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Exact solution of the flux perturbed Riemann problem for Cargo-LeRoux model in a van der Waals gas

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  • Jana, Sumita
  • Kuila, Sahadeb

Abstract

In this paper, we consider the pressureless Cargo-LeRoux model of conservation laws represented by a system of quasi-linear partial differential equations derived from the one-dimensional Euler equations with constant gravity. Considering flux perturbation of a van der Waals gas equation of state, we derive the exact solution of this Riemann problem based on the elementary wave analysis including shock wave, rarefaction wave and contact discontinuity wave. The Newton-Raphson method of two variables is applied to find the densities across the contact discontinuity wave of two nonlinear algebraic equations in all possible combinations of waves. Finally, this study exclusively reveals the influence of the growth of van der Waals excluded volume on the physical quantities: density, potential, velocity and total pressure through a series of test cases.

Suggested Citation

  • Jana, Sumita & Kuila, Sahadeb, 2022. "Exact solution of the flux perturbed Riemann problem for Cargo-LeRoux model in a van der Waals gas," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005793
    DOI: 10.1016/j.chaos.2022.112369
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    References listed on IDEAS

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    1. K. Ambika & R. Radha, 2016. "Riemann problem in non-ideal gas dynamics," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(3), pages 501-521, September.
    2. Nath, Triloki & Gupta, R.K. & Singh, L.P., 2017. "Solution of Riemann problem for ideal polytropic dusty gas," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 102-110.
    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.
    4. Sueet Millon Sahoo & T. Raja Sekhar & G. P. Raja Sekhar, 2020. "Exact Solutions of Generalized Riemann Problem for Nonhomogeneous Shallow Water Equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(3), pages 1225-1237, September.
    5. Kuila, S. & Raja Sekhar, T., 2018. "Interaction of weak shocks in drift-flux model of compressible two-phase flows," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 222-227.
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    Cited by:

    1. Karna, Ashutosh Kumar & Satapathy, Purnima, 2023. "Lie symmetry analysis for the Cargo–Leroux model with isentropic perturbation pressure equation of state," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Minhajul, & Mondal, Rakib, 2023. "Wave interaction in isothermal drift-flux model of two-phase flows," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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