TY - JOUR
T1 - Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method
AU - Sheri L. Martinelli
JO - Communications in Computational Physics
VL - 2
SP - 509
EP - 536
PY - 2014
DA - 2014/08
SN - 14
DO - http://doi.org/10.4208/cicp.130312.301012a
UR - https://global-sci.org/intro/article_detail/cicp/7171.html
KW - 
AB - <p style="text-align: justify;">We 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 is 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.</p>