Mimetic Metrics for the DGSEM

TL;DR

This paper introduces a mimetic approach for computing divergence-free metric terms in DGSEM, ensuring free-stream preservation and entropy stability on curvilinear grids through a projection method aligned with de Rham Cohomology.

Contribution

It presents a novel mimetic metric computation method for DGSEM that guarantees divergence-free metrics using projections based on de Rham Cohomology.

Findings

Ensures divergence-free metric terms in DGSEM.

Guarantees free-stream preservation on curvilinear grids.

Supports entropy stability in numerical solutions.

Abstract

Free-stream preservation is an essential property for numerical solvers on curvilinear grids. Key to this property is that the metric terms of the curvilinear mapping satisfy discrete metric identities, i.e., have zero divergence. Divergence-free metric terms are furthermore essential for entropy stability on curvilinear grids. We present a new way to compute the metric terms for discontinuous Galerkin spectral element methods (DGSEMs) that guarantees they are divergence-free. Our proposed mimetic approach uses projections that fit within the de Rham Cohomology.