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Numerical Front Propagation Using Kinematical Conservation Laws

  • K. R. ArunEmail author
  • M. Lukáčová-Medvi’ová
  • P. Prasad
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)

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.

Keywords

kinematical conservation laws kink weakly nonlinear ray theory wavefront polytropic gas 

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Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • K. R. Arun
    • 1
    Email author
  • M. Lukáčová-Medvi’ová
    • 2
  • P. Prasad
    • 3
  1. 1.Institut für Geometrie und Praktische MathematikRWTH AachenAachenGermany
  2. 2.Institut für MathematikJohannes Gutenberg-Universität MainzMainzGermany
  3. 3.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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