A new provably stable weighted state redistribution algorithm

TL;DR

This paper introduces a new finite volume method with a provably stable weighted state redistribution algorithm that maintains monotonicity and TVD properties, improving stability and accuracy in cut cell computations.

Contribution

It presents a novel, provably stable weighted state redistribution algorithm for finite volume methods on cut cells, with analysis explaining its effectiveness and benefits of pre-merging.

Findings

Algorithm is monotone, TVD, and GKS stable in many scenarios.

Shuts off smoothly as cut cell size approaches a target value.

Computational experiments demonstrate effectiveness in 2D and 3D.

Abstract

We propose a practical finite volume method on cut cells using state redistribution. Our algorithm is provably monotone, total variation diminishing, and GKS stable in many situations, and shuts off continuously as the cut cell size approaches a target value. Our analysis reveals why original state redistribution works so well: it results in a monotone scheme for most configurations, though at times subject to a slightly smaller CFL condition. Our analysis also explains why a pre-merging step is beneficial. We show computational experiments in two and three dimensions.