A node-conservative vorticity-preserving Finite Volume method for linear acoustics on unstructured grids

TL;DR

This paper introduces a novel finite volume method for linear acoustics on unstructured grids that conserves vorticity by splitting edges and using non-standard Riemann solvers with adjustable parameters.

Contribution

It proposes a new node-conservative, vorticity-preserving finite volume scheme utilizing non-standard Riemann solvers with free parameters to enhance conservation properties.

Findings

The method preserves vorticity on unstructured meshes.

It ensures flux conservation around nodes.

The approach is validated for linear acoustics.

Abstract

Instead of ensuring that fluxes across edges add up to zero, we split the edge in two halves and also associate different fluxes to each of its sides. This is possible due to non-standard Riemann solvers with free parameters. We then enforce conservation by making sure that the fluxes around a node sum up to zero, which fixes the value of the free parameter. We demonstrate that for linear acoustics one of the non-standard Riemann solvers leads to a vorticity preserving method on unstructured meshes.