Wave Interactions in Non-ideal Isentropic Magnetogasdynamics

被引：7

作者：

Kuila S. ^{[1
]}

Raja Sekhar T. ^{[2
]}

机构：

[1] Department of Mathematics, Jadavpur University, Kolkata

[2] Department of Mathematics, Indian Institute of Technology Kharagpur

来源：

International Journal of Applied and Computational Mathematics | 2017年 / 3卷 / 3期

关键词：

Magnetogasdynamics; Riemann problem; van der Waals gas; Wave interactions;

D O I：

10.1007/s40819-016-0195-2

中图分类号：

学科分类号：

摘要：

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. © 2016, Springer India Pvt. Ltd.

引用

页码：1809 / 1831

页数：22

共 26 条

[1]

Cabannes H., Theoretical magnetofluid dynamics, Applid Mathematics and Mechanics, 13, (1970)

[2]

Gundersen R., Linearized Analysis of One-Dimensional Magnetohydrodynamic Flows, (1964)

[3]

Shen C., The limits of Riemann solutions to the isentropic magnetogasdynamics, Appl. Math. Lett., 24, pp. 1124-1129, (2011)

[4]

Courant R., Friedrichs K.O., Supersonic Flow and Shock Waves, (1999)

[5]

Toro E.F., Riemann Solvers and Numerical Methods for Fluid Dynamics, (1997)

[6]

Godlewski E., Raviart P.A., Numerical Approximation of Hyperbolic System of Conservation Laws, (1996)

[7]

Lax P.D., Hyperbolic systems of conservation laws II, Commun. Pure Appl. Math., 10, pp. 537-566, (1957)

[8]

Smoller J., On the solution of the Riemann problem with general step data for an extended class of hyperbolic systems, J. Mich. Math., 16, pp. 201-210, (1969)

[9]

Smoller J., Shock Waves and Reaction-Diffusion Equations, (1994)

[10]

Smoller J., Temple B., Global solutions of relativistic Euler equations, Commun. Math. Phys., 156, pp. 67-99, (1993)

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