Verification and Validation

FiniteVolumeMethod.jl distinguishes between solver capabilities that have been numerically verified and validated, and supporting infrastructure (I/O, dashboards, checkpointing) that facilitates research workflows but does not itself constitute solver verification.

Solver Maturity Levels

Each solver capability is assigned a maturity level reflecting its verification and validation (V&V) status:

• Stable — the solver has passed code verification (convergence studies and/or manufactured solutions), has been validated against published benchmarks, and is suitable for publication-grade results.
• Provisional — automated verification exists and results are promising, but the V&V coverage is incomplete. Suitable for internal research and method development.
• Experimental — early-stage or opt-in work without formal V&V. Not suitable for drawing scientific conclusions.

See the Capability Matrix for the current status of each solver family.

V&V Methodology

The package uses a three-level verification and validation approach:

1. Code verification — convergence studies on problems with known exact solutions or manufactured solutions (MMS). Confirms that the discrete solution converges at the expected order of accuracy.
2. Solution verification — grid-refinement studies on problems without analytical solutions, using Richardson extrapolation or GCI to estimate discretization error.
3. Validation — comparison against published experimental data or established computational benchmarks from the literature.

Verification cases and their expected convergence rates are recorded in the validation manifest (validation/manifest.toml), which serves as the machine-readable source of truth.

Reproducibility

• julia --project=. scripts/verification_validation_report.jl regenerates the V&V report with executed summaries in validation/reports/.
• julia --project=. scripts/build_reproduction_bundles.jl creates per-feature benchmark archives in validation/reproduction_bundles/.
• julia --project=. scripts/build_release_outputs.jl --stable-only produces a release archive with V&V reports, benchmark data, and reproducibility metadata (git commit, Julia version, dependency versions).

Running Tests

All tests run locally via Docker (GitHub Actions are disabled during the v2 development cycle):

Support Policy

• Supported Julia versions: current stable release and current LTS.
• CPU Float64 is the reference baseline for all V&V results.
• GPU (CUDA) execution is an extension that must demonstrate parity against the CPU baseline before it inherits the same validation status.