Numerical Front Propagation Using Kinematical Conservation Laws
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.
Keywordskinematical conservation laws kink weakly nonlinear ray theory wavefront polytropic gas
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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.
- 1.Arun, K.R.: A numerical scheme for three-dimensional front propagation and control of Jordan mode. Tech. rep., Department of Mathematics, Indian Institute of Science, Bangalore (2010)Google Scholar
- 2.Arun, K.R., Lukáčová-Medvi’ová, M., Prasad, P., Raghurama Rao, S.V.: An application of 3-D kinematical conservation laws: propagation of a three dimensional wavefront. SIAM. J. Appl. Math. 70, 2604–2626 (2010)Google Scholar