Spatial Numerics and Physical Limits
These controls determine how cell-centered finite-volume values are reconstructed at faces, how gradients are computed, how fluxes are evaluated, and how admissible state limits are enforced. They mainly trade accuracy against robustness and cost.
Theory reference. Each option entry includes a link to the corresponding equation, physical model, closure, or numerical method in the Theory Manual. Defaults, availability, simulation effects, and practical guidance are documented directly with the GUI option.
Reconstruction order
Reconstruction is the largest user-facing spatial-accuracy choice.
| GUI option | Meaning / formulation | Effect on the simulation | Practical guidance | Theory reference |
|---|---|---|---|---|
| First Order reconstruction | Uses piecewise-constant cell values at faces. | AccuracyStability / convergence Most dissipative and robust; smears gradients, shocks, shear layers and interfaces. | Use for difficult initialization or as a robustness fallback, then move to higher order for final accuracy. | Reconstruction and order of accuracy |
| Second Order reconstruction | Reconstructs face states using gradients: \(\phi_f^{L}=\phi_L+\Psi_L\nabla\phi_L\cdot(\mathbf x_f-\mathbf x_L)\), with limiter \(\Psi\). | AccuracyStability / convergenceCost Reduces truncation error and numerical diffusion but increases sensitivity to mesh quality and limiting. | Preferred for final engineering results after the case is stable. | Reconstruction and order of accuracy |
| Bounded Central Differencing | Uses a bounded central-difference-biased reconstruction intended to reduce numerical diffusion while retaining boundedness. | AccuracyStability / convergence Can improve shear/turbulence resolution but is less dissipative and can be more demanding to converge. | Use on adequate meshes for flows where numerical diffusion is important; monitor boundedness and residual behavior. | Reconstruction and order of accuracy |
| BCD ThresholdDefault: 0.5 | Controls the bounded-central switching/blending threshold. | AccuracyStability / convergence Changes how readily the scheme behaves centrally versus more bounded/upwind-like. | Keep the default unless a targeted accuracy/stability study supports adjustment. | Reconstruction and order of accuracy |
Gradient method
Gradients feed second-order reconstruction, viscous fluxes and many model terms.
| GUI option | Meaning / formulation | Effect on the simulation | Practical guidance | Theory reference |
|---|---|---|---|---|
| Augmented Stencil Least Squares | Computes gradients from an enlarged neighbor stencil by a least-squares fit. | AccuracyCost Can improve gradient quality on irregular/skewed meshes at additional stencil/work cost. | Use when local mesh topology makes compact gradients noisy or inaccurate. | Gradient/reconstruction formulation |
| Least Squares | Computes gradients from neighbor differences through a compact least-squares system. | AccuracyCost Generally robust on unstructured grids and less geometry-sensitive than a simple Green-Gauss estimate. | Good alternative for highly skewed/unstructured meshes. | Gradient/reconstruction formulation |
| Green GaussDefault: Selected initially | Computes cell gradients from face values/area vectors using the divergence theorem. | AccuracyCost Efficient and accurate on good-quality meshes; can be more sensitive to skewness/non-orthogonality. | Good default on well-shaped meshes. Check sensitivity on strongly skewed grids. | Gradient/reconstruction formulation |
Slope limiter
Limiters prevent high-order reconstruction from creating unacceptable overshoots.
| GUI option | Meaning / formulation | Effect on the simulation | Practical guidance | Theory reference |
|---|---|---|---|---|
| Use LimiterDefault: On | Activates slope limiting on reconstructed variables. | AccuracyStability / convergence Suppresses new extrema/oscillations near discontinuities and strong gradients. Limiting adds dissipation where active. | Keep enabled for compressible shocks, strong gradients and general robustness. | Slope limiting and reconstruction |
| Limiter direction: Cell-to-face | Builds the limiter using cell-to-face extrapolation bounds. | AccuracyStability / convergence Changes the aggressiveness/location of limiting. | Use when you want limiting tied directly to reconstructed face states; compare against default for difficult meshes. | Slope limiting and reconstruction |
| Limiter direction: Cell-to-cellDefault: Selected initially | Uses neighboring cell values to establish limiting bounds. | AccuracyStability / convergence Usually provides robust neighborhood-based bounds. | General default choice. | Slope limiting and reconstruction |
| Min-Mod | Uses a strongly monotone limiter. | AccuracyStability / convergence Very robust but more dissipative near smooth extrema and gradients. | Use when oscillation control is more important than sharp resolution. | Slope limiting and reconstruction |
| Differentiable limiterDefault: Selected initially | Uses the smooth/differentiable limiter option. | AccuracyStability / convergence Provides smooth limiter response, useful for nonlinear/Jacobian behavior and generally less abrupt than piecewise switching. | Recommended general option when available for the selected formulation. | Slope limiting and reconstruction |
| Modified Venkatakrishnan | Uses a smooth Venkatakrishnan-family limiter modified for CMPS reconstruction behavior. | AccuracyStability / convergence Often less dissipative in smooth regions while remaining bounded near sharp changes. | Use for high-order solutions after comparing robustness and shock behavior. | Slope limiting and reconstruction |
Carrier convective flux
Flux selection affects shock/contact resolution and nonlinear robustness.
