Oscillation-Eliminating Discontinuous Galerkin Methods for Multicomponent Chemically Reacting Flows  

作　　者：Jie Du Chuan Fan Kailiang Wu 

机构地区：[1]School of Mathematical Sciences,Key Laboratory of MEA(Ministry of Education)&Shanghai Key Laboratory of PMMP,East China Normal University,Shanghai 200241,China [2]Department of Mathematics and Shenzhen International Center for Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong 518055,China

出　　处：《Annals of Applied Mathematics》2024年第4期411-443,共33页应用数学年刊(英文版)

基　　金：supported by National Key R&D Program of China(Grant No.2021YFA0719200);supported by the Shenzhen Science and Technology Program(Grant No.RCJC20221008092757098);supported by the Postdoctoral Science Foundation of China(Grant No.2024M751284)。

摘　　要：This paper proposes a robust and efficient oscillation-eliminating discontinuous Galerkin(OEDG)method for solving multicomponent chemically reacting flows,which is an extension and application of the recent work[M.Peng,Z.Sun,and K.Wu,Math.Comput.,2024,doi.org/10.1090/mcom/3998].Following recently developed high-order bound-preserving discontinuous Galerkin method in[J.Du and Y.Yang,J.Comput.Phys.,469(2022),111548],we incorporate an OE procedure after each Runge-–Kutta time stage to suppress spurious oscillations.The OE procedure is defined by the solution operator of a damping equation,which can be analytically solved without requiring discretization,making its implementation straightforward,non-intrusive,and efficient.Through careful design of the damping coefficients,the proposed OEDG method not only achieves the essentially non-oscillatory(ENO)property without compromising accuracy but also preserves the conservative property—an indispensable aspect of the bound-preserving technique introduced in[J.Du and Y.Yang,J.Comput.Phys.,469(2022),111548].The effectiveness and robustness of the OEDG method are demonstrated through a series of one-and two-dimensional numerical tests on the compressible Euler and Navier–Stokes equations for chemically reacting flows.These results highlight the method's capability to handle complex flow dynamics while maintaining stability and high-order accuracy.

关 键 词：Oscillation elimination discontinuous Galerkin(OEDG)method modal filter bound-preserving multicomponent chemically reacting flows 

分 类 号：O35[理学—流体力学]