Sharpening methods for finite volume schemes
For researchers in computational fluid dynamics and numerical PDEs, this is a review paper that consolidates existing sharpening techniques without introducing new results.
This paper reviews sharpening methods for finite volume schemes, covering high-order methods, nonlinear techniques, and their interaction with PDE structures. It presents the algorithmic structure of the downwind method for a two-component problem.
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.