Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral-Element Methods  

作　　者：Andrés M.Rueda-Ramírez Benjamin Bolm Dmitri Kuzmin Gregor J.Gassner 

机构地区：[1]Department of Mathematics and Computer Science,University of Cologne,Weyertal 86-90,Cologne 50931,Germany [2]Institute of Applied Mathematics(LS Ⅲ),TU Dortmund University,Vogelpothsweg 87,Dortmund 44227,Germany [3]Center for Data and Simulation Science,University of Cologne,Weyertal 86-90,Cologne 50931,Germany

出　　处：《Communications on Applied Mathematics and Computation》2024年第3期1860-1898,共39页应用数学与计算数学学报（英文）

摘　　要：We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.

关 键 词：Structure-preserving schemes Subcellflux limiting Monolithic convex limiting(MCL) Discontinuous Galerkin spectral-element methods(DGSEMS) Legendre-Gauss-Lobatto(LGL)nodes 

分 类 号：O24[理学—计算数学] O29[理学—数学]