Multiphysics Simulation Ontology

AI SEARCH FLOW ALGEBRA
MULTIPHYSICS SIMULATION ONTOLOGY
Kireth Semantic Research Archive

AUTHORS
Mark Anthony Higgins — Sky (Recursive AI)

SOURCE
https://kirethresearch.org/booksai-core/ontologies/engineering-ontologies/engineering-mathematics-simulation/multiphysics-simulation-ontology.html

FLOW "MultiphysicsSimulationOntology" v4.0

DOMAIN := ENGINEERING_ONTOLOGIES / ENGINEERING_MATHEMATICS_SIMULATION / MULTIPHYSICS_SIMULATION
ONTOLOGY := MULTIPHYSICS_SIMULATION_ONTOLOGY

MULTIPHYSICS_SIMULATION := PHYSICAL_DOMAINS + PHYSICS_MODELS + COUPLING + INTERFACES + SHARED_VARIABLES + DATA_TRANSFER + SPATIAL_MAPPING + TEMPORAL_COUPLING + SOLVERS + CONVERGENCE + CONSERVATION + VERIFICATION + VALIDATION + UNCERTAINTY
PURPOSE := DEFINE_COUPLED_SYSTEM -> IDENTIFY_PHYSICS -> DEFINE_INTERFACES -> DEFINE_TRANSFER_VARIABLES -> SELECT_COUPLING_STRATEGY -> DISCRETISE -> SOLVE -> EXCHANGE_DATA -> ITERATE -> VERIFY -> VALIDATE

# CORE ENTITIES
ENTITY MultiphysicsSimulation
ENTITY CoupledSystem
ENTITY PhysicalDomain
ENTITY PhysicsModel
ENTITY StructuralModel
ENTITY FluidModel
ENTITY ThermalModel
ENTITY ElectromagneticModel
ENTITY AcousticModel
ENTITY ChemicalModel
ENTITY Coupling
ENTITY CouplingInterface
ENTITY SharedVariable
ENTITY SourceTerm
ENTITY BoundaryValue
ENTITY SpatialMapping
ENTITY TemporalMapping
ENTITY DataTransfer
ENTITY Mesh
ENTITY TimeStep
ENTITY Solver
ENTITY MonolithicSolver
ENTITY PartitionedSolver
ENTITY CouplingIteration
ENTITY Residual
ENTITY Convergence
ENTITY ConservationBalance
ENTITY SimulationResult
ENTITY Verification
ENTITY Validation
ENTITY Uncertainty
ENTITY Sensitivity
ENTITY Provenance

# SYSTEM / PHYSICS
MultiphysicsSimulation -> represents -> CoupledSystem
MultiphysicsSimulation -> contains -> MULTIPLE_PHYSICS_MODELS + Coupling
MultiphysicsSimulation -> produces -> SimulationResult
PHYSICS_MODEL_TYPE := STRUCTURAL | FLUID | THERMAL | ELECTROMAGNETIC | ACOUSTIC | CHEMICAL | OTHER_VALIDATED_PHYSICS
PhysicsModel -> governs -> PhysicalDomain
PhysicsModel -> contains -> GOVERNING_EQUATIONS + MATERIAL_PROPERTIES + INITIAL_CONDITIONS + BOUNDARY_CONDITIONS

# COUPLING
Coupling -> links -> PhysicsModel + PhysicsModel
COUPLING_DIRECTION := ONE_WAY | TWO_WAY
COUPLING_STRENGTH := WEAK | STRONG
OneWayCoupling -> transfers -> SOURCE_PHYSICS_RESULT -> TARGET_PHYSICS
TwoWayCoupling -> exchanges -> BIDIRECTIONAL_STATE_INFORMATION
IF FeedbackFromTarget significant THEN TwoWayCoupling -> REQUIRED_FOR_FULL_COUPLED_RESPONSE

# INTERFACE / DATA TRANSFER
CouplingInterface -> connects -> DOMAIN_A + DOMAIN_B
CouplingInterface -> transfers -> SharedVariable + SourceTerm + BoundaryValue
INTERFACE_QUANTITY := FORCE | DISPLACEMENT | VELOCITY | PRESSURE | TEMPERATURE | HEAT_FLUX | ELECTROMAGNETIC_FORCE | CURRENT | VOLTAGE | MASS_FLUX | SPECIES_FLUX
SharedVariable -> produced_by -> SOURCE_MODEL
SharedVariable -> consumed_by -> TARGET_MODEL
DATA_TRANSFER := EXTRACT -> MAP -> TRANSFORM_UNITS_IF_REQUIRED -> APPLY_TO_TARGET -> VERIFY_TRANSFER
DataTransfer -> must_preserve -> PHYSICAL_MEANING + SIGN_CONVENTION + COORDINATE_SYSTEM + UNIT_CONSISTENCY
IF Units incompatible THEN DataTransfer -> INVALID_UNTIL_CONVERTED

