CMPSTheory & User Reference Manual
Spatial Numerics and Physical Limits
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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 optionMeaning / formulationEffect on the simulationPractical guidanceTheory reference
First Order reconstructionUses 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 reconstructionReconstructs 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 DifferencingUses 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: 0.5Controls 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 optionMeaning / formulationEffect on the simulationPractical guidanceTheory reference
Augmented Stencil Least SquaresComputes 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 SquaresComputes 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 initiallyComputes 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 optionMeaning / formulationEffect on the simulationPractical guidanceTheory reference
Use LimiterDefault: OnActivates 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-faceBuilds 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 initiallyUses neighboring cell values to establish limiting bounds.AccuracyStability / convergence
Usually provides robust neighborhood-based bounds.
General default choice.Slope limiting and reconstruction
Min-ModUses 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 initiallyUses 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 VenkatakrishnanUses 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 optionMeaning / formulationEffect on the simulationPractical guidanceTheory reference
AUSM+up carrier fluxDefault: DefaultUses 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 fluxUses 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 materialThe 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 optionMeaning / formulationEffect on the simulationPractical guidanceTheory reference
Minimum PressureDefault: 1 PaLower 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 KLower 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 KUpper 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/sLower 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-14Lower 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: 1e5Caps 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 KLower 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 KUpper 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: 0.63Upper 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