Computational high frequency  wave diffraction by a corner via the Liouville equation and geometric theory of diffraction

Shi Jin; Dongsheng Yin

doi:10.3934/krm.2011.4.295

Article Contents

2011, Volume 4, Issue 1: 295-316. Doi: 10.3934/krm.2011.4.295

This issue Previous Article Celebrating Cercignani's conjecture for the Boltzmann equation Next Article Fourteen moment theory for granular gases

Computational high frequency wave diffraction by a corner via the Liouville equation and geometric theory of diffraction

Shi Jin^1, and
Dongsheng Yin^2,

1.
Department of Mathematics, University of Wisconsin, Madison, WI 53706
2.
Department of Mathematical Sciences, Tsinghua University, Beijing, 100084

Received: August 2010

Revised: November 2010

Published: March 2011

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Abstract

We construct a numerical scheme based on the Liouville equation of geometric optics coupled with the Geometric Theory of Diffraction (GTD) to simulate the high frequency linear waves diffracted by a corner. While the reflection boundary conditions are used at the boundary, a diffraction condition, based on the GTD theory, is introduced at the vertex. These conditions are built into the numerical flux for the discretization of the geometrical optics Liouville equation. Numerical experiments are used to verify the validity and accuracy of this new Eulerian numerical method which is able to capture the physical observable of high frequency and diffracted waves without fully resolving the high frequency numerically.

Keywords:

Mathematics Subject Classification: Primary: 65M06, 78A45, 35L05; Secondary: 65Z05, 34E05.

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