Bound preserving {P}oint-{A}verage-{M}oment {P}olynomi{A}l-interpreted ({PAMPA}) on polygonal meshes

TL;DR

This paper introduces a new discretisation method called PAMPA, inspired by Roe's Active Flux scheme, which preserves bounds on scalar and Euler equations solutions on polygonal meshes, demonstrating improved accuracy and robustness.

Contribution

The paper presents a novel bound-preserving discretisation strategy for scalar and Euler equations on polygonal meshes, inspired by Roe's Active Flux scheme, with proven stability and improved performance.

Findings

Method is provably bound preserving for scalar and Euler equations.

Demonstrates high-quality results and improvements over previous methods.

Applicable to polygonal meshes, enhancing flexibility and accuracy.

Abstract

We present a novel discretisation strategy, strongly inspired from Roe's Active Flux scheme. It can use polygonal meshes and is provably bound preserving for scalar problems and the Euler equations. Several cases demonstrates the quality of the method, and improvements with respect to previous work of the authors. This paper is a summary of \cite{BPPampa}.