Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method (Communications in Computational Physics, 2014)
We study the simulation of specular reflection in a level set method implementationfor wavefront propagation in high frequency acoustics using WENO spatialoperators. To implement WENO efficiently and maintain convergence rate, a rectangulargrid is used over the physical space. When the physical domain does not conform tothe rectangular grid, appropriate boundary conditions to represent reflection must bederived 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 is required to formulate the reflection condition. A separate level set method is appliedto pre-compute the boundary normals which are then stored for use in the wavefrontmethod. Two approaches to handling the reflection boundary condition are proposedand studied: one uses an approximation to the boundary location, and the other usesa local reflection principle. The second method is shown to produce superior results.