Convergence of a Generalized Riemann Problem Scheme for the Burgers Equation

被引：1
|
作者：
Lukacova-Medvid'ova, Maria [1 ]
Yuan, Yuhuan [2 ]
机构：
[1] Johannes Gutenberg Univ Mainz, Inst Math, Staudingerveg 9, D-55128 Mainz, Germany
[2] Nanjing Univ Aeronaut & Astronaut, Sch Math, Nanjing 211106, Jiangsu, Peoples R China
来源：
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION | 2024年 / 6卷 / 04期
关键词：
Scalar conservation law; Finite volume method; Generalized Riemann problem (GRP) solver; Entropy stability; Consistency; Convergence; FINITE-VOLUME APPROXIMATIONS; SCALAR CONSERVATION-LAWS; MEASURE-VALUED SOLUTIONS; HYPERBOLIC SYSTEMS;
D O I：
10.1007/s42967-023-00338-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：2215 / 2238
页数：24
相关论文
共 50 条
  • [31] Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise
    Bauzet, Caroline
    Nabet, Flore
    Schmitz, Kerstin
    Zimmermann, Aleksandra
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2023, 57 (02) : 745 - 783
  • [32] The Riemann Problem for a Macroscopic Production Model with Logarithmic Equation of State
    Liu, Xiaoli
    Guo, Lihui
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2025, 48 (01)
  • [33] Convergence analysis of finite volume scheme for nonlinear aggregation population balance equation
    Singh, Mehakpreet
    Kaur, Gurmeet
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (09) : 3236 - 3254
  • [34] A HIGHER-ORDER APPROACH FOR TIME-FRACTIONAL GENERALIZED BURGERS' EQUATION
    Taneja, Komal
    Deswal, Komal
    Kumar, Devendra
    Baleanu, Dumitru
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2023, 31 (07)
  • [35] A HIGHER-ORDER APPROACH FOR TIME-FRACTIONAL GENERALIZED BURGERS' EQUATION
    Taneja, Komal
    Deswal, Komal
    Kumar, Devendra
    Baleanu, Dumitru
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2023,
  • [36] Pointwise error estimate of conservative difference scheme for supergeneralized viscous Burgers' equation
    Shi, Yang
    Yang, Xuehua
    ELECTRONIC RESEARCH ARCHIVE, 2024, 32 (03): : 1471 - 1497
  • [37] An adaptive finite point scheme for the two-dimensional coupled burgers' equation
    Sreelakshmi, A.
    Shyaman, V. P.
    Awasthi, Ashish
    NUMERICAL ALGORITHMS, 2024,
  • [38] Crank-Nicolson finite difference scheme for the Rosenau-Burgers equation
    Hu, Bing
    Xu, Youcai
    Hu, Jinsong
    APPLIED MATHEMATICS AND COMPUTATION, 2008, 204 (01) : 311 - 316
  • [39] An efficient, second order accurate, universal generalized Riemann problem solver based on the HLLI Riemann solver
    Balsara, Dinshaw S.
    Li, Jiequan
    Montecinos, Gino, I
    JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 375 : 1238 - 1269
  • [40] Numerical solutions of nonlinear Burgers-Huxley equation through the Richtmyer type nonstandard finite difference scheme
    Izadi, F.
    Najafi, H. Saberi
    Sheikhani, A. H. Refahi
    INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2022, 13 (01): : 1507 - 1518
12345