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Building a van Leer-type numerical scheme for a model of two-phase flows

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  • Thanh, Mai Duc
  • Cuong, Dao Huy

Abstract

A van Leer-type numerical scheme for a model of two-phase flows is constructed. The governing equations were derived from the modeling of deflagration-to-detonation transitions in granular materials. The system contains source terms in nonconservative form, which cause lots of inconveniences for standard numerical schemes. Our proposed scheme is relied on exact solutions of local Riemann problems. Then, we provide many numerical tests, in which the errors and orders of accuracy of this scheme are computed. These tests show that our proposed van Leer-type scheme has a much better accuracy than the Godunov-type scheme, and that the scheme is well-balanced in the sense that it can capture exactly stationary waves. Furthermore, comparisons between van Leer’s limiter and Roe’s superbee limiter are given.

Suggested Citation

  • Thanh, Mai Duc & Cuong, Dao Huy, 2020. "Building a van Leer-type numerical scheme for a model of two-phase flows," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    • Handle: RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307404
    DOI: 10.1016/j.amc.2019.124748
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    References listed on IDEAS

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    1. Cuong, Dao Huy & Thanh, Mai Duc, 2015. "A Godunov-type scheme for the isentropic model of a fluid flow in a nozzle with variable cross-section," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 602-629.
    2. Thanh, Mai Duc, 2018. "The Riemann problem for the shallow water equations with horizontal temperature gradients," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 159-178.
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    2. Cuong, Dao Huy & Thanh, Mai Duc, 2017. "Constructing a Godunov-type scheme for the model of a general fluid flow in a nozzle with variable cross-section," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 136-160.
    3. Thanh, Mai Duc, 2018. "The Riemann problem for the shallow water equations with horizontal temperature gradients," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 159-178.

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