Living technical documentation

Technical

This section provides a living overview of the current mathematical, numerical and computational state of the Multiphysics project.

It documents the present project state. Formal dissertations, papers and releases remain independently citable scientific outputs.

Numerical formulation

Spatial methods

technical preview

FDM — 1D

Current cell-centred finite-difference formulation, physical closures, semi-discrete system, time-integration relationship and verification evidence.

 technical preview

FEM — 1D

Current cell-centred P1 Galerkin formulation, including weak form, element assembly, mass lumping, half-cell completion, physical flux coupling and stability reference.

 implemented / limited scope

FVM — 1D

The 1D finite-volume solver has an implemented-and-verified fixed-geometry/current-heating path. Geometry-changing welding stages remain unpromoted and are not presented as experimentally validated.

Implementations

Calculation environments

active sibling

GNU Octave

An active sibling engine with the broadest current process-workflow coverage. MATLAB compatibility and high-level matrix/vector operations make it useful for numerical development, inspection and scientific prototyping.

 active sibling

C++

An active independent C++17 sibling engine used for same-method cross-engine verification, explicit compiled implementations and LLM-assisted development. Its current workflow coverage is narrower than Octave, but its architectural role is not secondary.

 planned sibling

Julia

A planned third independent engine for the same formulations, intended to broaden implementation redundancy and investigate numerical expressiveness and execution efficiency on selected workloads. No performance advantage is claimed before equivalent benchmarks exist.

Scientific tooling

Automation and evidence infrastructure

active supporting tooling

Python

Python supports validation, governance, material-data workflows, package isolation, provenance, semantics, diagnostics and neutral cross-engine comparison. It is supporting scientific infrastructure, not a calculation engine.

Verification

Evidence and validation boundaries

technical preview

Verification framework

How analytical/reference cases, conservation, refinement, cross-method and cross-engine evidence fit together without being confused with experimental validation.

 active / consolidating

Numerical verification

Current evidence includes conservation checks, analytical/reference cases, spatial refinement, stability references and controlled FDM/FEM/FVM studies.

 future evidence

Experimental validation

Physical calibration and an independent validation case require traceable experimental observables and uncertainty treatment; the complete FBW model is not currently presented as experimentally validated.