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Assessment of mixture two-phase flow equations for volcanic flows using Godunov-type methods

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  • Zeidan, D.

Abstract

This paper is concerned with the numerical solution of the equations governing two-phase gas–magma mixture in the framework of thermodynamically compatible systems theory. The equations constitute a non-homogeneous system of nonlinear hyperbolic conservation laws. A total variation diminishing (TVD) slope limiter center (SLIC) numerical scheme, based on the Riemann problem, is presented and applied for the solution of the initial boundary value problem for the equations. The model equations and the numerical methods are systematically assessed through a series of numerical test cases. Simulation results are compared and validated with different model equations available in the literature. The computed results compare well with the exact results provided for validation. Strong evidence shows that the model and the methods are accurate, robust and conservative. The model correctly describes the formation of shocks and rarefactions in two-phase gas–magma flow.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:272:y:2016:i:p3:p:707-719
    DOI: 10.1016/j.amc.2015.09.038
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    Cited by:

    1. 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.
    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. 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).
    5. 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.

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