Local characteristic decomposition based central-upwind scheme

Chertock，Alina1; Chu，Shaoshuai2; Herty，Michael3; Kurganov，Alexander4; Lukáčová-Medvid'ová，Mária5

2023-01-15

10.1016/j.jcp.2022.111718

JOURNAL OF COMPUTATIONAL PHYSICS   Impact Factor & Quartile

0021-9991

1090-2716

We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the studied systems come from the complicated wave structures, such as shocks, rarefactions and contact discontinuities, arising even for smooth initial conditions. In order to reduce the diffusion in the original central-upwind schemes, we use a local characteristic decomposition procedure to develop a new class of central-upwind schemes. We apply the developed schemes to the one- and two-dimensional Euler equations of gas dynamics to illustrate the performance on a variety of examples. The obtained numerical results clearly demonstrate that the proposed new schemes outperform the original central-upwind schemes.

Central-upwind schemes Euler equations of gas dynamics Hyperbolic systems of conservative laws Local characteristic decomposition

SCI

English

Corresponding

National Natural Science Foundation of China[12111530004];National Natural Science Foundation of China[12171226];Deutsche Forschungsgemeinschaft[19-2];Deutsche Forschungsgemeinschaft[20021702/GRK2326];Guangdong Provincial Key Laboratory Of Computational Science And Material Design[2019B030301001];Deutsche Forschungsgemeinschaft[22-1];Deutsche Forschungsgemeinschaft[23-1];Deutsche Forschungsgemeinschaft[333849990/IRTG-2379];National Science Foundation[DMS-1818684];National Science Foundation[DMS-2208438];Deutsche Forschungsgemeinschaft[Germany's Excellence Strategy EXC-2023 Internet of Production 390621612];Deutsche Forschungsgemeinschaft[HE5386/18-1];Deutsche Forschungsgemeinschaft[SFB/TRR 146 Multiscale Simulation Methods for Soft Matter Systems];

WOS:000879385400002

PHYSICS

2-s2.0-85140437212

Scopus

1.Department of Mathematics,North Carolina State University,Raleigh,27695,United States
2.Department of Mathematics,Southern University of Science and Technology,Shenzhen,518055,China
3.Department of Mathematics,RWTH Aachen University,Aachen,52056,Germany
4.Department of Mathematics,SUSTech International Center for Mathematics,Guangdong Provincial Key Laboratory of Computational Science and Material Design,Southern University of Science and Technology,Shenzhen,518055,China
5.Institute of Mathematics,University of Mainz,Germany

Chertock，Alina,Chu，Shaoshuai,Herty，Michael,et al. Local characteristic decomposition based central-upwind scheme[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2023,473.

Chertock，Alina,Chu，Shaoshuai,Herty，Michael,Kurganov，Alexander,&Lukáčová-Medvid'ová，Mária.(2023).Local characteristic decomposition based central-upwind scheme.JOURNAL OF COMPUTATIONAL PHYSICS,473.

Chertock，Alina,et al."Local characteristic decomposition based central-upwind scheme".JOURNAL OF COMPUTATIONAL PHYSICS 473(2023).