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A Runge–Kutta discontinuous Galerkin scheme for hyperbolic conservation laws with discontinuous fluxes

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  • Qiao, Dian-Liang
  • Zhang, Peng
  • Lin, Zhi-Yang
  • Wong, S.C.
  • Choi, Keechoo

Abstract

The paper proposes a scheme by combining the Runge–Kutta discontinuous Galerkin method with a δ-mapping algorithm for solving hyperbolic conservation laws with discontinuous fluxes. This hybrid scheme is particularly applied to nonlinear elasticity in heterogeneous media and multi-class traffic flow with inhomogeneous road conditions. Numerical examples indicate the scheme’s efficiency in resolving complex waves of the two systems. Moreover, the discussion implies that the so-called δ-mapping algorithm can also be combined with any other classical methods for solving similar problems in general.

Suggested Citation

  • Qiao, Dian-Liang & Zhang, Peng & Lin, Zhi-Yang & Wong, S.C. & Choi, Keechoo, 2017. "A Runge–Kutta discontinuous Galerkin scheme for hyperbolic conservation laws with discontinuous fluxes," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 309-319.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:309-319
    DOI: 10.1016/j.amc.2016.07.030
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    References listed on IDEAS

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    Cited by:

    1. Tingting Xiang & Guodong Wang & Suping Zhang, 2021. "High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space," Mathematics, MDPI, vol. 9(10), pages 1-15, May.

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