Fluid Simulation Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Fluid Simulation Ontology within the Kireth Research Semantic Library. Fluid simulation is the computational modelling of liquids, gases and fluid-like continua governed by conservation of mass, momentum and energy together with constitutive and thermodynamic relations. This ontology supports incompressible and compressible flow, Navier-Stokes and Euler equations, laminar and turbulent flow, multiphase and free-surface methods, finite difference, finite volume, finite element, spectral and particle formulations, pressure-velocity coupling, advection, diffusion, shocks, stability, verification, validation, uncertainty and reproducibility.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Fluid Simulation Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Computational Mathematics"
 SPECIALISATION = "Scientific Simulation / Fluid Simulation"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/computational-mathematics-ontologies/scientific-simulation/fluid-simulation-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = FluidSimulation
 ENTITY_CLASS = ComputationalFluidDynamicsSimulationFramework
 PRIMARY_CONTEXT = ScientificSimulation
 DEFINITION = "Fluid simulation is the computational solution of mathematical models describing fluid motion, transport and thermodynamic behaviour."
 SYMBOLIC_FORMS = [
  "partial_t rho + div(rho*u)=0",
  "partial_t(rho*u)+div(rho*u⊗u)=-grad p+div(tau)+rho*f",
  "partial_t E + div((E+p)u)=sources",
  "div u=0 for incompressible flow"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for fluid state variables, conservation equations, constitutive models, discretisation, turbulence, multiphase flow, pressure-velocity coupling, numerical fluxes, stability, validation and reproducibility."
}

