IndisputableMonolith.ClassicalBridge.Fluids.Discrete
This module supplies type definitions and parameters for discretizing incompressible Navier-Stokes within Recognition Science. Researchers constructing the RS-classical fluid bridge cite it to fix dimension, viscosity, and model structure before stating simulation relations. It consists entirely of declarations for NSParams, TimeStep, DiscretizationKind, DiscreteModel, and EnergyFunctional.
claimThe module introduces $NSParams$ as a pair (spatial dimension, viscosity coefficient) for incompressible Navier-Stokes, together with $DiscreteModel$ (discrete state evolution) and $EnergyFunctional$ (associated energy).
background
The module resides in ClassicalBridge.Fluids and supplies the discrete layer that the RS-Navier-Stokes interface later consumes. Its central object NSParams records the dimension and viscosity needed to specialize the incompressible equations. Sibling declarations introduce TimeStep, DiscretizationKind, DiscreteModel, and EnergyFunctional as the concrete carriers for discrete evolution and energy.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The declarations feed directly into the RS ↔ Navier–Stokes Bridge interface, which requires a discrete NS approximation (DiscreteModel), an LNAL spatial semantics, and a simulation statement relating the two. By fixing NSParams and the model skeleton, the module closes the first item on the Bridge specification.
scope and limits
- Does not encode any simulation relation between discrete states and continuous NS.
- Does not supply an LNAL spatial semantics or encoding/decoding maps.
- Does not instantiate CPM on the discrete state.
- Does not contain numerical schemes or convergence statements.