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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2405.09408 |
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| _version_ | 1866917985394884608 |
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| author | Rozier, Ezra Behrens, Jörn |
| author_facet | Rozier, Ezra Behrens, Jörn |
| contents | In convection-dominated flows, robustness of the spatial discretisation is a key property. While Interior Penalty Galerkin (IPG) methods already proved efficient in the situation of large mesh Peclet numbers, Arbitrary Lagrangian-Eulerian (ALE) methods are able to reduce the convection-dominance by moving the mesh. In this paper, we introduce and analyse a velocity-based moving mesh discontinuous Galerkin (DG) method for the solution of the linear advection-diffusion equation. By introducing a smooth parameterized velocity $\Tilde{V}$ that separates the flow into a mean flow, also called moving mesh velocity, and a remaining advection field $V-\Tilde{V}$, we made a convergence analysis based on the smoothness of the mesh velocity. Furthermore, the reduction of the advection speed improves the stability of an explicit time-stepping. Finally, by adapting the existing robust error criteria to this moving mesh situation, we derived robust \textit{a posteriori} error criteria that describe the potentially small deviation to the mean flow and include the information of a transition towards $V=\Tilde{V}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A velocity-based moving mesh Discontinuous Galerkin method for the advection-diffusion equation Rozier, Ezra Behrens, Jörn Numerical Analysis 65N15, 65N30 In convection-dominated flows, robustness of the spatial discretisation is a key property. While Interior Penalty Galerkin (IPG) methods already proved efficient in the situation of large mesh Peclet numbers, Arbitrary Lagrangian-Eulerian (ALE) methods are able to reduce the convection-dominance by moving the mesh. In this paper, we introduce and analyse a velocity-based moving mesh discontinuous Galerkin (DG) method for the solution of the linear advection-diffusion equation. By introducing a smooth parameterized velocity $\Tilde{V}$ that separates the flow into a mean flow, also called moving mesh velocity, and a remaining advection field $V-\Tilde{V}$, we made a convergence analysis based on the smoothness of the mesh velocity. Furthermore, the reduction of the advection speed improves the stability of an explicit time-stepping. Finally, by adapting the existing robust error criteria to this moving mesh situation, we derived robust \textit{a posteriori} error criteria that describe the potentially small deviation to the mean flow and include the information of a transition towards $V=\Tilde{V}$. |
| title | A velocity-based moving mesh Discontinuous Galerkin method for the advection-diffusion equation |
| topic | Numerical Analysis 65N15, 65N30 |
| url | https://arxiv.org/abs/2405.09408 |