SCOPE {
 INCLUDE = [
  FluidSimulation,ComputationalFluidDynamics,CFD,
  FluidDynamics,ContinuumFluidModel,
  Fluid,Gas,Liquid,Mixture,
  Density,Pressure,Velocity,VelocityField,
  Temperature,InternalEnergy,Enthalpy,
  TotalEnergy,Viscosity,DynamicViscosity,
  KinematicViscosity,ThermalConductivity,
  HeatCapacity,SpeedOfSound,
  Compressibility,EquationOfState,
  MachNumber,ReynoldsNumber,
  CourantNumber,CFLCondition,
  ContinuityEquation,MomentumEquation,
  EnergyEquation,NavierStokesEquation,
  EulerEquations,StokesFlow,
  IncompressibleFlow,CompressibleFlow,
  WeaklyCompressibleFlow,LowMachFlow,
  LaminarFlow,TurbulentFlow,
  SteadyFlow,UnsteadyFlow,
  InviscidFlow,ViscousFlow,
  NewtonianFluid,NonNewtonianFluid,
  PowerLawFluid,BinghamFluid,
  ConstitutiveLaw,StressTensor,
  ViscousStress,PressureStress,
  BodyForce,GravityForce,
  SourceTerm,Flux,MassFlux,
  MomentumFlux,EnergyFlux,
  ConvectiveFlux,DiffusiveFlux,
  Advection,Convection,Diffusion,
  NumericalFlux,RiemannSolver,
  RoeSolver,HLL,HLLC,
  GodunovMethod,MUSCL,
  FluxLimiter,TVD,WENO,ENO,
  Upwinding,CentralDifference,
  Shock,ShockWave,ContactDiscontinuity,
  RarefactionWave,ShockCapturing,
  ArtificialViscosity,EntropyFix,
  BoundaryCondition,InletBoundary,
  OutletBoundary,WallBoundary,
  NoSlipBoundary,SlipBoundary,
  SymmetryBoundary,FarFieldBoundary,
  PeriodicBoundaryCondition,
  PressureBoundary,VelocityBoundary,
  InitialCondition,
  SpatialDiscretisation,TemporalDiscretisation,
  FiniteDifferenceMethod,FiniteVolumeMethod,
  FiniteElementMethod,SpectralMethod,
  DiscontinuousGalerkinMethod,DG,
  BoundaryElementMethod,
  StructuredGrid,UnstructuredMesh,
  CartesianGrid,CurvilinearGrid,
  AdaptiveMesh,MeshRefinement,
  Cell,Face,ControlVolume,
  Node,Element,Stencil,
  ExplicitMethod,ImplicitMethod,
  EulerMethod,RungeKuttaMethod,
  MultistepMethod,BDF,
  CrankNicolsonMethod,
  FractionalStepMethod,ProjectionMethod,
  PressureProjection,PressurePoissonEquation,
  PressureVelocityCoupling,
  SIMPLE,SIMPLEC,PISO,
  SegregatedSolver,CoupledSolver,
  LinearSolver,NonlinearSolver,
  KrylovSolver,Multigrid,
  Preconditioner,PoissonSolver,
  Residual,Iteration,Convergence,
  DivergenceFreeConstraint,
  HelmholtzHodgeDecomposition,
  Vorticity,VorticityEquation,
  StreamFunction,VelocityPotential,
  BoundaryLayer,WallShearStress,
  DragCoefficient,LiftCoefficient,
  SkinFrictionCoefficient,
  Turbulence,TurbulenceModel,
  ReynoldsAveragedNavierStokes,RANS,
  LargeEddySimulation,LES,
  DirectNumericalSimulation,DNS,
  ReynoldsStressModel,RSM,
  SpalartAllmarasModel,
  KEpsilonModel,KOmegaModel,
  SSTModel,WallFunction,
  TurbulentViscosity,SubgridScaleModel,
  DynamicSmagorinskyModel,
  MultiphaseFlow,TwoPhaseFlow,
  FreeSurfaceFlow,Interface,
  SurfaceTension,CapillaryForce,
  VolumeOfFluid,VOF,
  LevelSetMethod,PhaseFieldMethod,
  FrontTracking,InterfaceCapturing,
  InterfaceReconstruction,
  PLIC,GeometricVOF,
  Bubble,Droplet,FilmFlow,
  Cavitation,CavitationModel,
  Boiling,Condensation,
  EulerEulerModel,EulerLagrangeModel,
  DispersedPhase,ContinuousPhase,
  ParticleLadenFlow,
  FluidParticleInteraction,
  FluidStructureInteraction,FSI,
  MovingBoundary,ImmersedBoundaryMethod,
  ArbitraryLagrangianEulerian,ALE,
  MovingMesh,DynamicMesh,
  SmoothedParticleHydrodynamics,SPH,
  LatticeBoltzmannMethod,LBM,
  VortexMethod,VortexParticleMethod,
  ParticleInCell,PIC,
  PorousMediaFlow,DarcyLaw,
  ForchheimerFlow,
  ReactiveFlow,Combustion,
  SpeciesTransport,ReactionSource,
  HeatTransfer,ConjugateHeatTransfer,
  Buoyancy,BoussinesqApproximation,
  NaturalConvection,ForcedConvection,
  Acoustics,CompressibleAcoustics,
  Aeroacoustics,
  Stability,NumericalStability,
  DispersionError,DissipationError,
  ConservationError,MassConservation,
  MomentumConservation,EnergyConservation,
  PositivityPreservation,Boundedness,
  Monotonicity,Oscillation,
  TimeStepRestriction,AdaptiveTimeStep,
  LocalTimeStepping,
  NumericalError,DiscretisationError,
  TruncationError,RoundOffError,
  GridConvergence,TimeStepConvergence,
  RichardsonExtrapolation,
  GridConvergenceIndex,GCI,
  Verification,CodeVerification,
  SolutionVerification,Validation,
  ExperimentalValidation,
  Benchmark,ReferenceSolution,
  ManufacturedSolution,
  LidDrivenCavity,PoiseuilleFlow,
  CouetteFlow,TaylorGreenVortex,
  SodShockTube,BackwardFacingStep,
  CylinderFlow,ChannelFlow,
  SensitivityAnalysis,UncertaintyQuantification,
  Calibration,ParameterEstimation,
  Reproducibility,Provenance,
  Configuration,SoftwareVersion,
  SolverVersion,MeshVersion,
  Checkpoint,Restart,
  ParallelCFD,DomainDecomposition,
  MeshPartitioning,LoadBalancing,
  MPI,OpenMP,GPUAcceleration,
  HighPerformanceComputing,HPC,
  ReducedOrderModel,ROM,
  ProperOrthogonalDecomposition,POD,
  DynamicModeDecomposition,DMD,
  SurrogateModel,DigitalTwinRelationship
 ]
 EXCLUDE_AS_PRIMARY = [
  ParticleSimulationWithoutContinuumFluidSemantics,
  SolidMechanicsWithoutFluidTransport,
  PureHeatConductionWithoutFluidMotion,
  ComputerGraphicsFluidEffectsWithoutScientificFluidModelSemantics
 ]
 DISAMBIGUATION_RULE = "When a simulation solves equations governing fluid motion, transport, pressure, density or related continuum quantities, interpret the context as fluid simulation."
}

