报告时间：2024年10月18日（星期五）16:00-17:00

报告地点：翡翠科教楼B座1710

报  告 人：Jacobus van der Vegt教授

工作单位：特文特大学

主办单位：数学学院

报告简介：In this presentation an overview will be given of a novel approach to ensure positivity and bounds preservation of Local Discontinuous Galerkin (LDG) discretizations coupled with implicit time discretization methods. Most currently existing positivity preserving numerical discretizations can only be combined with explicit time integration methods. Both the chemically reactive Euler equations and a class of incompletely parabolic partial differential equations will be considered.

To ensure positivity and bounds preservation of the numerical solution, we use the Karush-Kuhn-Tucker (KKT) limiter, which imposes these bounds explicitly by coupling these conditions with time-implicit LDG discretizations using Lagrange multipliers. This results in the well-known Karush-Kuhn-Tucker equations, which are solved using a semi-smooth Newton method. First, the basic algorithm will be explained for incompletely parabolic partial differential equations and demonstrated on some models problems. Next, we will consider the chemically reactive Euler equations. To account for the large disparity between the convective and chemical time scales in the chemically reactive Euler equations, a second order Strang operator splitting approach is used to split these equations into the homogeneous Euler equations and a reaction equation. The KKT limiter to ensure positivity and bounds preservation is then applied to both equations. Special attention will be given to the proper treatment of the chemical reactions in shock and detonation regions since an inaccurate position of discontinuities can strongly influence the chemical reactions and result in spurious numerical solutions.

Numerical results will be presented to demonstrate the accuracy and positivity preservation for several model problems, including chemical reactions, shocks and detonations, that require a positivity and bounds preserving limiter.

报告人简介：Jacobus van der Vegt为荷兰University of Twente大学的荣誉教授和中国科学技术大学的访问教授，曾任荷兰特文特大学应用数学系主任和电子工程、数学和计算机学院的院长。其于1988年博士毕业于荷兰Delft大学，于Stanford大学做博士后，1991年开始先后工作于NASA研究中心，荷兰国家宇宙空间实验室，荷兰University of Twente大学。2021年获得安徽省“黄山”友谊奖。

Jacobus van der Vegt教授是世界知名的计算数学家，在时空间断有限元领域取得了众多重要成果，担任Journal of Scientific Computing，Communications on Applied Mathematics and Computation等期刊主编，在业内顶尖期刊SIAM Journal on Scientific Computing, Journal of Computational Physics等发表60余篇科研论文。