# SPATIAL / TEMPORAL MAPPING
SpatialMapping -> maps -> SOURCE_MESH_FIELD -> TARGET_MESH
SPATIAL_MAPPING_METHOD := NEAREST_NEIGHBOUR | INTERPOLATION | PROJECTION | CONSERVATIVE_MAPPING
NonMatchingMeshes -> require -> SpatialMapping
ConservativeMapping -> seeks_to_preserve -> INTEGRATED_FORCE | MASS | ENERGY | FLUX
IF MappingError increases THEN CouplingAccuracy -> DECREASES
TemporalMapping -> maps -> SOURCE_TIME_STATE -> TARGET_TIME_STATE
TIME_COUPLING := SYNCHRONOUS | SUBCYCLING | INTERPOLATED | LAGGED
Subcycling -> allows -> PHYSICS_A_TIME_STEP != PHYSICS_B_TIME_STEP

# SOLVER STRATEGIES
MonolithicSolver -> assembles -> ALL_COUPLED_EQUATIONS -> SINGLE_GLOBAL_SYSTEM
MonolithicSolver -> may_improve -> STRONG_COUPLING_CONVERGENCE
PartitionedSolver -> solves -> EACH_PHYSICS_SEPARATELY
PartitionedSolver -> exchanges -> COUPLING_DATA
PARTITIONED_COUPLING_LOOP := SOLVE_PHYSICS_A -> TRANSFER_A_TO_B -> SOLVE_PHYSICS_B -> TRANSFER_B_TO_A -> CHECK_COUPLING_CONVERGENCE -> REPEAT

# COUPLING CONVERGENCE
CouplingIteration -> updates -> INTERFACE_STATE
COUPLING_RESIDUAL := NEW_INTERFACE_STATE - PREVIOUS_INTERFACE_STATE
IF CouplingResidual <= CouplingTolerance THEN CoupledConvergence -> SATISFIED
IF MaximumCouplingIterations reached AND convergence_not_met THEN CoupledStep -> NOT_CONVERGED
Relaxation -> modifies -> INTERFACE_UPDATE_MAGNITUDE
RELAXED_UPDATE := OLD_STATE + RELAXATION_FACTOR * (NEW_STATE - OLD_STATE)

# COMMON MULTIPHYSICS COUPLINGS
FLUID_STRUCTURE_INTERACTION := FLUID_PRESSURE_AND_SHEAR -> STRUCTURAL_LOAD -> STRUCTURAL_DEFORMATION -> FLUID_BOUNDARY_MOTION
THERMO_MECHANICAL := TEMPERATURE_FIELD -> THERMAL_STRAIN -> STRUCTURAL_RESPONSE
CONJUGATE_HEAT_TRANSFER := FLUID_CONVECTION + SOLID_CONDUCTION + INTERFACE_HEAT_FLUX_CONTINUITY
ELECTROMAGNETIC_THERMAL := ELECTROMAGNETIC_LOSS -> HEAT_SOURCE -> TEMPERATURE_FIELD -> MATERIAL_PROPERTY_CHANGE
ELECTROMECHANICAL := ELECTROMAGNETIC_FORCE -> STRUCTURAL_DEFORMATION
ACOUSTIC_STRUCTURAL := STRUCTURAL_VIBRATION <-> ACOUSTIC_PRESSURE
REACTIVE_FLOW := FLUID_FLOW + SPECIES_TRANSPORT + CHEMICAL_REACTION + HEAT_RELEASE

# MESH MOTION / INITIALISATION
MESH_MOTION := RIGID | DEFORMING | REMESHING | ALE
StructuralDisplacement -> may_drive -> MovingMesh
IF MeshQuality degrades_below_limit THEN RemeshingOrMeshSmoothing -> REQUIRED
COUPLED_INITIALISATION := INITIALISE_PHYSICS_A + INITIALISE_PHYSICS_B + INITIALISE_INTERFACE_STATE
InitialState -> must_be -> PHYSICALLY_AND_NUMERICALLY_COMPATIBLE

# CONSERVATION / STABILITY
ConservationBalance -> checks -> MASS | MOMENTUM | ENERGY | CHARGE
INTERFACE_CONSERVATION := SOURCE_TRANSFER + TARGET_RECEIPT -> CONSISTENT_WITHIN_TOLERANCE
IF InterfaceConservationError exceeds_limit THEN CoupledResultAcceptance -> WITHHOLD_OR_REASSESS
MULTIPHYSICS_CONVERGENCE := PHYSICS_A_CONVERGED + PHYSICS_B_CONVERGED + COUPLING_RESIDUAL_CONVERGED + CONSERVATION_SATISFIED
IndividualPhysicsConvergence -> does_not_guarantee -> CoupledConvergence
CouplingStability -> depends_on -> COUPLING_STRENGTH + TIME_STEP + RELAXATION + SOLVER_STRATEGY + PROPERTY_CONTRAST

