CMPS Numerical and Mathematical Theory Manual

A source-aligned theory reference for carrier flow, artificial compressibility, homogeneous VOF, dilute dispersed phase and IATE, reacting species, material properties, turbulence, wall/solid thermal physics, rotating reference frames, scalable linear and multigrid solvers, and parallel CPU/GPU execution.

Source authority: 13 August 2026 project archiveVOF: fully coupled N-phase formulationCPU: Intel MKLGPU: NVIDIA CUDA

Foundations and carrier flow

Theory sectionIntroduction Theory sectionGoverning Carrier-Flow Equations Theory sectionImplementation Conventions and Coupled Jacobian Theory sectionArtificial Compressibility for Constant-Density Flow Theory sectionNumerical Approach Theory sectionCarrier Flux Discretization on Interior Faces Theory sectionTime Integration, CFL Control and Initialization Theory sectionCoordinate Systems, Body Forces and Rotating Reference Frames

Multiphase flow

Theory sectionHomogeneous Volume-of-Fluid (VOF) Model Theory sectionVOF Interface Capturing and Coupled Discretization Theory sectionDilute Dispersed-Phase and Interfacial-Area Model Theory sectionDiscretization of the Dispersed-Phase Equations Theory sectionModel Coupling and Compatibility

Thermochemistry and transport

Theory sectionThermochemistry and Mixture Properties Theory sectionEquations of State and Caloric Models Theory sectionTransport Properties and Material Closures Theory sectionSpecies Transport and Reacting Flow

Turbulence and wall physics

Theory sectionGE \(k-\omega\) Turbulence Model Theory sectionUNSTEADY TURBULENCE MODELS Theory sectionWall Boundary Layers Theory sectionWall Distance Theory sectionWall Functions and Thermal Boundary Treatment Theory sectionBoundary Conditions and Face Closures

Solid and material response

Theory sectionSolid Energy, Conjugate Heat Transfer and Thermal Coupling Theory sectionBoundary-Attached One-Dimensional Charring-Material Response

Linear, nonlinear and multigrid solution

Theory sectionSparse Linear Solver Theory sectionAgglomeration Multigrid and FMG Theory sectionSchur-Complement Pressure–Velocity Coupling

Parallel and accelerated execution

Theory sectionParallel Computing in CMPS

Advanced solution methods

Theory sectionNeuralFlow Solver-Trained Recurrent GNO

Monitoring and qualification

Theory sectionSolution Monitoring and Integral Reports Theory sectionImplementation Status and Model Compatibility Theory sectionSource-Aligned CMPS Capability Map Theory sectionReferences

Deep source-audit additions

The current edition adds a four-part source-audited treatment of NeuralFlow as a solver-trained recurrent GNO, a complete nonlinear admissibility chapter, and rebuilt GE \(k-\omega\)/scale-adaptive turbulence chapters. These revisions replace earlier schematic or placeholder equations with the active implementation mathematics.