A posteriori subcell Finite Volume limiting for Discontinuous Galerkin schemes

：Raphaël Loubère（法国波尔多大学）
：2024-04-29 16:30
：海韵园实验楼105报告厅

报告人：Raphaël Loubère（法国波尔多大学）

时  间：2024年4月29日16:30

地  点：海韵园实验楼105报告厅

内容摘要:

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. 

个人简介：

Raphaël Loubère, Director of Research at CNRS, Institut de Mathématiques de Bordeaux (IMB), University of Bordeaux, France. He got his PhD in applied mathematics in 2002 from the University of Bordeaux, and then held a postdoc position for 3 years at the Los Alamos National Laboratory, U.S.A. In 2006 he won a CR CNRS position at the Mathematical Institute in Toulouse (IMT UMR 5219), and in 2016 he became a DR CNRS at IMB. His research mainly focuses on developing numerical methods that are used as simulation code engines. Those codes are dedicated to simulate complex physical phenomena, such as compressible fluids, multi-phase and multi-material flows, elasto-plastic material, magneto-hydrodynamics, inertial confinement fusion, etc. These fields of research were in close relationship with industrial partners who are the end-users of such innovative numerical methods run on massively parallel machines. He has published more than 70 articles in top-ranked international journals, including JCP, SINUM, SISC, etc.

 

联系人：赵状