Solution to the Riemann problem for drift-flux model with modified Chaplygin two-phase flows |
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Authors: | Dia Zeidan Sumita Jana Sahadeb Kuila T. Raja Sekhar |
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Affiliation: | 1. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan;2. Department of Mathematics, SRM Institute of Science and Technology, Chennai, Tamil Nadu, India;3. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India |
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Abstract: | In this paper, we concern about the Riemann problem for compressible no-slip drift-flux model which represents a system of quasi-linear partial differential equations derived by averaging the mass and momentum conservation laws with modified Chaplygin two-phase flows. We obtain the exact solution of Riemann problem by elaborately analyzing characteristic fields and discuss the elementary waves namely, shock wave, rarefaction wave and contact discontinuity wave. By employing the equality of pressure and velocity across the middle characteristic field, two nonlinear algebraic equations with two unknowns as gas density ahead and behind the middle wave are formed. The Newton–Raphson method of two variables is applied to find the unknowns with a series of initial data from the literature. Finally, the exact solution for the physical quantities such as gas density, liquid density, velocity, and pressure are illustrated graphically. |
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Keywords: | drift-flux model elementary waves modified Chaplygin flows Riemann problem |
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