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Analysis of (3+1)-dimensional unsteady gas flow using optimal system of Lie symmetries

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  • Rashed, A.S.

Abstract

Unsteady gas flow in (3+1)-dimensions is studied and analyzed here using an optimal system of Lie symmetry vectors. The governing equations admit thirteen Lie dimensions space. An optimal system of linear combinations of these vectors was formulated to determine the most suitable combinations for solving the governing equations. Unique, double, triple and quadruple combinations were used here to detect analytical solutions. Adiabatic index effect on the attained velocity, density and pressure profiles was also studied. Analysis of the results showed that the velocity profile components increase throughout increasing a distinct spatial variable and throughout the increment of adiabatic index. For density and pressure distributions, analysis of some obtained cases leads to that both of them decrease throughout increment in spatial variable or adiabatic index as long as the solution is non-singular. In case of singular solutions at zero, a reverse result was obtained.

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  • 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.
    • Handle: RePEc:eee:matcom:v:156:y:2019:i:c:p:327-346
    DOI: 10.1016/j.matcom.2018.08.008
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Murata, Souichi, 2005. "New class of symmetries and exact solution to the unsteady equations of adiabatic gas dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 579-582.
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    Cited by:

    1. Kumar, Sachin & Dhiman, Shubham Kumar & Chauhan, Astha, 2022. "Symmetry reductions, generalized solutions and dynamics of wave profiles for the (2+1)-dimensional system of Broer–Kaup–Kupershmidt (BKK) equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 319-335.

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