15  Physical models

Flow equations, regime, and turbulence

15.1 What this setting is

Physical models declare which flow phenomena Wake CFD calculates. Select inviscid Euler or viscous Navier–Stokes, the compressibility regime, and the turbulence model here. These choices affect the required mesh resolution and how results are interpreted, so first assess the Reynolds number and the presence of shocks, boundary layers, and separation.

15.2 Configure in the GUI

Figure 15.1: The Models dialog for a compressible Navier–Stokes case using the Spalart–Allmaras turbulence model. Model-specific controls appear after the turbulence model is selected.

The Desktop currently authors the DBNS model path. PBNS and FR can be configured through JSONC, though their solver choices are disabled in the Desktop Analysis dialog. The Models dialog writes its available choices to the models block.

GUI control	Input key	What to choose
Regime	models.regime	Compressible for DBNS. The dialog disables incompressible while DBNS is selected.
Physics	models.type	Euler for inviscid flow; Navier–Stokes for viscous flow.
Turbulence → Model	models.turbulence.model	With Navier–Stokes, choose Laminar (none), SA, or SST. Other listed models are disabled.
SA controls	models.turbulence.sa.*	Variant, S̃ form, ft2, QCR2000, and rotation correction appear when SA is selected.
SST controls	models.turbulence.sst.*	Variant and production form appear when SST is selected.

models.axisymmetric, wall-treatment constants, and closure-constant overrides are not exposed in this dialog. Set them in JSONC when needed; the accepted values and restrictions are described below. The JSONC examples come after the model choices.

15.3 type

Value	Meaning
euler	Inviscid flow.
navier_stokes	Viscous flow; turbulence distinguishes laminar from RANS.

15.4 regime

Value	Meaning
compressible (default)	Available with DBNS, PBNS, and FR; use a gas-law equation of state.
incompressible	PBNS constant-density flow or FR artificial compressibility (AC). DBNS rejects it; fluid materials must use eos.type: "constant_density".

PBNS is not inherently incompressible: its default regime is compressible. For incompressible PBNS, use velocity_inlet and pressure_outlet rather than farfield or a total-conditions inlet. FR AC requires numerical_method.fr.ac_zeta > 0 and dual-time stepping; see Numerical methods. The freesurface enum value parses but is rejected before the run: regime=freesurface is under development and not available yet.

The energy equation follows from the regime and is not a separate key. A compressible case carries the total-energy equation, including pressure work and, for viscous flow, viscous work. Incompressible PBNS and FR AC carry no energy equation: PBNS keeps temperature at its initial value and FR AC has no temperature state, so an isothermal or heat-flux wall is rejected there. Setting numerical_method.pbns.coupling.energy.max_iter to 0 is not a way to freeze temperature in compressible PBNS; it is rejected.

models.gravity is reserved and rejected if supplied, even as false.

15.5 axisymmetric

axisymmetric enables the 2D, no-swirl body-of-revolution formulation. The mesh uses x as the axis and y as the radius, so every mesh coordinate must have y ≥ 0; define the axis itself as a symmetry boundary. It is not a post-processing revolution of a planar solution: Wake CFD adds the axisymmetric source terms and uses ring measures for applicable surface quantities.

Key	Values	Default	Use
axisymmetric	false, true	false	Enable the 2D axisymmetric, no-swirl formulation.

Wake CFD validates this mode before a run starts. It requires a 2D wake_2d_<tier> build, analysis.dimension: 2, analysis.solver: "dbns", and regime: "compressible". Euler, laminar Navier–Stokes, SA, and SST are available. Multigrid, PBNS, FR, rotating domains, interfaces, wall functions, and SA-QCR2000 are rejected rather than treated as planar cases.

For a body of revolution, force monitors must be axial (direction: [1, 0, 0] or [-1, 0, 0]), and moment monitors are not meaningful. These limits are intentional: radial and lateral components cancel over a full revolution.

15.6 turbulence

turbulence.model selects the turbulence model; model-specific subblocks (sa, sst) override closure constants. Omitted constants use the solver’s baseline defaults.

15.6.1 model

Value	Meaning
none	Laminar Navier–Stokes or inviscid Euler.
sa	Spalart–Allmaras RANS.
sst	k-ω SST RANS.

Use sa or sst with viscous DBNS. PBNS has no turbulence equations and rejects these models; FR does not use these RANS models. Other model names visible in the schema or disabled in the GUI are not implemented and are rejected rather than silently falling back to laminar flow.

15.6.2 Model-constant overrides

15.6.2.1 SA (Spalart-Allmaras)

variant, shat_form, and ft2 are covered below; cfl_reduction has its own section. All fields are optional.

