A high-order immersed boundary method to approximate flow problems in domains with curved boundaries
High-order h/p solvers in computational fluid dynamics offer scalability, efficiency, and superior error reduction compared to traditional low-order methods. Immersed boundary methods eliminate the need for body-fitted meshes but often degrade the order of the solution near boundaries, which can dam...
| Autores: | , , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/426444 |
| Acceso en línea: | https://hdl.handle.net/2117/426444 https://dx.doi.org/10.1016/j.jcp.2025.113807 |
| Access Level: | acceso abierto |
| Palabra clave: | Immersed boundary method Curved boundary conditions High-order h/p solvers Discontinuous Galerkin Horses3D Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| Sumario: | High-order h/p solvers in computational fluid dynamics offer scalability, efficiency, and superior error reduction compared to traditional low-order methods. Immersed boundary methods eliminate the need for body-fitted meshes but often degrade the order of the solution near boundaries, which can damage the overall accuracy of the high-order solver. This paper presents a new approach to impose boundary conditions in high-order finite element or finite volume flow solvers that retain high-order P+1 convergence, where P is the polynomial order. Furthermore, the methodology takes into account curved boundary conditions without loss in accuracy. It introduces a surrogate boundary that eliminates instabilities due to badly cut elements. We test the methodology using a high-order discontinuous Galerkin framework to solve purely elliptic problems and the compressible Navier-Stokes equations (2D and 3D), to show that we retain the formal order of convergence P+1 . Finally, we compare the results with a volume penalization approach and show that spurious pressure oscillations on the immersed boundary are eliminated when the proposed methodology is used. |
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