL_GATE +EQUILIBRIUM_WALL_MODEL_GATE +NON_EQUILIBRIUM_WALL_MODEL_GATE +SLIP_WALL_MODEL_GATE +``` + +Warden checks: + +```text +y+ range +wall shear target +separation / pressure gradient +roughness +heat transfer +wall curvature +mesh resolution +``` + +## 14. Project-specific witness closures + +These are the project's additions on top of classical models. + +### 16D FAMM witness closure + +```text +FAMM_16D_WITNESS_CLOSURE_GATE +``` + +Purpose: + +```text +augment classical turbulence model with 16D audit packet: geometry, torsion, chirality, semantic/witness mass, recurrence, delta memory, scars, residuals, invariant overlap, route cost, receipt strength +``` + +Role: + +```text +not a replacement closure by itself; an audit/control layer for where a closure is safe or blind +``` + +### Shadow Control Gap Map + +```text +SHADOW_CONTROL_GAP_TURBULENCE_GATE +``` + +Purpose: + +```text +explicitly record where the witness packet does not control the dangerous term +``` + +3D danger term: + +```math +(\omega\cdot\nabla)u +``` + +Gap shape: + +```math +\mathcal S_{\mathrm{gap}} += +\left[ +\| (\omega\cdot\nabla)u\|_{\mathrm{unwitnessed}} +- +C\,\mathcal W_{16D} +\right]_+ +``` + +### Photonic / Burgers residual witness + +```text +PHOTONIC_BURGERS_RESIDUAL_WITNESS_GATE +``` + +Purpose: + +```text +use fixed-point Burgers/triad solver plus external/stochastic witness channel as unresolved-mode indicator +``` + +### Plasma chiral drag / Alfvénic witness + +```text +PLASMA_CHIRAL_DRAG_TURBULENCE_WITNESS_GATE +``` + +Purpose: + +```text +use chiral/Alfvénic wave rotation as signed torsion/witness receipt in MHD-like regions +``` + +### OR-Tools regional model scheduler + +```text +OR_TOOLS_TURBULENCE_REGION_SCHEDULER_GATE +``` + +Purpose: + +```text +choose which turbulence model applies to which mesh region under budget and risk constraints +``` + +Decision variables: + +```text +x_region_model = 1 if model m is selected for region r +``` + +Objective: + +```text +minimize CPU cost + residual risk + scar pressure +maximize witness strength + invariant coverage +``` + +Constraints: + +```text +budget ≤ B +wall regions must satisfy wall-treatment guard +high-gap regions cannot use algebraic-only closure +scarred closures blocked unless explicitly reopened +DNS/LES only where mesh/time budget supports them +``` + +## FAMM residual score for any turbulence model + +```math +R_{\mathrm{model}} += +\lambda_1 R_{\mathrm{closure}} ++ +\lambda_2 R_{\mathrm{wall}} ++ +\lambda_3 R_{\mathrm{grid}} ++ +\lambda_4 R_{\mathrm{time}} ++ +\lambda_5 R_{\mathrm{invariant}} ++ +\lambda_6 \Omega_{\mathrm{scar}} +``` + +Promotion condition: + +```math +R_{\mathrm{model}}\le\Theta_{\mathrm{region}} +``` + +## Suggested region routing + +| Region / flow situation | Candidate model family | Warden caution | +|---|---|---| +| low-Re benchmark / small domain | DNS | cost explosion at high Re | +| separated unsteady flow | LES / DES / IDDES / SAS | grid and gray-area scars | +| attached aerodynamic boundary layer | SA / SST / algebraic if simple | adverse pressure gradient scars | +| industrial steady approximation | k-epsilon / SST / RSM | closure validity by regime | +| strong anisotropy / swirl / curvature | RSM / EARSM / nonlinear EVM | pressure-strain/model constants | +| near-wall heat transfer | low-Re / wall-resolved / enhanced wall | y+ and thermal wall functions | +| transition-sensitive flow | gamma-Re-theta / e^N / k-kl-omega | transition correlation domain | +| compressible/shock flow | compressible corrections + shock gate | shock/turbulence interaction scars | +| MHD/plasma-like flow | MHD turbulence + Alfvén witness | coupling assumptions | +| constrained compute browser/demo | algebraic / SA / reduced-order | never call it full physics | + +## Stack placement + +```text +TURBULENCE_MODEL_ATLAS_GATE +→ DNS / LES / RANS / hybrid / algebraic model candidates +→ 16D Shell Atlas / PathEpigenetic gate / Chaos Game shrinker +→ FAMM shadow-gap audit +→ OR-Tools regional scheduler +→ Anti-FAMM closure-blindness attack +→ NUVMAP route memory +→ Warden promote / scar / reopen +``` + +## Anti-FAMM checks + +For every turbulence model, Anti-FAMM asks: + +```text +What term did the closure hide? +Where does the model look stable while the dangerous physics escapes? +Which wall/mesh/time guard failed? +Is the model outside its calibration regime? +Did numerical dissipation masquerade as physics? +Did the residual move into an unobserved shadow channel? +``` + +## Best project sentence + +The turbulence model atlas converts DNS, LES, DES, RANS, Reynolds-stress, k-epsilon, k-omega, Spalart-Allmaras, algebraic, transition, wall, compressible, multiphase, MHD, and data-driven closures into explicit witness gates. The Warden no longer asks only which model has more physics or less CPU cost; it asks which regional closure preserves the necessary invariants, exposes its unresolved residual, satisfies its wall/grid/validity guards, and carries enough 16D/FAMM witness strength to be promoted. + +## References + +```bibtex +@book{pope2000turbulent, + title = {Turbulent Flows}, + author = {Pope, Stephen B.}, + publisher = {Cambridge University Press}, + year = {2000} +} + +@book{wilcox2006turbulence, + title = {Turbulence Modeling for CFD}, + author = {Wilcox, David C.}, + publisher = {DCW Industries}, + year = {2006} +} + +@article{spalart1992one, + title = {A one-equation turbulence model for aerodynamic flows}, + author = {Spalart, P. R. and Allmaras, S. R.}, + journal = {AIAA Paper 92-0439}, + year = {1992} +} + +@article{menter1994two, + title = {Two-equation eddy-viscosity turbulence models for engineering applications}, + author = {Menter, F. R.}, + journal = {AIAA Journal}, + volume = {32}, + number = {8}, + pages = {1598--1605}, + year = {1994} +} + +@article{smagorinsky1963general, + title = {General circulation experiments with the primitive equations}, + author = {Smagorinsky, Joseph}, + journal = {Monthly Weather Review}, + volume = {91}, + number = {3}, + pages = {99--164}, + year = {1963} +} + +@article{germano1991dynamic, + title = {A dynamic subgrid-scale eddy viscosity model}, + author = {Germano, M. and Piomelli, U. and Moin, P. and Cabot, W. H.}, + journal = {Physics of Fluids A}, + volume = {3}, + number = {7}, + pages = {1760--1765}, + year = {1991} +} + +@article{spalart1997comments, + title = {Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach}, + author = {Spalart, P. R. and Jou, W.-H. and Strelets, M. and Allmaras, S. R.}, + journal = {Advances in DNS/LES}, + year = {1997} +} + +@article{launder1975progress, + title = {Progress in the development of a Reynolds-stress turbulence closure}, + author = {Launder, B. E. and Reece, G. J. and Rodi, W.}, + journal = {Journal of Fluid Mechanics}, + volume = {68}, + number = {3}, + pages = {537--566}, + year = {1975} +} +```