Abstract
In the present paper, we study the Riemann problem for quasilinear hyperbolic system of partial differential equations governing the one dimensional ideal isentropic magnetogasdynamics with transverse magnetic field. We discuss the properties of rarefaction waves, shocks and contact discontinuities. Differently from single equation methods rooted in the ideal gasdynamics, the new approach is based on the system of two nonlinear equations imposing the equality of total pressure and velocity, assuming as unknowns the two values of densities, on both sides of the contact discontinuity. Newton iterative method is used to obtain densities. The resulting exact solver is implemented with the examples of general applicability of the proposed approach. For comparisons with exact solution we also shown numerical results obtained by the total variation diminishing slope limiter centre scheme. It is shown that both analytical and numerical results demonstrate the broad applicability and robustness of the new Riemann solver.
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Acknowledgments
Research support from National Board for Higher Mathematics, Department of Atomic Energy, Government of India (Ref. No. 2/48(1)/2011/-R&D II/4715) is gratefully acknowledged. The authors gratefully acknowledge the critical comments and suggestions made by the anonymous referees. We thank Dr. Dia Zeidan, School of Natural Resources Engineering and Management, German Jordanian University, Amman, Jordan, for his help in computation.
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Kuila, S., Sekhar, T.R. Riemann solution for ideal isentropic magnetogasdynamics. Meccanica 49, 2453–2465 (2014). https://doi.org/10.1007/s11012-014-0009-8
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DOI: https://doi.org/10.1007/s11012-014-0009-8