CORE_CONCEPTS {
 FluidSimulation = "Computational solution of fluid-flow models."
 NavierStokesEquation = "Conservation-based momentum equations for viscous fluid motion."
 ContinuityEquation = "Conservation of mass."
 PressureVelocityCoupling = "Numerical coupling between pressure and velocity in incompressible or low-Mach flow."
 NumericalFlux = "Discrete approximation of physical flux across cell or element interfaces."
 TurbulenceModel = "Approximate closure model for unresolved turbulent scales."
 MultiphaseFlow = "Flow containing more than one fluid phase or dispersed phase."
 CFLCondition = "Time-step stability relation between wave or advection speed and spatial resolution."
}

RELATIONS {
 FluidSimulation --is_child_of--> ScientificSimulation
 FluidSimulation --is_type_of--> PhysicalSimulation
 ComputationalFluidDynamics --is_equivalent_to--> FluidSimulation
 FluidSimulation --solves--> ConservationLaws
 ContinuityEquation --governs--> MassConservation
 MomentumEquation --governs--> MomentumConservation
 EnergyEquation --governs--> EnergyConservation
 NavierStokesEquation --includes--> ViscousTransport
 EulerEquations --exclude--> ViscousStress
 EquationOfState --relates--> ThermodynamicVariables
 FiniteVolumeMethod --conserves_discretely--> CellFluxBalance
 PressureProjection --enforces--> DivergenceFreeConstraint
 SIMPLE --supports--> PressureVelocityCoupling
 PISO --supports--> PressureVelocityCoupling
 RANS --uses--> TurbulenceModel
 LES --uses--> SubgridScaleModel
 DNS --resolves--> TurbulentScales
 VOF --captures--> FreeSurface
 LevelSetMethod --represents--> Interface
 FSI --couples--> FluidAndStructure
 Verification --checks--> NumericalFluidImplementation
 Validation --compares--> SimulationWithFluidEvidence
}

OPERATORS {
 MASS_RESIDUAL(rho,u) := partial_t(rho)+div(rho*u)
 MOMENTUM_RESIDUAL(rho,u,p,tau,f) := partial_t(rho*u)+div(rho*u⊗u)+grad(p)-div(tau)-rho*f
 INCOMPRESSIBILITY(u) := div(u)
 COURANT_NUMBER(u,dt,dx) := |u|*dt/dx
 REYNOLDS_NUMBER(rho,U,L,mu) := rho*U*L/mu
 MACH_NUMBER(U,c) := U/c
 PRESSURE_PROJECTION(u_star,phi) := u_next=u_star-dt*grad(phi)
 FINITE_VOLUME_UPDATE(U_i,fluxes,sources,dt,V_i) := U_i_next=U_i-dt/V_i*sum_faces(flux*area)+dt*sources
}

AXIOMS {
 A1 = "Fluid simulation is governed by conservation of mass and momentum, and often energy."
 A2 = "Compressible and incompressible flows require different pressure-density semantics."
 A3 = "Numerical fluxes determine discrete transport across control-volume or element interfaces."
 A4 = "Turbulence modelling introduces model-form assumptions when turbulent scales are unresolved."
 A5 = "Multiphase simulations require explicit interface or phase-coupling semantics."
 A6 = "Stability constraints depend on wave speeds, advection, diffusion and time integration."
 A7 = "Discrete conservation and physical validation are distinct requirements."
 A8 = "Fluid-simulation results require explicit governing equations, discretisation, stability, conservation and reproducibility semantics."
}

