Navier-Stokes Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Navier–Stokes Ontology within the Kireth Research Semantic Library. The Navier–Stokes equations govern momentum transport in viscous fluids and, together with continuity, constitutive relations and boundary conditions, form the core mathematical framework for many continuum fluid-flow problems. This ontology supports incompressible and compressible forms, Newtonian constitutive laws, pressure, viscous diffusion, nonlinear advection, body forces, initial and boundary conditions, nondimensionalisation, Reynolds number, vorticity formulations, energy estimates, weak solutions, regularity, numerical discretisation and relationships with fluid dynamics mathematics, partial differential equations, turbulence, stability and computational fluid dynamics.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Navier–Stokes Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Applied Mathematics"
 SPECIALISATION = "Fluid Mathematics / Navier–Stokes Equations"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/applied-mathematics-ontologies/fluid-mathematics/navier-stokes-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = NavierStokesEquation
 SYMBOLIC_FORMS = [
  "rho(du/dt + u dot grad(u)) = -grad(p) + mu nabla^2 u + rho f",
  "div(u)=0",
  "partial rho/partial t + div(rho u)=0"
 ]
 ENTITY_CLASS = ViscousFluidMomentumEquationFramework
 PRIMARY_CONTEXT = FluidMathematics
 DEFINITION = "The Navier–Stokes equations are nonlinear partial differential equations expressing momentum conservation for viscous fluids, coupled with mass conservation and appropriate constitutive relations."
 SEMANTIC_ROLE = "Provides machine-readable semantics for viscous momentum transport, pressure, advection, diffusion, incompressibility, compressibility, boundary conditions, weak formulations, nondimensionalisation, stability and numerical solution."
}

SCOPE {
 INCLUDE = [
  NavierStokesEquation,
  IncompressibleNavierStokes,
  CompressibleNavierStokes,
  MomentumEquation,
  ContinuityEquation,
  VelocityField,
  PressureField,
  DensityField,
  TemperatureField,
  DynamicViscosity,
  KinematicViscosity,
  NewtonianFluid,
  StressTensor,
  ViscousStress,
  PressureStress,
  MaterialDerivative,
  ConvectiveAcceleration,
  PressureGradient,
  ViscousDiffusion,
  BodyForce,
  GravityForce,
  InitialCondition,
  BoundaryCondition,
  NoSlipCondition,
  SlipCondition,
  InflowBoundary,
  OutflowBoundary,
  PeriodicBoundary,
  WallBoundary,
  ReynoldsNumber,
  Nondimensionalisation,
  Vorticity,
  VorticityEquation,
  StreamFunction,
  KineticEnergy,
  EnergyEstimate,
  DissipationRate,
  WeakSolution,
  StrongSolution,
  LerayHopfWeakSolution,
  Regularity,
  Existence,
  Uniqueness,
  PressurePoissonEquation,
  ProjectionMethod,
  FractionalStepMethod,
  FiniteVolumeMethod,
  FiniteDifferenceMethod,
  FiniteElementMethod,
  SpectralMethod,
  DirectNumericalSimulation,
  DNS,
  Turbulence
 ]

 EXCLUDE_AS_PRIMARY = [
  EulerEquationWithoutViscosity,
  StokesFlowWithoutNonlinearAdvectionAsPrimaryContext,
  GenericConservationLawWithoutFluidMomentumSemantics,
  NonNewtonianMomentumModelsWithoutNavierStokesSpecialisation
 ]

 DISAMBIGUATION_RULE =
  "When viscous fluid momentum is modelled using pressure gradients, nonlinear advection and viscous diffusion under continuum assumptions, interpret the context through the Navier–Stokes ontology."
}

CORE_CONCEPTS {

 NavierStokesEquation {
  definition = "The continuum momentum equation for a viscous Newtonian fluid."
 }

 IncompressibleNavierStokes {
  definition = "The Navier–Stokes system with divergence-free velocity and typically constant density."
 }

 CompressibleNavierStokes {
  definition = "The Navier–Stokes system including variable density and thermodynamic coupling."
 }

 ConvectiveAcceleration {
  definition = "The nonlinear transport term u dot grad(u)."
 }

