h-Adaptive FV Subcell Shock-Capturing for DGSEM on Heterogeneous Curvilinear Meshes
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913076655161344 |
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| author | Schwarz, Anna Keim, Jens Rohde, Christian Beck, Andrea |
| author_facet | Schwarz, Anna Keim, Jens Rohde, Christian Beck, Andrea |
| contents | High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscosity is common, but often degrades sub-element resolution. Conversely, subcell resolution preserving limiting strategies such as the finite volume subcell method are typically restricted to uniform topologies, such as purely hexahedral, or simplex meshes. This leaves a significant gap in treating the hybrid-element topologies necessary for complex engineering geometries. This paper presents a robust shock-capturing approach for the discontinuous Galerkin spectral element method on mixed curvilinear meshes containing hexahedral, prismatic, tetrahedral, and pyramid elements. Non-hexahedral elements are handled via collapsed coordinate transformations. The proposed method utilizes an h-adaptive finite volume subcell scheme with arbitrary subcell resolution; 2N + 1 in this work. The schemes essential properties, including conservation, spatial convergence, and the shock capturing capabilities are verified. Finally, the method's applicability to complex configurations is demonstrated through a simulation of the flow around a NACA 0012 airfoil. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27735 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | h-Adaptive FV Subcell Shock-Capturing for DGSEM on Heterogeneous Curvilinear Meshes Schwarz, Anna Keim, Jens Rohde, Christian Beck, Andrea Numerical Analysis High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscosity is common, but often degrades sub-element resolution. Conversely, subcell resolution preserving limiting strategies such as the finite volume subcell method are typically restricted to uniform topologies, such as purely hexahedral, or simplex meshes. This leaves a significant gap in treating the hybrid-element topologies necessary for complex engineering geometries. This paper presents a robust shock-capturing approach for the discontinuous Galerkin spectral element method on mixed curvilinear meshes containing hexahedral, prismatic, tetrahedral, and pyramid elements. Non-hexahedral elements are handled via collapsed coordinate transformations. The proposed method utilizes an h-adaptive finite volume subcell scheme with arbitrary subcell resolution; 2N + 1 in this work. The schemes essential properties, including conservation, spatial convergence, and the shock capturing capabilities are verified. Finally, the method's applicability to complex configurations is demonstrated through a simulation of the flow around a NACA 0012 airfoil. |
| title | h-Adaptive FV Subcell Shock-Capturing for DGSEM on Heterogeneous Curvilinear Meshes |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.27735 |