Roe: use a simpler wave problem while preserving the jump in conserved quantities

What changed

Roe constructed approximate Riemann solvers with consistent flux-jump linearizations and a parameter-vector representation simplifying perfect-gas Euler equations, while explicitly identifying entropy and multidimensional limitations.

Scientific scope

Roe constructed approximate Riemann solvers with consistent flux-jump linearizations and a parameter-vector representation simplifying perfect-gas Euler equations, while explicitly identifying entropy and multidimensional limitations. The approximate solver uses a state-dependent linearization satisfying the stated consistency, conservation and wave-decomposition properties. Degeneracy, physical admissibility and entropy behavior need care; an entropy fix may be necessary. It is not a universal exact Riemann solver or automatic positivity/convergence guarantee for every conservation law.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• P. L. Roe · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

• P. L. Roe, Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes(1981),357-372 — original article web text

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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