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Published on: June 28, 2024
Mimetic Metrics for the DGSEM
Daniel Bach1, Andrés Rueda-Ramírez2, David A Kopriva3
1University of Cologne, Cologne, Germany.
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.
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