Key	Default	Meaning
variant	standard	Negative ν̃ handling; neg enables SA-neg.
shat_form	blend2012	S̃ safeguard; floor is also available.
ft2	false	Classic SA laminar-suppression term.
cv1	7.1	Viscous sublayer correction.
cb1, cb2	0.1355, 0.622	Production and diffusion constants.
sigma, kappa	2/3, 0.41	Diffusion denominator and von Kármán constant.
cw2, cw3	0.3, 2.0	Destruction constants.
cn1	16.0	SA-neg negative-branch constant.
ct3, ct4	1.2, 0.5	ft2 constants; ct3 also enters the SA-neg negative branch.
c2, c3	0.7, 0.9	S̄ limiter constants.
r_max	10.0	Upper bound on r.
prandtl_turb	0.9	Turbulent Prandtl number of the energy closure.
cfl_reduction	1.0	Factor on the SA pseudo-time step.
qcr2000	false	Anisotropic QCR2000 stress correction; not with axisymmetry.
rotation_correction	false	SA rotation/curvature correction.

15.6.2.2 variant: treatment of negative ν̃

variant	Meaning
standard (default)	Disallows negative ν̃; clips with max(ν̃, 0) after update
neg	SA-neg (Allmaras 2012); permits negative values with a negative-source branch and fn diffusion correction

For solutions converging to ν̃ ≥ 0, the two variants are theoretically equivalent. neg is a robustness extension.

Note

The noft2 variant was renamed standard. The ft2 term is now a separate ft2 boolean, independent of variant. edwards was removed from the enum to prevent silent fallback from a stub implementation.

15.6.2.3 ft2: laminar-suppression term

With ft2: true, the source term includes ft2 = ct3·exp(−ct4·χ²) (classic SA). The default false corresponds to SA-noft2.

Combinations of variant and ft2 correspond to names used in the literature.

Combination	Literature name
standard + ft2: false	SA-noft2
standard + ft2: true	classic SA
neg + ft2: true	SA-neg (complete 2012 form)

15.6.2.4 shat_form: form preventing negative S̃

Value	Meaning
blend2012 (default)	Allmaras 2012 smooth c2/c3 blend; standard for SA-neg
floor	Simple floor max(Ω + S̄, ε) for reproducing classic reference data

Using floor with neg is a nonstandard combination and emits a warning.

15.6.2.5 cfl_reduction

dt_sa = dt_flow × cfl_reduction reduces only the turbulence-equation pseudo-time step. The default is 1.0; values of 0.5–0.8 can suppress turbulence-residual oscillations in stiff boundary layers or high-aspect-ratio meshes.

15.6.2.6 SA-QCR2000 (Quadratic Constitutive Relation)

Replaces Boussinesq isotropic stress with an anisotropic QCR form (Spalart 2000):

τ_QCR = τ_Bouss − 0.3·Σ_k (O_ik·τ_jk + O_jk·τ_ik)
O_ik = (∂u_i/∂x_k − ∂u_k/∂x_i) / |∇u|_F

The SA source term is unchanged; only mean-flow viscous stress is modified. Recommended for corner-separation and secondary-flow cases. It is variant-independent and combines freely with standard or neg.

15.6.2.7 SA-RC (Rotation Correction)

Suppresses runaway production in vortex cores (Dacles-Mariani et al.):

Prod = Shat + CRot·min(0, ||S|| − ||ω||),  CRot = 2.0

It has no effect in shear-dominated boundary layers where ||S|| ≈ ||ω||, acting only in vortex cores. It is variant-independent and compatible with QCR2000. Recommended for rotor, propeller, and wing-tip vortex cases.

NASA TMR’s recommended SA-RC-QCR2000 baseline is rotation_correction: true, qcr2000: true.

15.6.2.8 SST (k-ω SST)

Key	Default	Meaning
variant	v2003	See SST variant below.
production	strain	Production form: strain (P = μt·S²), vorticity (P = μt·Ω²), or kato_launder (P = μt·S·Ω).
sigma_k1, sigma_w1, beta_1	0.85, 0.5, 0.075	Inner-layer (k-ω) constants.
a1	0.31	Shear-stress limiter constant.
sigma_k2, sigma_w2, beta_2	1.0, 0.856, 0.0828	Outer-layer (k-ε) constants.
beta_star	0.09	Shared constant.
kappa	0.41	von Kármán constant.
prandtl_turb	0.85	Turbulent Prandtl number of the energy closure.
cfl_reduction	1.0	Factor on the SST pseudo-time step; lower values can help stiff cases.
max_update_fraction	1.0	Per-point relative k/ω update cap.

15.6.2.9 SST variant

Value	Meaning
v2003 (default)	Menter 2003 SST with the selected production form.
sust	Adds sustaining production floors based on freestream k and ω; they prevent ambient turbulence from decaying below its prescribed level.

sust is implemented, not merely a schema placeholder. Its freestream values come from the turbulence inflow settings described below.

Note

v1994 was removed on 2026-06-05 after a silent hybrid bug occurred when only the γ branch was implemented. There are no plans to restore it: NASA TMR SST-V changes only the production term to vorticity while retaining the 2003 limiter and constants, whereas V1994 changes the limiter and constants as well and therefore moves farther from the reference.