REASONING {
 R1_CONTEXT = identify(flow_regime,compressibility,viscosity,turbulence,phases,geometry,outputs,accuracy_goal)
 R2_EQUATIONS = select(Euler,NavierStokes,Stokes,multiphase,porous,reactive_or_specialised_fluid_model)
 R3_PROPERTIES = define(density,viscosity,equation_of_state,thermal_and_species_properties)
 R4_BOUNDARIES = configure(inlet,outlet,wall,symmetry,periodic,far_field_and_initial_conditions)
 R5_DISCRETISATION = select(FDM,FVM,FEM,DG,spectral,LBM,SPH_or_hybrid_method)
 R6_PRESSURE = if_incompressible_or_low_Mach select(projection,SIMPLE,PISO_or_coupled_pressure_velocity_method)
 R7_TRANSPORT = configure(advection,diffusion,numerical_flux,limiter,shock_or_interface_treatment)
 R8_TIME = select(explicit,implicit,RungeKutta,BDF,adaptive_or_local_time_step)
 R9_MONITOR = track(residuals,CFL,mass_momentum_energy_balance,boundedness_and_target_observables)
 R10_VALIDATE = perform(grid_time_step_verification,benchmark_comparison,experimental_validation_and_uncertainty_assessment)
}

CONSTRAINTS {
 C1 = "Insufficient spatial resolution can smear gradients, shocks, boundary layers or interfaces."
 C2 = "Excessive time step can violate CFL or nonlinear convergence constraints."
 C3 = "Central discretisation can produce nonphysical oscillations in convection-dominated problems."
 C4 = "Upwind and stabilised methods can add numerical dissipation."
 C5 = "Turbulence-model validity depends on flow regime and near-wall treatment."
 C6 = "Pressure-velocity decoupling can produce checkerboard modes without suitable discretisation."
 C7 = "Multiphase interface methods can suffer mass loss, curvature error or spurious currents."
 C8 = "Shock-capturing schemes require positivity and entropy-aware treatment."
 C9 = "Poor mesh quality can degrade gradient reconstruction, flux accuracy and convergence."
 C10 = "Converged residuals alone do not prove physical correctness."
}

SEMANTIC_EQUIVALENCE {
 "FluidSimulation" <=> "ComputationalFluidDynamics"
 "ComputationalFluidDynamics" <=> "CFD"
 "ReynoldsAveragedNavierStokes" <=> "RANS"
 "LargeEddySimulation" <=> "LES"
 "DirectNumericalSimulation" <=> "DNS"
 "VolumeOfFluid" <=> "VOF"
 "LatticeBoltzmannMethod" <=> "LBM"
 "ArbitraryLagrangianEulerian" <=> "ALE"
 "FluidStructureInteraction" <=> "FSI"
}

