New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties  

作　　者：Alina Chertock Michael Herty Arsen S.Iskhakov Safa Janajra Alexander Kurganov Maria Lukacova-Medvid'ova 

机构地区：[1]Department of Mathematics,North Carolina State University,Raleigh,NC,USA [2]Department of Mathematics,RWTH Aachen University,Aachen,Germany [3]Department of Mathematics,Shenzhen International Center for Mathematics,and Guangdong Provincial Key Laboratory of Computational Science and Material Design,Southern University of Science and Technology,Shenzhen 518055,Guangdong,China [4]Institute of Mathematics,Johannes Gutenberg University Mainz,Mainz,Germany

出　　处：《Communications on Applied Mathematics and Computation》2024年第3期2011-2044,共34页应用数学与计算数学学报（英文）

基　　金：supported in part by the NSF grant DMS-2208438.The work of M.Herty was supported in part by the DFG(German Research Foundation)through 20021702/GRK2326,333849990/IRTG-2379,HE5386/18-1,19-2,22-1,23-1;under Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612;The work of A.Kurganov was supported in part by the NSFC grant 12171226;the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design,China(No.2019B030301001).

摘　　要：In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory(WENO)interpolations in(multidimensional)random space combined with second-order piecewise linear reconstruction in physical space.Compared with spectral approximations in the random space,the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy.The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations.In the latter case,the methods are also proven to be well-balanced and positivity-preserving.

关 键 词：Hyperbolic conservation and balance laws with uncertainties Finite-volume methods Central-upwind schemes Weighted essentially non-oscillatory(WENO)interpolations 

分 类 号：O241.8[理学—计算数学]