15.6.3 Wall treatment (global defaults)

Shared constants for boundaries using wall_treatment: "automatic" (see Domains). DBNS RANS uses the SA analytic wall law or SST Spalding/White–Christoph law. The treatment is continuous across y+; the former switching threshold has been removed.

Key	Default	Meaning
kappa	0.41	von Kármán constant.
B	5.0	Spalding log-law intercept.
relaxation	0.5	Wall-law Newton solve relaxation factor.
relaxation_turb	0.7	k/ω relaxation; SST wall function only.
max_iter	200	Wall-law Newton iteration cap.
tol	1e-12	Wall-law Newton convergence tolerance.

For FR, wall_treatment: "automatic" means a wall-modeled LES stress law, not RANS. It requires compressible Navier–Stokes and a no-slip wall; FR artificial-compressibility cases cannot use it. The following additional models.wall_treatment keys are for the FR path:

Key	Default	Meaning
exchange.type, exchange.value	element_fraction, 0.5	Exchange point as a fraction of wall-element height; exchange.value must be in (0, 2).
energy_work	false	Include wall shear work in the modeled energy flux.
ldg_state	no_slip	Auxiliary wall state: no_slip, slip_mirror, or non_corrected.
inviscid_state	slip_mirror	Inviscid ghost state: slip_mirror or no_slip.
tau_jump	false	Apply the LDG penalty on the modeled wall face.
coarse_level	true	Evaluate the wall model on p-multigrid coarse levels.
wall_filter.alpha, wall_filter.order, wall_filter.kc	0, 8, 1	Wall-normal modal filter; alpha: 0 disables it.
eddy_viscosity, eddy_viscosity_layers	false, 1	Optional wall-cell eddy viscosity and its number of element layers.

Note

Location of prandtl_turb varies by model

prandtl_turb is a RANS closure constant, not a gas property. It belongs in the model-specific subblock (models.turbulence.sa.prandtl_turb or models.turbulence.sst.prandtl_turb), with different recommended values (SA: 0.9, SST: 0.85).

15.7 Four-axis solver identity

models.type and models.turbulence are two of the four axes. The other two are analysis.solver and analysis.time; their combination determines the solver mode.

euler         + none    → Euler (inviscid)
navier_stokes + none    → laminar NS
navier_stokes + sa      → RANS-SA
navier_stokes + sst     → RANS-SST

15.8 Location of freestream turbulence quantities

Set freestream or inlet turbulence in that boundary’s turbulence subblock, not in models. The same fields are available for uniform initialization.

Key	Applies to	Meaning
nu_factor	SA	Inflow ν̃/ν ratio; default 3.
intensity	SST	Turbulence intensity as a fraction; default 0.05 (5%).
eddy_viscosity_ratio	SST	Inflow μt/μ; default 10 when no length scale is supplied.
length_scale	SST	Turbulence length scale in metres.
hydraulic_diameter	SST	Hydraulic diameter; the length scale becomes 0.07 times this value.

For SST, set at most one of eddy_viscosity_ratio, length_scale, and hydraulic_diameter. The former turb2lam_ratio is not a current input key. intermittency is reserved for a transition model and is rejected if supplied. See Domains for boundary-condition-specific usage.

15.9 JSONC examples

The GUI writes the same keys for the controls it exposes. For a CLI case or a setting not yet available in the GUI, use JSONC. turbulence must be an object: "turbulence": "sa" is not accepted.

Compressible DBNS with SA and an explicit total-energy setting:

{
  "analysis": { "solver": "dbns", "dimension": 3 },
  "models": {
    "type": "navier_stokes",
    "regime": "compressible",
    "turbulence": {
      "model": "sa",
      "sa": { "variant": "standard", "ft2": false, "qcr2000": true }
    }
  }
}

Incompressible PBNS with no energy equation (the fluid material must use eos.type: "constant_density"):

{
  "analysis": { "solver": "pbns", "dimension": 3 },
  "models": {
    "type": "navier_stokes",
    "regime": "incompressible",
    "turbulence": { "model": "none" }
  }
}

Compressible FR with total energy (FR also needs its numerical-method and time-stepping settings):

{
  "analysis": { "solver": "fr", "time": "unsteady", "dimension": 3 },
  "models": {
    "type": "navier_stokes",
    "regime": "compressible",
    "turbulence": { "model": "none" }
  }
}

SST with the sustaining variant and one valid set of inflow turbulence values:

{
  "models": {
    "type": "navier_stokes",
    "turbulence": {
      "model": "sst",
      "sst": { "variant": "sust", "production": "strain" }
    }
  },
  "domains": [{
    "boundaries": [{
      "name": "farfield", "type": "farfield", "mesh_markers": ["FARFIELD"],
      "mach": 0.5, "pressure": 101325.0, "temperature": 288.15,
      "turbulence": { "intensity": 0.05, "eddy_viscosity_ratio": 10.0 }
    }]
  }]
}

These are configuration fragments, not complete runnable cases; mesh, materials, and other required blocks are omitted. See Input-file structure for a full case layout.