Kinematical conservation laws in inhomogeneous media

Baskar, S and Murti, R and Prasad, P (2018) Kinematical conservation laws in inhomogeneous media. In: 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016, 1 - 5 August 2016, Aachen, Germany, pp. 349-361.

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Abstract

The system of kinematical conservation laws (KCLs) in two dimensions involves a pair of first-order partial differential equations in a ray coordinate system written in the conservation form. The KCL system governs the evolution of a propagating front (a wavefront or a shock front) in 2D media, which involves four unknown variables, and therefore, we need additional equations to close the system. Such additional relation(s) can be obtained by a weakly nonlinear ray theory (WNLRT) for wavefront propagation and a shock ray theory (SRT) in the case of shock front propagation. The WNLRT and the SRT are well-studied for front propagation in homogeneous media and are successfully applied for an uniform medium filled with a polytropic gas. As these theories are shown to be applicable in the study of sonic boom propagation, it is important to develop these theories in the case of inhomogeneous media. This article summarizes the derivation and a basic numerical test of these two theories in an inhomogeneous medium. We also show that the derived systems are hyperbolic under the condition that the wave speed is greater than the sound speed in the unperturbed medium ahead of these waves. © Springer International Publishing AG, part of Springer Nature 2018.

Item Type:	Conference Paper
Publication:	Springer Proceedings in Mathematics and Statistics
Publisher:	Springer New York LLC
Additional Information:	The copyright for this article belongs to the Springer International Publishing AG, part of Springer Nature
Keywords:	Computational mechanics; Physical properties; Wavefronts, Additional equations; First order partial differential equations; Front propagation; Hyperbolic system; Kinematical conservation laws; Ray coordinate systems; Sonic boom propagation; Wavefront propagation, Shock waves
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	26 Aug 2022 06:09
Last Modified:	26 Aug 2022 06:09
URI:	https://eprints.iisc.ac.in/id/eprint/76045

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