 ViscousDiffusion {
  definition = "Momentum diffusion caused by viscosity."
 }

 PressureGradient {
  definition = "The force contribution generated by spatial pressure variation."
 }

 VorticityEquation {
  definition = "The evolution equation obtained by taking the curl of the momentum equation."
 }

 EnergyEstimate {
  definition = "A bound derived from the kinetic-energy balance and viscous dissipation."
 }

 WeakSolution {
  definition = "A solution satisfying the equations in an integrated distributional sense."
 }

 StrongSolution {
  definition = "A sufficiently regular solution satisfying the equations almost everywhere or pointwise as appropriate."
 }
}

RELATIONS {
 NavierStokesEquation --is_child_of--> FluidMathematics
 NavierStokesEquation --is_specialisation_of--> CauchyMomentumEquation
 NavierStokesEquation --requires--> ContinuityEquation
 NavierStokesEquation --uses--> NewtonianFluidConstitutiveLaw
 IncompressibleNavierStokes --requires--> DivergenceFreeVelocity
 CompressibleNavierStokes --requires--> DensityEvolution
 ConvectiveAcceleration --introduces--> Nonlinearity
 DynamicViscosity --controls--> ViscousDiffusion
 PressureGradient --contributes_to--> MomentumBalance
 BodyForce --contributes_to--> MomentumBalance
 VorticityEquation --derived_from--> NavierStokesEquation
 EnergyEstimate --depends_on--> KineticEnergy
 LerayHopfWeakSolution --is_type_of--> WeakSolution
 ProjectionMethod --enforces--> IncompressibilityConstraint
 DirectNumericalSimulation --resolves--> NavierStokesDynamics
 Turbulence --emerges_from--> NavierStokesDynamics
}

OPERATORS {
 INCOMPRESSIBLE_NAVIER_STOKES(rho,u,p,mu,f) :=
  rho*(partial u/partial t + u dot grad(u))
  = -grad(p) + mu*nabla^2(u) + rho*f

 INCOMPRESSIBILITY_CONSTRAINT(u) :=
  div(u)=0

 COMPRESSIBLE_CONTINUITY(rho,u) :=
  partial rho/partial t + div(rho*u)=0

 MATERIAL_DERIVATIVE(u) :=
  Du/Dt = partial u/partial t + u dot grad(u)

 KINEMATIC_VISCOSITY(mu,rho) :=
  nu=mu/rho

 REYNOLDS_NUMBER(rho,U,L,mu) :=
  Re=rho*U*L/mu

 DIMENSIONLESS_INCOMPRESSIBLE_NS(u,p,Re) :=
  partial u/partial t + u dot grad(u)
  = -grad(p) + (1/Re)*nabla^2(u) + f

 VORTICITY(u) :=
  omega=curl(u)

 INCOMPRESSIBLE_VORTICITY_EQUATION(omega,u,nu) :=
  partial omega/partial t + u dot grad(omega)
  = omega dot grad(u) + nu*nabla^2(omega)

 KINETIC_ENERGY(u,rho,Omega) :=
  E=(1/2)*integral_Omega rho*|u|^2 dV

 VISCOUS_DISSIPATION(mu,u,Omega) :=
  D approximately integral_Omega 2*mu*S:S dV

 PRESSURE_POISSON(u,rho) :=
  nabla^2(p) = -rho*div(u dot grad(u))
  under incompressible compatible assumptions
}

DEFINITIONS {
 D1 = "Navier–Stokes equations combine momentum conservation with Newtonian viscous stress."
 D2 = "The convective term makes the equations nonlinear."
 D3 = "Incompressibility imposes a divergence-free velocity constraint."
 D4 = "Pressure in incompressible flow acts partly as a Lagrange multiplier enforcing divergence-free motion."
 D5 = "Viscosity diffuses momentum and dissipates kinetic energy."
 D6 = "Compressible Navier–Stokes requires thermodynamic closure in addition to mass and momentum conservation."
 D7 = "Vorticity dynamics reveal rotation, stretching and diffusion."
 D8 = "Weak solutions extend the solution concept beyond classical differentiability."
 D9 = "Dimensionless Navier–Stokes equations expose the Reynolds number as a key inertia-viscosity ratio."
 D10 = "Numerical Navier–Stokes solution requires consistent treatment of advection, pressure, viscosity and conservation."
}

