Validating a low-dissipation scheme on shock-tube & wave problems
Benchmarking a fourth-order CABARET scheme against standard finite-volume methods for compressible flows where numerical dissipation was masking real physics.
Problem
Standard second-order finite-volume schemes were over-dissipating fine-scale wave structures in a compressible flow problem, smoothing out gradients the client needed to resolve accurately.
Approach
We benchmarked a fourth-order, low-dissipation CABARET (Compact Accurately Boundary-Adjusting high-REsolution Technique) scheme against the classical Sod and Lax shock-tube problems and standard finite-volume solutions, quantifying dispersion and dissipation error directly against the exact Riemann solutions.
Outcome
The CABARET scheme held shock and contact-discontinuity sharpness at a fraction of the cell count needed by standard upwind schemes to reach comparable accuracy, informing which production cases justify the extra implementation complexity.
// CANONICAL REFERENCES
The literature behind this run
- Goloviznin, V. M. & Samarskii, A. A. (1998). Difference Approximation of Convective Transport with Spatial Splitting of Time Derivative. Matematicheskoe Modelirovanie, 10(1)
- Karabasov, S. A. & Goloviznin, V. M. (2009). Compact Accurately Boundary-Adjusting High-REsolution Technique for Fluid Dynamics. Journal of Computational Physics, 228(19)
- Sod, G. A. (1978). A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws. Journal of Computational Physics, 27(1)
These are the foundational papers the underlying method or validation approach is built on — not client deliverables. Full citation details are provided so the physics can be checked independently.
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