Speaker：Raphaël Loubère（University of Bordeaux）

Time：2024-4-29, 16:30

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

In this talk we propose a simple, robust and accurate nonlinear a posteriori stabilization of the Discontinuous Galerkin (DG) finite element method for the solution of nonlinear hyperbolic PDE systems on unstructured triangular and tetrahedral meshes in two and three space dimensions. This a posteriori limiter is able to resolve discontinuities at a sub-grid scale and is substantially extended here to general unstructured simplex meshes in 2D and 3D. Our new DG limiter entirely recomputes the troubled cells by solving the governing PDE system again starting from valid data at the old time level tn, but using this time a more robust scheme on the sub-grid level. The new a posteriori sub-cell stabilization approach is developed within a high order accurate one-step ADER-DG framework on multidimensional unstructured meshes for hyperbolic systems of conservation laws as well as for hyperbolic PDE with non-conservative products. The method is applied to the Euler equations of compressible gas dynamics, to the ideal magneto-hydrodynamics equations (MHD) as well as to the seven-equation Baer-Nunziato model of compressible multi-phase flows. A large set of standard test problems is solved in order to assess the accuracy and robustness of the new limiter.