Characteristic boundary conditions for Hybridizable Discontinuous Galerkin methods
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908834860105728 |
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| author | Ellmenreich, Jan Giacomini, Matteo Huerta, Antonio Lederer, Philip L. |
| author_facet | Ellmenreich, Jan Giacomini, Matteo Huerta, Antonio Lederer, Philip L. |
| contents | In this work we introduce the concept of characteristic boundary conditions (CBCs) within the framework of Hybridizable Discontinuous Galerkin (HDG) methods, including both the Navier-Stokes characteristic boundary conditions (NSCBCs) and a novel approach to generalized characteristic relaxation boundary conditions (GRCBCs). CBCs are based on the characteristic decomposition of the compressible Euler equations and are designed to prevent the reflection of waves at the domain boundaries. We show the effectiveness of the proposed method for weakly compressible flows through a series of numerical experiments by comparing the results with common boundary conditions in the HDG setting and reference solutions available in the literature. In particular, HDG with CBCs show superior performance minimizing the reflection of vortices at artificial boundaries, for both inviscid and viscous flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characteristic boundary conditions for Hybridizable Discontinuous Galerkin methods Ellmenreich, Jan Giacomini, Matteo Huerta, Antonio Lederer, Philip L. Numerical Analysis Computational Engineering, Finance, and Science Computational Physics Fluid Dynamics In this work we introduce the concept of characteristic boundary conditions (CBCs) within the framework of Hybridizable Discontinuous Galerkin (HDG) methods, including both the Navier-Stokes characteristic boundary conditions (NSCBCs) and a novel approach to generalized characteristic relaxation boundary conditions (GRCBCs). CBCs are based on the characteristic decomposition of the compressible Euler equations and are designed to prevent the reflection of waves at the domain boundaries. We show the effectiveness of the proposed method for weakly compressible flows through a series of numerical experiments by comparing the results with common boundary conditions in the HDG setting and reference solutions available in the literature. In particular, HDG with CBCs show superior performance minimizing the reflection of vortices at artificial boundaries, for both inviscid and viscous flows. |
| title | Characteristic boundary conditions for Hybridizable Discontinuous Galerkin methods |
| topic | Numerical Analysis Computational Engineering, Finance, and Science Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2503.19684 |