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A velocity-based moving mesh Discontinuous Galerkin method for the advection-diffusion equation
- Publication Year :
- 2024
-
Abstract
- 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 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 and the use of the nonconservative ALE formulation changes the coercivity condition. 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 $V=\tilde{V}$.<br />Comment: 20 pages, 2 figures, Submitted to SINUM on 16/05/2024, not yet reviewed (15/05/2024)
- Subjects :
- Mathematics - Numerical Analysis
65N15, 65N30
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.09408
- Document Type :
- Working Paper