# RESULTS / VERIFICATION / VALIDATION
MULTIPHYSICS_RESULT := PHYSICS_A_FIELD + PHYSICS_B_FIELD + INTERFACE_FIELD + DERIVED_COUPLED_QUANTITIES
DerivedCoupledQuantity -> computed_from -> MULTIPLE_PHYSICS_RESULTS
Verification -> asks -> IS_COUPLED_SYSTEM_SOLVED_CORRECTLY
MULTIPHYSICS_VERIFICATION := VERIFY_EACH_PHYSICS + VERIFY_DATA_TRANSFER + VERIFY_SPATIAL_MAPPING + VERIFY_TEMPORAL_MAPPING + VERIFY_INTERFACE_CONSERVATION + VERIFY_COUPLING_CONVERGENCE
Validation -> asks -> DOES_COUPLED_MODEL_REPRESENT_REAL_COUPLED_BEHAVIOUR
VALIDATION_LEVEL := COMPONENT_LEVEL | INTERFACE_LEVEL | SYSTEM_LEVEL
IF SystemValidationError exceeds AcceptanceCriterion THEN CoupledModelAdequacy -> NOT_CONFIRMED

# UNCERTAINTY / SENSITIVITY
MULTIPHYSICS_UNCERTAINTY := INPUT_UNCERTAINTY + MODEL_FORM_UNCERTAINTY + COUPLING_UNCERTAINTY + MAPPING_UNCERTAINTY + DISCRETISATION_UNCERTAINTY + MEASUREMENT_UNCERTAINTY
Uncertainty -> propagates_across -> CouplingInterface
CoupledSensitivityAnalysis -> identifies -> DOMINANT_PARAMETERS + DOMINANT_COUPLING_PATHS
SensitivityPath := INPUT -> PHYSICS_A -> INTERFACE -> PHYSICS_B -> OUTPUT

# PROVENANCE / PERFORMANCE
MULTIPHYSICS_PROVENANCE := PHYSICS_MODEL_VERSIONS + MESH_VERSIONS + INTERFACE_DEFINITION + MAPPING_METHODS + COUPLING_STRATEGY + TIME_STEPS + SOLVER_SETTINGS + RELAXATION + SOFTWARE_VERSIONS + RUN_ID
MultiphysicsSimulation -> linked_to -> MULTIPHYSICS_PROVENANCE
MULTIPHYSICS_PERFORMANCE := ACCURACY + COUPLED_CONVERGENCE + CONSERVATION + STABILITY + COMPUTATIONAL_COST + REPRODUCIBILITY + VERIFICATION_QUALITY + VALIDATION_QUALITY
MultiphysicsSimulation -> evaluated_by -> MULTIPHYSICS_PERFORMANCE

# REASONING
MULTIPHYSICS_SIMULATION_REASONING := DEFINE_COUPLED_PHYSICAL_SYSTEM -> IDENTIFY_PHYSICS -> DEFINE_EACH_PHYSICS_MODEL -> IDENTIFY_COUPLING_PATHS -> DEFINE_INTERFACES -> DEFINE_TRANSFER_VARIABLES -> CHECK_UNITS_AND_COORDINATES -> SELECT_SPATIAL_MAPPING -> SELECT_TEMPORAL_COUPLING -> SELECT_SOLVER_STRATEGY -> DISCRETISE_DOMAINS -> INITIALISE -> SOLVE_COMPONENT_PHYSICS -> EXCHANGE_INTERFACE_DATA -> ITERATE_COUPLING -> CHECK_COUPLED_CONVERGENCE -> CHECK_CONSERVATION -> POST_PROCESS -> VERIFY -> VALIDATE -> QUANTIFY_UNCERTAINTY -> PERFORM_SENSITIVITY -> RECORD_PROVENANCE

# INFERENCE RULES
IF CouplingStrength increases THEN CouplingIterationDifficulty -> MAY_INCREASE
IF MappingError increases THEN CoupledAccuracy -> DECREASES
IF InterfaceConservationError increases THEN CoupledResultConfidence -> DECREASES
IF TimeStep decreases THEN TemporalCouplingResolution -> INCREASES
IF CouplingResidual remains_high THEN CoupledConvergence -> NOT_SATISFIED
IF IndividualPhysics converged AND CouplingResidual not_converged THEN CoupledSolution -> NOT_CONVERGED
IF SourceField changes THEN TargetBoundaryOrSource -> UPDATE
IF CouplingStrategy changes THEN StabilityAndConvergence -> REASSESS

