Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method

Abstract

AbstractWe study the simulation of specular reflection in a level set method implementation for wavefront propagation in high frequency acoustics using WENO spatial operators. To implement WENO efficiently and maintain convergence rate, a rectangular grid is used over the physical space. When the physical domain does not conform to the rectangular grid, appropriate boundary conditions to represent reflection must be derived to apply at grid locations that are not coincident with the reflecting boundary. A related problem is the extraction of the normal vectors to the boundary, which are required to formulate the reflection condition. A separate level set method is applied to pre-compute the boundary normals which are then stored for use in the wavefront method. Two approaches to handling the reflection boundary condition are proposed and studied: one uses an approximation to the boundary location, and the other uses a local reflection principle. The second method is shown to produce superior results.