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Wave Interactions in Non-ideal Isentropic Magnetogasdynamics

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Abstract

In this paper, we consider the Riemann problem and wave interactions for a quasi-linear hyperbolic system of partial differential equations governing the one dimensional unsteady simple wave flow of an isentropic, non-ideal, inviscid and perfectly conducting compressible fluid, subject to a transverse magnetic field. This class of equations includes, as a special case of ideal isentropic magnetogasdynamics. We study the shock and rarefaction waves and their properties, and show the existence and uniqueness of the solution to the Riemann problem for arbitrary initial data under certain conditions and then we discuss the vacuum state in non-ideal isentropic magnetogasdynamics. We discuss numerical tests and study the solution influenced by the van der Waals excluded volume for different initial data along with all possible interactions of elementary waves.

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Acknowledgments

Research support from the Human Resource Development (HRD) Group of Council of Scientific and Industrial Research (CSIR), New Delhi, under the Senior Research Fellowship (SRF) scheme and Science and Engineering Research Board, Department of Science and Technology, Government of India (Ref. No.: SB/FTP/MS-047/2013) gratefully acknowledged by first and second authors respectively.

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    Sahadeb Kuila

  2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-2, India

    T. Raja Sekhar

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  1. Sahadeb Kuila
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  2. T. Raja Sekhar
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Correspondence to Sahadeb Kuila.

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Kuila, S., Raja Sekhar, T. Wave Interactions in Non-ideal Isentropic Magnetogasdynamics. Int. J. Appl. Comput. Math 3, 1809–1831 (2017). https://doi.org/10.1007/s40819-016-0195-2

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  • DOI: https://doi.org/10.1007/s40819-016-0195-2

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