報(bào)告時(shí)間：2024年10月18日（星期五）16:00-17:00
報(bào)告地點(diǎn)：翡翠湖校區(qū)科教樓B座1710室
報(bào) 告 人：Jacobus van der Vegt 教授
工作單位：特文特大學(xué)
舉辦單位：數(shù)學(xué)學(xué)院
報(bào)告簡介：
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.
報(bào)告人簡介：
Jacobus van der Vegt為荷蘭University of Twente大學(xué)的榮譽(yù)教授和中國科學(xué)技術(shù)大學(xué)的訪問教授，曾任荷蘭特文特大學(xué)應(yīng)用數(shù)學(xué)系主任和電子工程、數(shù)學(xué)和計(jì)算機(jī)學(xué)院的院長。其于1988年博士畢業(yè)于荷蘭Delft大學(xué)，于Stanford大學(xué)做博士后，1991年開始先后工作于NASA研究中心，荷蘭國家宇宙空間實(shí)驗(yàn)室，荷蘭University of Twente大學(xué)。2021年獲得安徽省“黃山”友誼獎(jiǎng)。
Jacobus van der Vegt教授是世界知名的計(jì)算數(shù)學(xué)家，在時(shí)空間斷有限元領(lǐng)域取得了眾多重要成果，擔(dān)任Journal of Scientific Computing，Communications on Applied Mathematics and Computation等期刊主編，在業(yè)內(nèi)頂尖期刊SIAM Journal on Scientific Computing, Journal of Computational Physics 等發(fā)表60余篇科研論文。
