Mimetic Metrics for the DGSEM
This work addresses a fundamental numerical issue for high-order methods on curvilinear grids, providing a provably divergence-free metric computation.
The paper presents a new method for computing metric terms in discontinuous Galerkin spectral element methods that guarantees divergence-free properties, essential for free-stream preservation and entropy stability on curvilinear grids.
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.