Mimetic Metrics for the DGSEM
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.
Authors
- Andrés M. Rueda-Ramírez (ORCID: https://orcid.org/0000-0001-6557-9162)
- Gregor J. Gassner (ORCID: https://orcid.org/0000-0002-1752-1158)
- David A. Kopriva (ORCID: https://orcid.org/0000-0002-8076-0856)
- Daniel Bach (ORCID: https://orcid.org/0009-0009-1145-3893)
Institutions
- Florida State University (US)
- University of Cologne (DE)
- Universidad Politécnica de Madrid (ES)
Publication Details
- Journal
- Journal of Scientific Computing
- Published
- 2025-10-14
- DOI
- https://doi.org/10.1007/s10915-025-03082-x
- Primary Topic
- Model Reduction and Neural Networks
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Bundesministerium für Bildung und Forschung