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High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space

Author

Listed:
  • Tingting Xiang

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Guodong Wang

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Suping Zhang

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

Abstract

A new modified Engquist–Osher-type flux-splitting scheme is proposed to approximate the scalar conservation laws with discontinuous flux function in space. The fact that the discontinuity of the fluxes in space results in the jump of the unknown function may be the reason why it is difficult to design a high-order scheme to solve this hyperbolic conservation law. In order to implement the WENO flux reconstruction, we apply the new modified Engquist–Osher-type flux to compensate for the discontinuity of fluxes in space. Together the third-order TVD Runge–Kutta time discretization, we can obtain the high-order accurate scheme, which keeps equilibrium state across the discontinuity in space, to solve the scalar conservation laws with discontinuous flux function. Some examples are given to demonstrate the good performance of the new high-order accurate scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1079-:d:552035
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    References listed on IDEAS

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    1. 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.
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