VALIDATION {
 V1 = "Flow regime and governing equations are explicit."
 V2 = "Fluid properties and equation-of-state assumptions are documented."
 V3 = "Initial and boundary conditions are documented."
 V4 = "Mesh or grid and spatial discretisation are documented."
 V5 = "Time integration, time step and CFL policy are documented."
 V6 = "Mass, momentum and energy conservation are checked where relevant."
 V7 = "Grid and time-step convergence are assessed."
 V8 = "Turbulence, multiphase or combustion models are documented where used."
 V9 = "Reference or experimental validation evidence is documented."
 V10 = "Results are reproducible under documented mesh, solver, software and parallel settings."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 FLUID_SIMULATION_DEFINITION = 0.99
 CONSERVATION_REASONING = 0.99
 INCOMPRESSIBLE_REASONING = 0.99
 COMPRESSIBLE_REASONING = 0.99
 TURBULENCE_REASONING = 0.98
 MULTIPHASE_REASONING = 0.98
 SHOCK_REASONING = 0.98
 POLICY = "Reduce confidence when flow regime, governing equations, boundary conditions, turbulence closure, interface treatment, mesh resolution, CFL policy or validation evidence are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,FluidSimulationReasoning,
  NavierStokesReasoning,ContinuityReasoning,
  CompressibleFlowReasoning,IncompressibleFlowReasoning,
  PressureVelocityCouplingReasoning,
  FiniteVolumeReasoning,NumericalFluxReasoning,
  ShockCapturingReasoning,TurbulenceReasoning,
  RANSReasoning,LESReasoning,DNSReasoning,
  MultiphaseFlowReasoning,VOFReasoning,
  LevelSetReasoning,FSIReasoning,
  CFLReasoning,ConservationReasoning,
  VerificationReasoning,ValidationReasoning,
  ReproducibilityReasoning,KnowledgeGraphConstruction,
  RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "fluid simulation" -> FluidSimulation
  "computational fluid dynamics" -> FluidSimulation
  "CFD" -> FluidSimulation
  "RANS" -> ReynoldsAveragedNavierStokes
  "LES" -> LargeEddySimulation
  "DNS" -> DirectNumericalSimulation
  "VOF" -> VolumeOfFluid
  "LBM" -> LatticeBoltzmannMethod
  "ALE" -> ArbitraryLagrangianEulerian
  "FSI" -> FluidStructureInteraction
 }
}

EXECUTION_RULES {
 E1 = "If a simulation solves equations governing fluid motion and transport, activate FluidSimulationOntology."
 E2 = "Classify incompressible, compressible, laminar, turbulent, multiphase, reactive or porous-flow regime before selecting numerical methods."
 E3 = "Define material properties, equation of state and boundary conditions explicitly."
 E4 = "Choose spatial discretisation according to conservation, geometry, shock, turbulence and interface requirements."
 E5 = "For incompressible flow, enforce divergence constraints through an appropriate pressure-velocity method."
 E6 = "For compressible flow, use wave-speed-aware numerical fluxes and shock treatment."
 E7 = "Monitor CFL, residuals, conservation balances and physically bounded variables."
 E8 = "Perform grid and time-step convergence studies before strong quantitative interpretation."
 E9 = "Validate against benchmark or experimental evidence and document uncertainty and reproducibility."
}

