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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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    1. Lebacque, Jean-Patrick & Mammar, Salim & Haj-Salem, Habib, 2007. "The Aw-Rascle and Zhang's model: Vacuum problems, existence and regularity of the solutions of the Riemann problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 710-721, August.
    2. Wong, G. C. K. & Wong, S. C., 2002. "A multi-class traffic flow model - an extension of LWR model with heterogeneous drivers," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(9), pages 827-841, November.
    3. Tang, T.Q. & Huang, H.J. & Xu, G., 2008. "A new macro model with consideration of the traffic interruption probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6845-6856.
    4. Jin, W. L. & Zhang, H. M., 2003. "On the distribution schemes for determining flows through a merge," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 521-540, July.
    5. W.L. Jin & L. Chen & Elbridge Gerry Puckett, 2009. "Supply-demand Diagrams and a New Framework for Analyzing the Inhomogeneous Lighthill-Whitham-Richards Model," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 603-635, Springer.
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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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