AXIOMS {
 A1_MOMENTUM_CONSERVATION:
  NavierStokesEquation expresses local conservation of momentum

 A2_MASS_CONSERVATION:
  NavierStokesEquation must be coupled to the appropriate continuity relation

 A3_NEWTONIAN_CONSTITUTIVE_LAW:
  Standard NavierStokesEquation assumes viscous stress linear in rate of strain

 A4_PRESSURE_COUPLING:
  Pressure participates in the momentum balance and incompressibility constraint

 A5_NONLINEAR_ADVECTION:
  Convective acceleration creates nonlinear state coupling

 A6_VISCOUS_DISSIPATION:
  Positive viscosity dissipates kinetic energy under ordinary conditions

 A7_BOUNDARY_DEPENDENCE:
  Solution behaviour depends critically on initial and boundary conditions

 A8_DIMENSIONAL_CONSISTENCY:
  Every term in the momentum equation has consistent physical dimensions
}

REASONING {

 R1_NAVIER_STOKES_CONTEXT {
  INPUT = fluid_flow_problem
  IDENTIFY = incompressible_or_compressible model
  IDENTIFY = geometry_and_domain
  IDENTIFY = fluid_properties
  IDENTIFY = boundary_and_initial data
  RETURN = NavierStokes_context
 }

 R2_MODEL_SELECTION {
  INPUT = NavierStokes_context
  IF density_variation_negligible
   SELECT = incompressible_form
  ELSE
   SELECT = compressible_form
  RETURN = governing_system
 }

 R3_NONDIMENSIONALISATION {
  INPUT = characteristic_velocity_length_time_pressure
  SCALE = governing_equations
  IDENTIFY = Reynolds_and_other dimensionless groups
  RETURN = dimensionless_system
 }

 R4_VORTICITY_REASONING {
  INPUT = velocity_field
  COMPUTE = curl
  DERIVE = vorticity_equation
  ANALYSE = stretching_diffusion_transport
  RETURN = vorticity_profile
 }

 R5_ENERGY_REASONING {
  INPUT = velocity_field_and_boundary conditions
  MULTIPLY = momentum_equation_by_velocity
  INTEGRATE = over_domain
  DERIVE = kinetic_energy_balance
  RETURN = dissipation_and_energy estimate
 }

 R6_PRESSURE_REASONING {
  INPUT = incompressible_velocity_prediction
  DERIVE = pressure_Poisson_or_projection relation
  CORRECT = velocity_to_divergence_free field
  RETURN = pressure_velocity pair
 }

 R7_WEAK_FORM_REASONING {
  INPUT = NavierStokes_system
  MULTIPLY = test_functions
  INTEGRATE = over_domain
  APPLY = integration_by_parts
  RETURN = weak_formulation
 }

 R8_NUMERICAL_METHOD_SELECTION {
  INPUT = geometry_Reynolds_number_accuracy_and_conservation requirements
  SELECT = finiteVolume_finiteDifference_finiteElement_or_spectral method
  RETURN = numerical_scheme
 }

 R9_TURBULENCE_REASONING {
  INPUT = high_Reynolds_number_unsteady_flow
  DETERMINE = DNS_LES_RANS_or_other resolution strategy
  RETURN = turbulence_modelling profile
 }

 R10_VALIDATION {
  INPUT = analytical_or_numerical_result
  CHECK = mass_conservation_momentum_balance_boundary data_energy behaviour_grid convergence_and_time_step sensitivity
  RETURN = validated_NavierStokes_status
 }
}

