Sharpening methods for finite volume schemes

2016/08/09 by Bruno Després, Després, B, Samuel Kokh +3
Engineering · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1608.02719

openalex publication_date 2016/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We review sharpening methods for finite volume schemes, with an emphasis on the basic structure of sharpening methods. It covers high order methods and non linear techniques for linear advection, Glimm's method, anti-diffusion techniques, the interaction of these techniques with the PDE structures. Additional approaches like level sets, interface reconstruction and Vofire are also discussed. We also present the algorithmic structure of the downwind method for a simple two components problem.

Citations

• High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
• High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Finite volume transport schemes
• Volume of fluid (VOF) method for the dynamics of free boundaries
• On the Construction and Comparison of Difference Schemes

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