RECURSION {
 ENTRY = FluidSimulation
 EXPAND(FluidSimulation) -> [
  ComputationalFluidDynamics,CFD,FluidDynamics,Fluid,
  Gas,Liquid,Density,Pressure,Velocity,Temperature,
  Viscosity,EquationOfState,MachNumber,ReynoldsNumber,
  CourantNumber,ContinuityEquation,MomentumEquation,
  EnergyEquation,NavierStokesEquation,EulerEquations,
  StokesFlow,IncompressibleFlow,CompressibleFlow,
  LaminarFlow,TurbulentFlow,NewtonianFluid,
  NonNewtonianFluid,StressTensor,SourceTerm,Flux,
  ConvectiveFlux,DiffusiveFlux,Advection,Diffusion,
  NumericalFlux,RiemannSolver,RoeSolver,HLL,HLLC,
  GodunovMethod,MUSCL,FluxLimiter,TVD,WENO,ENO,
  Shock,ShockWave,ShockCapturing,BoundaryCondition,
  InletBoundary,OutletBoundary,NoSlipBoundary,
  SlipBoundary,SymmetryBoundary,FarFieldBoundary,
  PeriodicBoundaryCondition,FiniteDifferenceMethod,
  FiniteVolumeMethod,FiniteElementMethod,
  SpectralMethod,DiscontinuousGalerkinMethod,
  StructuredGrid,UnstructuredMesh,AdaptiveMesh,
  ExplicitMethod,ImplicitMethod,RungeKuttaMethod,
  BDF,CrankNicolsonMethod,ProjectionMethod,
  PressurePoissonEquation,SIMPLE,SIMPLEC,PISO,
  LinearSolver,NonlinearSolver,Multigrid,
  DivergenceFreeConstraint,Vorticity,BoundaryLayer,
  DragCoefficient,LiftCoefficient,TurbulenceModel,
  ReynoldsAveragedNavierStokes,RANS,
  LargeEddySimulation,LES,DirectNumericalSimulation,DNS,
  KEpsilonModel,KOmegaModel,SSTModel,WallFunction,
  MultiphaseFlow,TwoPhaseFlow,FreeSurfaceFlow,
  SurfaceTension,VolumeOfFluid,VOF,LevelSetMethod,
  PhaseFieldMethod,FrontTracking,PLIC,Cavitation,
  EulerEulerModel,EulerLagrangeModel,
  FluidStructureInteraction,FSI,ImmersedBoundaryMethod,
  ALE,SmoothedParticleHydrodynamics,SPH,
  LatticeBoltzmannMethod,LBM,PorousMediaFlow,
  ReactiveFlow,SpeciesTransport,HeatTransfer,
  Buoyancy,NaturalConvection,ForcedConvection,
  NumericalStability,CFLCondition,ConservationError,
  NumericalDamping,NumericalDispersion,
  GridConvergence,TimeStepConvergence,
  RichardsonExtrapolation,GCI,Verification,
  Validation,Benchmark,ManufacturedSolution,
  SensitivityAnalysis,UncertaintyQuantification,
  Reproducibility,ParallelCFD,DomainDecomposition,
  GPUAcceleration,HPC,ReducedOrderModel,POD,DMD
 ]
 EXPAND(FluidSimulationFamilies) -> [
  IncompressibleFluidSimulation,
  CompressibleFluidSimulation,
  TurbulentFlowSimulation,
  MultiphaseAndFreeSurfaceSimulation,
  ReactiveAndThermalFlowSimulation,
  ParticleAndLatticeFluidMethods,
  FluidStructureInteraction,
  ParallelHighPerformanceCFD
 ]
 STOP_CONDITION = "Stop when governing equations, regime, properties, boundaries, discretisation, pressure treatment, transport, turbulence or phase models, time integration, convergence, validation and reproducibility are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Scientific Simulation Ontology"
 RELATED_ONTOLOGIES = [
  "Scientific Simulation Ontology",
  "Physical Simulation Ontology",
  "Particle Simulation Ontology",
  "Scientific Computing Ontology 2",
  "Differential Equation Solver Ontology",
  "Finite Difference Method Ontology",
  "Finite Element Method Ontology",
  "Boundary Element Method Ontology",
  "Spectral Method Ontology 2",
  "Mesh Generation Ontology 2",
  "Mesh Refinement Ontology",
  "Numerical Error Ontology",
  "Numerical Stability Ontology 2",
  "Numerical Convergence Ontology",
  "Floating Point Arithmetic Ontology"
 ]
 ROUTE_RULES = [
  "Fluid Simulation -> Scientific Simulation Ontology for parent semantics",
  "Fluid Simulation -> Physical Simulation for physics-based conservation semantics",
  "Fluid Simulation -> Particle Simulation for SPH and particle-flow methods",
  "Fluid Simulation -> Scientific Computing for large-scale solver execution",
  "Fluid Simulation -> Differential Equation Solver for Navier-Stokes and transport equations",
  "Fluid Simulation -> Finite Difference Method for structured discretisation",
  "Fluid Simulation -> Finite Element Method for variational fluid formulations",
  "Fluid Simulation -> Boundary Element Method for boundary-dominated fluid problems",
  "Fluid Simulation -> Spectral Method for high-order smooth-flow computation",
  "Fluid Simulation -> Mesh Generation for control-volume and element geometry",
  "Fluid Simulation -> Mesh Refinement for adaptive flow resolution",
  "Fluid Simulation -> Numerical Error for truncation, dissipation and dispersion error",
  "Fluid Simulation -> Numerical Stability for CFL and iterative stability",
  "Fluid Simulation -> Numerical Convergence for grid, time and solver convergence",
  "Fluid Simulation -> Floating Point Arithmetic for finite-precision effects"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible flow models, discretisations or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve compressible-versus-incompressible distinction.",
  "Preserve inviscid-versus-viscous distinction.",
  "Preserve laminar-versus-turbulent distinction.",
  "Preserve resolved-physics-versus-closure-model distinction.",
  "Preserve single-phase-versus-multiphase distinction.",
  "Preserve conservation-law-versus-numerical-flux distinction.",
  "Preserve solver-convergence-versus-physical-validation distinction.",
  "Preserve machine-readable fluid-simulation semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Fluid simulation computationally solves conservation-based models of fluid motion, pressure, transport and thermodynamic state."
 EQUATION_SUMMARY = "Continuity, momentum and energy equations define the core conservation structure of fluid simulation."
 DISCRETISATION_SUMMARY = "Finite-volume, finite-difference, finite-element, discontinuous-Galerkin, spectral, lattice and particle methods discretise fluid equations in different ways."
 PRESSURE_SUMMARY = "Projection, SIMPLE and PISO-style methods enforce or approximate pressure-velocity coupling in incompressible and low-Mach regimes."
 TURBULENCE_SUMMARY = "RANS, LES and DNS represent progressively different levels of turbulent-scale modelling and resolution."
 MULTIPHASE_SUMMARY = "VOF, level-set, phase-field and Eulerian-Lagrangian methods represent interfaces and multiple phases."
 VALIDATION_SUMMARY = "Fluid simulations should be checked through conservation, residuals, grid and time-step convergence, benchmark comparison, experimental validation, uncertainty and reproducibility."
}