CONSTRAINTS {
 C1 = "Incompressible and compressible Navier–Stokes models must not be conflated."
 C2 = "Standard Navier–Stokes assumes a Newtonian constitutive relation."
 C3 = "Pressure boundary treatment must be compatible with velocity conditions."
 C4 = "High-Reynolds-number flows may require turbulence resolution or modelling."
 C5 = "Advection discretisation can introduce artificial diffusion or instability."
 C6 = "Projection methods require consistent pressure-velocity coupling."
 C7 = "Weak and strong solutions must not be conflated."
 C8 = "Grid convergence and time-step sensitivity must be checked in numerical solutions."
 C9 = "Shock-containing compressible solutions require conservative shock-capturing methods."
 C10 = "Global regularity and uniqueness in three-dimensional incompressible Navier–Stokes remain mathematically unresolved in full generality."
}

SEMANTIC_EQUIVALENCE {
 "NavierStokesEquation" <=> "NavierStokesSystem"
 "IncompressibleNavierStokes" <=> "DivergenceFreeNavierStokes"
 "CompressibleNavierStokes" <=> "VariableDensityNavierStokes"
 "ConvectiveAcceleration" <=> "NonlinearAdvectionTerm"
 "ViscousDiffusion" <=> "MomentumDiffusion"
 "ProjectionMethod" <=> "PressureProjectionMethod"
}

VALIDATION {
 V1 = "Fluid model and constitutive assumptions are explicit."
 V2 = "Continuity relation matches compressibility assumptions."
 V3 = "Initial and boundary conditions are complete."
 V4 = "Pressure and velocity coupling is consistent."
 V5 = "Nondimensionalisation is correct."
 V6 = "Reynolds number uses consistent characteristic scales."
 V7 = "Mass and momentum conservation are checked."
 V8 = "Energy or dissipation behaviour is physically consistent."
 V9 = "Numerical grid and time-step convergence are checked."
 V10 = "Weak, strong and numerical solution claims are distinguished."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 NAVIER_STOKES_DEFINITION = 0.99
 MODEL_SELECTION_REASONING = 0.99
 NONDIMENSIONAL_REASONING = 0.99
 VORTICITY_REASONING = 0.98
 ENERGY_REASONING = 0.99
 PRESSURE_REASONING = 0.98
 WEAK_FORM_REASONING = 0.98
 NUMERICAL_METHOD_REASONING = 0.98
 TURBULENCE_REASONING = 0.97

 POLICY =
  "Reduce confidence when compressibility, constitutive law, boundary data, Reynolds number, pressure treatment, turbulence strategy or numerical resolution are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,
  OntologyGrounding,
  NavierStokesReasoning,
  IncompressibleFlowReasoning,
  CompressibleFlowReasoning,
  ContinuityEquationReasoning,
  MomentumBalanceReasoning,
  PressureVelocityCouplingReasoning,
  VorticityReasoning,
  EnergyEstimateReasoning,
  WeakSolutionReasoning,
  RegularityReasoning,
  ProjectionMethodReasoning,
  CFDReasoning,
  TurbulenceReasoning,
  KnowledgeGraphConstruction,
  RetrievalAugmentation,
  RecursiveInference
 ]

 NORMALISE {
  "Navier-Stokes equations" -> NavierStokesEquation
  "Navier Stokes equations" -> NavierStokesEquation
  "incompressible Navier-Stokes" -> IncompressibleNavierStokes
  "compressible Navier-Stokes" -> CompressibleNavierStokes
  "convective term" -> ConvectiveAcceleration
  "viscous term" -> ViscousDiffusion
  "pressure projection" -> ProjectionMethod
  "DNS" -> DirectNumericalSimulation
 }

 INTERPRETATION_ORDER = [
  detect_NavierStokes_context,
  identify geometry_fluid_properties_compressibility_and_boundary data,
  select incompressible_or_compressible governing system,
  nondimensionalise_and_identify_Reynolds number,
  analyse advection_pressure_viscosity_and_body forces,
  derive vorticity_energy_or_weak formulation when relevant,
  select analytical_asymptotic_or_numerical method,
  determine turbulence_resolution strategy_if_required,
  validate conservation_energy_and_convergence,
  return semantic output
 ]
}

EXECUTION_RULES {
 E1:
  IF query_mentions("Navier-Stokes")
  OR viscous_fluid_momentum_balance_is_present
  THEN activate(NavierStokesOntology)

