A New Re-redistribution Scheme for Weighted State Redistribution with Adaptive Mesh Refinement

TL;DR

This paper introduces an extended weighted state redistribution algorithm that ensures conservation and stability in adaptive mesh refinement scenarios involving cut cells near coarse-fine interfaces.

Contribution

The work develops a new re-redistribution scheme for weighted state redistribution that preserves accuracy and conservation in AMR with embedded boundaries.

Findings

Algorithm maintains conservation across mesh interfaces.

Successfully applied to 2D and 3D flow problems.

Enhances stability of cut cell methods in adaptive meshes.

Abstract

State redistribution (SRD) is a recently developed technique for stabilizing cut cells that result from finite-volume embedded boundary methods. SRD has been successfully applied to a variety of compressible and incompressible flow problems. When used in conjunction with adaptive mesh refinement (AMR), additional steps are needed to preserve the accuracy and conservation properties of the solution if the embedded boundary is not restricted to a single level of the mesh hierarchy. In this work, we extend the weighted state redistribution algorithm to cases where cut cells live at or near a coarse-fine interface within the domain. The resulting algorithm maintains conservation and is demonstrated on several two- and three-dimensional example problems.