Exact solutions to drift-flux multiphase flow models through Lie group symmetry analysis

doi:10.1007/s10483-015-1968-7

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (8): 1105-1112.doi: https://doi.org/10.1007/s10483-015-1968-7

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Exact solutions to drift-flux multiphase flow models through Lie group symmetry analysis

B. BIRA¹, T. R. SEKHAR²

1. Department of Mathematics, National Institute of Science and Technology, Palur Hills, Berhampur 8, India;
2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 2, India

Received:2014-11-11 Revised:2015-01-28 Online:2015-08-01 Published:2015-08-01
Contact: T. R. SEKHAR E-mail:trajasekhar@maths.iitkgp.ernet.in
Supported by:
Project supported by the Ministry of Minority Affairs through UGC, Government of India (No. F1-17.1/2010/MANF-CHR-ORI-1839) and the Industrial Consultancy, IIT Kharagpur (No. IIT/SRIC/ISIRD/2013-14)

Abstract

Abstract: In the present paper, Lie group symmetry method is used to obtain some exact solutions for a hyperbolic system of partial differential equations (PDEs), which governs an isothermal no-slip drift-flux model for multiphase flow problem. Those symmetries are used for the governing system of equations to obtain infinitesimal transformations, which consequently reduces the governing system of PDEs to a system of ODEs. Further, the solutions of the system of ODEs which in turn produces some exact solutions for the PDEs are presented. Finally, the evolutionary behavior of weak discontinuity is discussed.

Key words: multiphase flow, weak discontinuity, exact solution, drift-flux models, Lie group analysis

2010 MSC Number:

TV314

B. BIRA, T. R. SEKHAR. Exact solutions to drift-flux multiphase flow models through Lie group symmetry analysis. Applied Mathematics and Mechanics (English Edition), 2015, 36(8): 1105-1112.

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References

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Exact solutions to drift-flux multiphase flow models through Lie group symmetry analysis

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