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Numerical simulation of converging nonlinear wavefronts

Published online by Cambridge University Press:  25 April 1999

PHOOLAN PRASAD  and
K. SANGEETA
PHOOLAN PRASAD
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India; email: prasad@math.iisc.ernet.in
K. SANGEETA
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India; email: prasad@math.iisc.ernet.in Present address: CSIR-Centre for Mathematical Modelling and Computer Simulation, Bangalore 560 037, India.
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Abstract

The propagation of a two-dimensional weakly nonlinear wavefront into a polytropic gas in a uniform state and at rest has been studied. Successive positions of the wavefront and the distribution of amplitude on it are obtained by solving a system of conservation forms of the equations of weakly nonlinear ray theory (WNLRT) using a TVB scheme based on the Lax–Friedrichs flux. The predictions of the WNLRT are found to be qualitatively quite different from the predictions of the linear theory. The linear wavefronts leading to the formation of caustics are replaced by nonlinear wavefronts with kinks. By varying the initial shape of the wavefront and the amplitude distribution on it, the formation and separation of kinks on the wavefront has been studied.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 385 , 25 April 1999 , pp. 1 - 20
Copyright
© 1999 Cambridge University Press

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