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On the wave interactions in the drift-flux equations of two-phase flows

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  • Minhajul,
  • Zeidan, D.
  • Raja Sekhar, T.

Abstract

In the present work, we investigate the Riemann problem and interaction of weak shocks for the widely used isentropic drift-flux equations of two-phase flows. The complete structure of solution is analyzed and with the help of Rankine–Hugoniot jump condition and Lax entropy conditions we establish the existence and uniqueness condition for elementary waves. The explicit form of the shock waves, contact discontinuities and rarefaction waves are derived analytically. Within this respect, we develop an exact Riemann solver to present the complete solution structure. A necessary and sufficient condition for the existence of solution to the Riemann problem is derived and presented in terms of initial data. Furthermore, we present a necessary and sufficient condition on initial data which provides the information about the existence of a rarefaction wave or a shock wave for one or three family of waves. To validate the performance and the efficiency of the developed exact Riemann solver, a series of test problems selected from the open literature are presented and compared with independent numerical methods. Simulation results demonstrate that the present exact solver is capable of reproducing the complete wave propagation using the current drift-flux equations as the numerical resolution. The provided computations indicate that accurate results be accomplished efficiently and in a satisfactory agreement with the exact solution.

Suggested Citation

  • Minhajul, & Zeidan, D. & Raja Sekhar, T., 2018. "On the wave interactions in the drift-flux equations of two-phase flows," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 117-131.
    • Handle: RePEc:eee:apmaco:v:327:y:2018:i:c:p:117-131
    DOI: 10.1016/j.amc.2018.01.021
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    References listed on IDEAS

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    1. Nguyen, Nguyen T. & Dumbser, Michael, 2015. "A path-conservative finite volume scheme for compressible multi-phase flows with surface tension," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 959-978.
    2. Dumbser, Michael & Casulli, Vincenzo, 2016. "A conservative, weakly nonlinear semi-implicit finite volume scheme for the compressible Navier−Stokes equations with general equation of state," Applied Mathematics and Computation, Elsevier, vol. 272(P2), pages 479-497.
    3. Kuila, Sahadeb & Raja Sekhar, T. & Zeidan, D., 2015. "A Robust and accurate Riemann solver for a compressible two-phase flow model," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 681-695.
    4. Zeidan, D., 2016. "Assessment of mixture two-phase flow equations for volcanic flows using Godunov-type methods," Applied Mathematics and Computation, Elsevier, vol. 272(P3), pages 707-719.
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    Cited by:

    1. Shah, Sarswati & Singh, Randheer & Jena, Jasobanta, 2022. "Steepened wave in two-phase Chaplygin flows comprising a source term," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    2. Lei Fu & Yaodeng Chen & Hongwei Yang, 2019. "Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    3. Rashed, A.S., 2019. "Analysis of (3+1)-dimensional unsteady gas flow using optimal system of Lie symmetries," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 327-346.
    4. Zhang, Ruigang & Yang, Liangui & Liu, Quansheng & Yin, Xiaojun, 2019. "Dynamics of nonlinear Rossby waves in zonally varying flow with spatial-temporal varying topography," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 666-679.
    5. 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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