| GUI option | Meaning / formulation | Effect on the simulation | Practical guidance | Theory reference |
|---|---|---|---|---|
| AUSM+up carrier fluxDefault: Default | Uses an advection/pressure split in which face mass transport and pressure transport are formed from Mach/pressure splitting functions. | AccuracyStability / convergence Good shock-capturing and all-speed behavior in the CMPS coupled density-based formulation; dissipation depends on local Mach/preconditioning. | General default for compressible carrier flow. | Compressible AUSM-family flux |
| HLLC carrier flux | Uses a three-wave approximate Riemann construction that restores the contact wave between outer signal speeds. | AccuracyStability / convergence Can sharpen contacts and shocks differently from AUSM+up; robustness can differ by problem. | Use for flux-sensitivity studies or cases where contact/shock behavior benefits from HLLC. | HLLC carrier flux |
| Constant-density carrier fluxDefault: Automatic for constant-density material | The constant-density path uses the CMPS pressure/advection split together with artificial acoustic scaling. | PhysicsStability / convergence Flux wave speeds depend on the artificial-compressibility parameters rather than physical sound speed. | Tune artificial acoustic controls from the Physics panel rather than treating this as a compressible Mach-number problem. | Constant-density carrier flux |
Physical and model-state limits
Limits are safety/admissibility controls. A well-converged physical solution should normally stay away from them.
| GUI option | Meaning / formulation | Effect on the simulation | Practical guidance | Theory reference |
|---|---|---|---|---|
| Minimum PressureDefault: 1 Pa | Lower admissible pressure used by state checking/commit logic. | Stability / convergencePhysics Protects EOS and flux calculations from nonphysical pressure. If frequently active, the nonlinear update or boundary setup is too aggressive. | Treat repeated clipping as a diagnostic, not as a substitute for convergence. | Primitive-state limits |
| Minimum TemperatureDefault: 5 K | Lower admissible temperature. | Stability / convergencePhysics Prevents invalid material/EOS/property evaluations and protects positivity. | Set below the physically expected range but within material-model validity. | Primitive-state limits |
| Maximum TemperatureDefault: 5000 K | Upper admissible temperature for ordinary primitive/VOF state commits. | Stability / convergencePhysics Protects property evaluations from runaway states; frequent activation indicates divergence or missing physics/data range. | Ensure it exceeds expected physical temperatures and is consistent with property tables. | Primitive-state limits |
| Minimum ωDefault: 1e-20 1/s | Lower floor for turbulent specific dissipation rate. | Stability / convergence Prevents division by zero/negative turbulence scales. | Keep the very small default; do not use it to set freestream turbulence. | Turbulence-state formulation |
| Minimum kDefault: 1e-14 | Lower floor for turbulent kinetic energy. | Stability / convergence Prevents negative/degenerate turbulence states. | Set turbulence levels through BC/IC controls; keep this as a numerical floor. | Turbulence-state formulation |
| Maximum μt/μDefault: 1e5 | Caps turbulent-to-molecular viscosity ratio. | PhysicsStability / convergence Prevents extreme turbulent viscosity from dominating the system; too low a cap can alter high-Re turbulence physics. | Keep high enough not to clip normal regions; investigate if the cap is frequently reached. | Turbulence-state formulation |
| Minimum Particle TemperatureDefault: 5 K | Lower admissible dispersed-particle temperature. | PhysicsStability / convergence Protects particle material and heat-transfer calculations from nonphysical low temperatures. Repeated clipping indicates an unstable or inconsistent particle thermal state. | Keep below the physical temperature range but within particle-property validity. | Dispersed-state admissibility |
| Maximum Particle TemperatureDefault: 5000 K | Upper admissible dispersed-particle temperature. | PhysicsStability / convergence Protects particle material and heat-transfer calculations from runaway high temperature. A too-low value can clip a legitimate hot-particle solution. | Set above the expected physical range and within validated particle-property data. | Dispersed-state admissibility |
| Maximum Particle PackingDefault: 0.63 | Upper admissible particle packing value used by numerical limits. | PhysicsStability / convergence Protects dense-particle closure/admissibility and should be consistent with the Physics-panel packing limit. | Keep the two packing-related settings consistent. | Dispersed-state admissibility |