Commun. Comput. Phys., 14 (2013), pp. 509-536.

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

Sheri L. Martinelli 1*

1 Torpedo Systems Department, Naval Undersea Warfare Center, 1176 Howell Street, Newport, Rhode Island 02841, USA; and Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA.

Received 13 March 2012; Accepted (in revised version) 30 October 2012
Available online 4 January 2013


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 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.

AMS subject classifications: 65M06, 65M22, 65M25
PACS: 43.30.Gv, 43.30.Zk
Key words: Modelling, Phase-field method, dendritic solidification, binary alloys, convection, magnetic-field, Magnetohydrodynamics, numerical simulations.

*Corresponding author.
Email: (S. Martinelli)

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