A Weighted State Redistribution Algorithm for Embedded Boundary Grids

TL;DR

This paper presents an extended, weighted state redistribution algorithm for embedded boundary grids that stabilizes complex cut cell geometries in three dimensions, applicable to various flow simulations and compatible with exascale computing frameworks.

Contribution

It introduces a three-dimensional, weighted state redistribution method that reduces dissipation and stabilizes combined advective and diffusive solutions in embedded boundary grid methods.

Findings

Effective stabilization of incompressible and compressible flows.

Reduced dissipation in the redistribution algorithm.

Successful implementation in exascale-ready simulation codes.

Abstract

State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions. Second, we discuss several algorithmic changes and improvements motivated by the more complicated cut cell geometries that can occur in higher dimensions. In particular, we introduce a weighted version with less dissipation in an easily generalizable framework. Third, we demonstrate that state redistribution can also stabilize a solution update that includes both advective and diffusive contributions. The stabilization algorithm is shown to be effective for incompressible as well as compressible reacting flows. Finally, we discuss the implementation of the algorithm for several exascale-ready simulation codes based on AMReX, demonstrating ease of use in combination with domain decomposition, hybrid parallelism and complex physics.