IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v327y2018icp117-131.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318300341
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.01.021?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Boscheri, Walter & Tavelli, Maurizio, 2022. "High order semi-implicit schemes for viscous compressible flows in 3D," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    3. Minhajul, & Mondal, Rakib, 2023. "Wave interaction in isothermal drift-flux model of two-phase flows," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. Saray Busto & Michael Dumbser & Laura Río-Martín, 2021. "Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows," Mathematics, MDPI, vol. 9(22), pages 1-38, November.
    5. Busto, S. & Río-Martín, L. & Vázquez-Cendón, M.E. & Dumbser, M., 2021. "A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    6. 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.
    7. 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.
    8. Jöns, Steven & Munz, Claus-Dieter, 2023. "Riemann solvers for phase transition in a compressible sharp-interface method," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    9. Busto, S. & Dumbser, M. & Río-Martín, L., 2023. "An Arbitrary-Lagrangian-Eulerian hybrid finite volume/finite element method on moving unstructured meshes for the Navier-Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    10. Chhatria, Balakrishna & Raja Sekhar, T. & Zeidan, Dia, 2024. "Limiting behaviour of the Riemann solution to a macroscopic production model with van der Waals equation of state," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    11. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:327:y:2018:i:c:p:117-131. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.