Article ID Journal Published Year Pages File Type
521993 Journal of Computational Physics 2008 34 Pages PDF
Abstract

We construct a class of numerical schemes for the Liouville equation of geometric optics coupled with the Geometric Theory of Diffractions to simulate the high frequency linear waves with a discontinuous index of refraction. In this work [S. Jin, X. Wen, A Hamiltonian-preserving scheme for the Liouville equation of geometric optics with partial transmissions and reflections, SIAM J. Numer. Anal. 44 (2006) 1801–1828], a Hamiltonian-preserving scheme for the Liouville equation was constructed to capture partial transmissions and reflections at the interfaces. This scheme is extended by incorporating diffraction terms derived from Geometric Theory of Diffraction into the numerical flux in order to capture diffraction at the interface. We give such a scheme for curved interfaces. This scheme is proved to be positive under a suitable time step constraint. Numerical experiments show that it can capture diffraction phenomena without fully resolving the wave length of the original wave equation.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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