# Mimetic Metrics for the DGSEM

## TL;DR

This paper introduces a new method to compute metric terms in DGSEMs that ensures they are divergence-free, which is important for accurate numerical simulations on curvilinear grids.

## Contribution

A novel mimetic approach is introduced to compute divergence-free metric terms for DGSEMs using projections within de Rham Cohomology.

## Key findings

- The new method guarantees divergence-free metric terms for DGSEMs.
- The approach is based on projections that fit within the de Rham Cohomology framework.

## 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. The proposed mimetic approach uses projections that fit within the de Rham Cohomology.