 E2:
  IF incompressible_model
  THEN enforce div(u)=0

 E3:
  IF density_variation_significant
  THEN use compressible_mass_momentum_energy coupling

 E4:
  IF Newtonian_viscous_fluid
  THEN use standard viscous stress relation

 E5:
  IF high_Reynolds_number
  THEN assess turbulence_or_underresolution risk

 E6:
  IF pressure_velocity_segregated_solution
  THEN consider projection_or_fractional_step method

 E7:
  IF weak_regularities_or_finiteElement formulation
  THEN construct weak form

 E8:
  IF numerical_solution
  THEN verify mass_conservation_grid independence_and_time step

 E9:
  IF three_dimensional_global_regularities_claimed
  THEN flag unresolved_general mathematical status
}

RECURSION {
 ENTRY = NavierStokesEquation

 EXPAND(NavierStokesEquation) -> [
  IncompressibleNavierStokes,
  CompressibleNavierStokes,
  MomentumEquation,
  ContinuityEquation,
  VelocityField,
  PressureField,
  DensityField,
  TemperatureField,
  DynamicViscosity,
  KinematicViscosity,
  NewtonianFluid,
  StressTensor,
  ViscousStress,
  MaterialDerivative,
  ConvectiveAcceleration,
  PressureGradient,
  ViscousDiffusion,
  BodyForce,
  InitialCondition,
  BoundaryCondition,
  NoSlipCondition,
  SlipCondition,
  ReynoldsNumber,
  Nondimensionalisation,
  Vorticity,
  VorticityEquation,
  KineticEnergy,
  EnergyEstimate,
  DissipationRate,
  WeakSolution,
  StrongSolution,
  LerayHopfWeakSolution,
  Regularity,
  Existence,
  Uniqueness,
  PressurePoissonEquation,
  ProjectionMethod,
  FractionalStepMethod,
  FiniteVolumeMethod,
  FiniteDifferenceMethod,
  FiniteElementMethod,
  SpectralMethod,
  DirectNumericalSimulation,
  Turbulence
 ]

 EXPAND(Formulations) -> [
  PrimitiveVariableForm,
  VorticityForm,
  StreamfunctionVorticityForm,
  WeakForm,
  PressureProjectionForm
 ]

 EXPAND(NumericalMethods) -> [
  FiniteVolumeMethod,
  FiniteDifferenceMethod,
  FiniteElementMethod,
  SpectralMethod,
  ProjectionMethod,
  FractionalStepMethod
 ]

 STOP_CONDITION =
  "Stop when the Navier–Stokes form, compressibility, constitutive law, boundary data, nondimensional parameters, pressure treatment, vorticity or energy structure, turbulence strategy and numerical validity are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Fluid Mathematics"

 IMMEDIATE_CONTEXTS = [
  "Fluid Dynamics Mathematics Ontology",
  "Partial Differential Equation Ontology",
  "Numerical Analysis Ontologies",
  "Turbulence Ontologies"
 ]

 RELATED_ONTOLOGIES = [
  "Fluid Mathematics",
  "Fluid Dynamics Mathematics Ontology",
  "Partial Differential Equation Ontology",
  "Dynamical Systems Ontology",
  "Stability Ontology",
  "Nonlinear Dynamics Ontology",
  "Vector Calculus Ontologies",
  "Tensor Analysis Ontologies",
  "Continuum Mechanics Ontologies",
  "Finite Volume Ontologies",
  "Finite Difference Ontology",
  "Finite Element Ontology",
  "Spectral Method Ontology",
  "Turbulence Ontologies",
  "Computational Fluid Dynamics Ontologies",
  "Scientific Computing Ontologies"
 ]