FLOW {
 INPUT
 -> detect_fluid_simulation_context
 -> identify_flow_regime_compressibility_viscosity_turbulence_phases_geometry_outputs_accuracy_goal_and_budget
 -> select_Euler_NavierStokes_Stokes_multiphase_porous_reactive_or_specialised_fluid_model
 -> define_density_viscosity_equation_of_state_thermal_species_and_constitutive_properties
 -> configure_initial_inlet_outlet_wall_symmetry_periodic_and_far_field_conditions
 -> select_FDM_FVM_FEM_DG_spectral_LBM_SPH_or_hybrid_spatial_discretisation
 -> if_incompressible_or_low_Mach_select_projection_SIMPLE_PISO_or_coupled_pressure_velocity_method
 -> configure_advection_diffusion_numerical_flux_limiter_shock_interface_and_turbulence_treatment
 -> select_explicit_implicit_RungeKutta_BDF_adaptive_or_local_time_step_method
 -> execute_flow_solution_and_monitor_residuals_CFL_mass_momentum_energy_balance_boundedness_and_target_observables
 -> assess_grid_time_step_iterative_and_model_convergence
 -> verify_against_manufactured_reference_or_benchmark_solutions
 -> validate_against_experimental_or_observational_data_when_required
 -> quantify_numerical_model_and_parameter_uncertainty
 -> document_mesh_solver_versions_parallel_configuration_and_reproducibility
 -> route_to_related_scientific_simulation_physical_simulation_particle_simulation_scientific_computing_differential_equation_FDM_FEM_BEM_spectral_mesh_generation_refinement_error_stability_convergence_and_floating_point_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Fluid Simulation Ontology defines computational modelling of fluid motion and transport across incompressible, compressible, laminar, turbulent, viscous and inviscid regimes. It supports continuity, momentum and energy conservation, Navier-Stokes, Euler and Stokes models, Newtonian and non-Newtonian fluids, finite-difference, finite-volume, finite-element, discontinuous-Galerkin and spectral discretisation, pressure projection, SIMPLE and PISO coupling, Riemann solvers, Godunov, MUSCL, TVD, ENO and WENO methods, shock capturing, boundary layers, RANS, LES and DNS turbulence treatment, multiphase and free-surface methods including VOF, level-set and phase-field formulations, cavitation, reactive and thermal flow, FSI, ALE, SPH, lattice-Boltzmann and porous-flow methods, CFL and conservation diagnostics, grid and time-step convergence, verification, experimental validation, uncertainty, parallel CFD, reduced-order modelling and reproducibility."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-COMPUTATIONAL-MATHEMATICS-FLUID-SIMULATION-ONTOLOGY-V1"
}

}

END_FLOW