首页|Convergence of a Generalized Riemann Problem Scheme for the Burgers Equation

Convergence of a Generalized Riemann Problem Scheme for the Burgers Equation

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In this paper,we study the convergence of a second-order finite volume approximation of the scalar conservation law.This scheme is based on the generalized Riemann problem(GRP)solver.We first investigate the stability of the GRP scheme and find that it might be entropy-unstable when the shock wave is generated.By adding an artificial viscosity,we propose a new stabilized GRP scheme.Under the assumption that numerical solutions are uniformly bounded,we prove the consistency and convergence of this new GRP method.

Scalar conservation lawFinite volume methodGeneralized Riemann problem(GRP)solverEntropy stabilityConsistencyConvergence

Mária Lukáčová-Medvid'ová、Yuhuan Yuan

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Institute of Mathematics,Johannes Gutenberg-University Mainz,Staudingerweg 9,55 128 Mainz,Germany

School of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,Jiangsu,China

2024

应用数学与计算数学学报
上海大学

应用数学与计算数学学报

影响因子:0.165
ISSN:1006-6330
年,卷(期):2024.6(4)