Abstract
We use the newly formulated three-dimensional (3-D) kinematical conservation laws (KCL) to study the propagation of a nonlinear wavefront in a polytropic gas in a uniform state at rest. The 3-D KCL forms an under-determined system of six conservation laws with three involutive constraints, to which we add the energy conservation equation of a weakly nonlinear ray theory. The resulting system of seven conservation laws is only weakly hyperbolic and therefore poses a real challenge in the numerical approximation. We implement a central finite volume scheme with a constrained transport technique for the numerical solution of the system of conservation laws. The results of a numerical experiment is presented, which reveals some interesting geometrical features of a nonlinear wavefront.
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MSC2010: 35L60, 35L65, 35L67, 35L80
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References
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Acknowledgements
K. R. A. wishes to thank the Alexander von Humboldt Foundation for a postdoctoral fellowship. P. P. is supported by the Department of Atomic Energy, Government of India, under Raja-Ramanna Fellowship Scheme.
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Arun, K.R., Lukáčová-Medvi’ová, M., Prasad, P. (2011). Numerical Front Propagation Using Kinematical Conservation Laws. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_6
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DOI: https://doi.org/10.1007/978-3-642-20671-9_6
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