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Solution of Riemann problem for ideal polytropic dusty gas

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  • Nath, Triloki
  • Gupta, R.K.
  • Singh, L.P.

Abstract

The Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady flow of an ideal polytropic gas with dust particles is solved analytically without any restriction on magnitude of the initial states. The elementary wave solutions of the Riemann problem, that is shock waves, rarefaction waves and contact discontinuities are derived explicitly and their properties are discussed, for a dusty gas. The existence and uniqueness of the solution for Riemann problem in dusty gas is discussed. Also the conditions leading to the existence of shock waves or simple waves for a 1-family and 3-family curves in the solution of the Riemann problem are discussed. It is observed that the presence of dust particles in an ideal polytropic gas leads to more complex expression as compared to the corresponding ideal case; however all the parallel results remain same. Also, the effect of variation of mass fraction of dust particles with fixed volume fraction (Z) and the ratio of specific heat of the solid particles and the specific heat of the gas at constant pressure on the variation of velocity and density across the shock wave, rarefaction wave and contact discontinuities are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:95:y:2017:i:c:p:102-110
    DOI: 10.1016/j.chaos.2016.12.004
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    References listed on IDEAS

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    1. Singh, L.P. & Ram, S.D. & Singh, D.B., 2011. "Exact solution of planar and nonplanar weak shock wave problem in gasdynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 964-967.
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    Cited by:

    1. Minhajul, & Mondal, Rakib, 2023. "Wave interaction in isothermal drift-flux model of two-phase flows," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. 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.
    3. 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).

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