Computational high frequency wave diffraction by a corner via the Liouville equation and geometric theory of diffraction
This paper deals with a numerical scheme to approximate the high frequency wave equation in two-dimension. In the first part of the paper under review there are reviewed geometric optics approximations by the Wigner transform for the wave equation. Next, the authors present the behavior of waves at a corner based on the geometric theory of diffraction, and provide the conditions that account for reflections at the boundary of the corner and diffractions at the vertex of the corner. These conditions are built into the numerical flux in the two space dimension. There are also studied the positivity and \(l^\infty\) stability of the numerical scheme. Numerical examples are given in the final section of this paper in order to validate the model and to verify the accuracy of the scheme against the full simulation based on the original wave equation.
scientific article; zbMATH DE number 5869607