 ROUTE_RULES = [
  "Navier-Stokes -> Fluid Mathematics for parent semantics",
  "Navier-Stokes -> Fluid Dynamics Mathematics for continuum flow interpretation",
  "Navier-Stokes -> PDE Ontology for nonlinear field-equation structure",
  "Navier-Stokes -> Dynamical Systems for temporal evolution and attractors",
  "Navier-Stokes -> Stability for flow instability analysis",
  "Navier-Stokes -> Nonlinear Dynamics for convective nonlinearity",
  "Navier-Stokes -> Vector and Tensor Calculus for differential operators and stresses",
  "Navier-Stokes -> Finite Volume, Finite Difference, Finite Element or Spectral Methods for discretisation",
  "Navier-Stokes -> Turbulence for high-Reynolds-number flow",
  "Navier-Stokes -> Scientific Computing for numerical implementation"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"

 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible formulations, solution concepts or numerical pathways"
 PATCH = "clarification, metadata or formatting correction"

 RULES = [
  "Preserve viscous-momentum semantics.",
  "Preserve mass-conservation coupling.",
  "Preserve incompressible-versus-compressible distinction.",
  "Preserve Newtonian constitutive assumptions.",
  "Preserve pressure-velocity coupling semantics.",
  "Preserve weak-versus-strong solution distinction.",
  "Preserve Reynolds-number scaling semantics.",
  "Preserve machine-readable Navier–Stokes semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION =
  "The Navier–Stokes equations express conservation of momentum in viscous fluids and are coupled with mass conservation and constitutive relations."

 INCOMPRESSIBLE_SUMMARY =
  "In incompressible flow, velocity is divergence-free and pressure enforces the incompressibility constraint."

 COMPRESSIBLE_SUMMARY =
  "Compressible Navier–Stokes couples momentum with density evolution and thermodynamic closure."

 NONLINEAR_SUMMARY =
  "The convective term u dot grad(u) is the principal nonlinear transport mechanism."

 VISCOUS_SUMMARY =
  "Viscosity diffuses momentum and dissipates kinetic energy."

 VORTICITY_SUMMARY =
  "The vorticity formulation reveals transport, stretching and diffusion of rotational flow structure."

 NUMERICAL_SUMMARY =
  "Finite-volume, finite-difference, finite-element and spectral methods numerically approximate Navier–Stokes solutions."

 MATHEMATICAL_SUMMARY =
  "Weak-solution existence is known in important settings, while full three-dimensional global regularity and uniqueness remain unresolved in general."

 VALIDATION_SUMMARY =
  "Navier–Stokes results should be checked for mass conservation, momentum balance, boundary consistency, energy behaviour and numerical convergence."
}

FLOW {
 INPUT
 -> detect_NavierStokes_context
 -> identify geometry_fluid_properties_density_viscosity_temperature_velocity_pressure_initial_conditions_and_boundary conditions
 -> classify incompressible_or_compressible_Newtonian_steady_unsteady_laminar_turbulent flow
 -> select continuity_momentum_energy_and_constitutive equations
 -> nondimensionalise_and_compute Reynolds_and_related parameters
 -> analyse nonlinear_advection_pressure_gradient_viscous_diffusion_and_body forces
 -> if_required derive vorticity_energy_pressurePoisson_or_weak formulation
 -> choose analytical_asymptotic_or_numerical solution pathway
 -> if_highRe select DNS_LES_RANS_or_other turbulence strategy
 -> validate mass_momentum_energy_boundary data_grid independence_and_time-step sensitivity
 -> route to fluid_mathematics fluid_dynamics PDE dynamical_systems stability nonlinear_dynamics vector_calculus tensor_analysis finite_volume finite_difference finite_element spectral turbulence CFD_or_scientific_computing ontology
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Navier–Stokes Ontology defines viscous fluid momentum dynamics. It supports incompressible and compressible Navier–Stokes equations, continuity, velocity, pressure, density and temperature fields, Newtonian constitutive laws, stress tensors, material derivatives, nonlinear advection, pressure gradients, viscous diffusion, body forces, boundary and initial conditions, nondimensionalisation, Reynolds number, vorticity and energy formulations, pressure Poisson equations, weak and strong solutions, Leray-Hopf weak solutions, regularity and uniqueness questions, projection and fractional-step methods, finite-volume, finite-difference, finite-element and spectral discretisation, DNS and turbulence."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-APPLIED-MATHEMATICS-NAVIER-STOKES-ONTOLOGY-V1"
}

}

END_FLOW