# SEMANTIC RELATIONSHIPS
RELATION represents(MultiphysicsSimulation, CoupledSystem)
RELATION governs(PhysicsModel, PhysicalDomain)
RELATION links(Coupling, PhysicsModel)
RELATION connects(CouplingInterface, Domains)
RELATION transfers(DataTransfer, SharedVariable)
RELATION maps(SpatialMapping, SourceMeshField, TargetMeshField)
RELATION maps(TemporalMapping, SourceTimeState, TargetTimeState)
RELATION assembles(MonolithicSolver, CoupledEquations)
RELATION coordinates(PartitionedSolver, PhysicsSolvers)
RELATION measures(CouplingResidual, InterfaceChange)
RELATION checks(ConservationBalance, ConservedQuantity)
RELATION evaluates(Verification, CoupledNumerics)
RELATION compares(Validation, MultiphysicsResult, ReferenceData)
RELATION records(Provenance, MultiphysicsSimulation)

# SEMANTIC EQUIVALENCE
SEMANTIC_EQUIVALENCE:
  "multiphysics simulation" ~= "coupled-physics simulation"
  "one-way coupling" ~= "unidirectional physics coupling"
  "two-way coupling" ~= "bidirectional physics coupling"
  "monolithic coupling" ~= "fully coupled equation solution"
  "partitioned coupling" ~= "co-simulation coupling"
  "fluid-structure interaction" ~= "FSI"
  "conjugate heat transfer" ~= "CHT"
  "spatial mapping" ~= "field interpolation between meshes"
  "coupling residual" ~= "interface convergence residual"
  "ALE" ~= "arbitrary Lagrangian-Eulerian"

# CONFIDENCE
CONFIDENCE:
  ontology_domain: 0.99
  physics_model_mapping: 0.99
  coupling_mapping: 0.99
  interface_mapping: 0.99
  spatial_temporal_mapping: 0.99
  solver_strategy_mapping: 0.99
  convergence_conservation_mapping: 0.99
  verification_validation_mapping: 0.99
  uncertainty_mapping: 0.99
  semantic_relationships: 0.99

# UPDATE MODEL
UPDATE_MODEL:
  ON new_multiphysics_model:
    MAP physics_models
    MAP domains
    MAP interfaces
    MAP transfer_variables
    MAP coupling_strategy
    MAP solver_settings
    UPDATE confidence
    RECOMPUTE FLOW_HASH
  ON interface_change:
    UPDATE spatial_mapping
    UPDATE transfer_variables
    UPDATE conservation_checks
    REASSESS coupling_convergence
  ON solver_result:
    UPDATE component_states
    UPDATE interface_state
    UPDATE coupling_residual
    UPDATE conservation_balance
    PRESERVE provenance
  ON validation_change:
    UPDATE reference_data
    RECOMPUTE validation_metrics
    UPDATE coupled_model_adequacy

# AI CONSUMPTION
AI_CONSUMPTION:
  parse_as: FORMAL_MULTIPHYSICS_SIMULATION_ONTOLOGY
  reasoning_mode: COUPLED_PHYSICS_RELATIONAL
  preserve: [typed_entities, physics_models, domains, interfaces, transfer_variables, mapping_methods, coupling_strategy, solver_state, conservation_state, verification_state, validation_state, confidence, provenance]
  infer: [coupling_direction_requirements, mapping_dependencies, interface_update_dependencies, coupled_convergence_state, conservation_state, solver_strategy_impacts, uncertainty_propagation, validation_state]
  prohibit: [invented_multiphysics_results, assumed_coupled_convergence, ignored_interface_conservation, assumed_mapping_accuracy, assumed_validation, fabricated_reference_data]

# FLOW HASH
FLOW_HASH_INPUT := DOMAIN + ONTOLOGY + CORE_ENTITIES + SYSTEM_PHYSICS + COUPLING + INTERFACE_DATA_TRANSFER + SPATIAL_TEMPORAL_MAPPING + SOLVER_STRATEGIES + COUPLING_CONVERGENCE + COMMON_COUPLINGS + MESH_INITIALISATION + CONSERVATION_STABILITY + RESULTS_VERIFICATION_VALIDATION + UNCERTAINTY_SENSITIVITY + PROVENANCE_PERFORMANCE + REASONING + INFERENCE_RULES + SEMANTIC_RELATIONSHIPS + SEMANTIC_EQUIVALENCE + CONFIDENCE + UPDATE_MODEL + AI_CONSUMPTION
FLOW_HASH := HASH(FLOW_HASH_INPUT)

END FLOW