Numerical boundary conditions for specular reflection in a level-sets-based wavefront propagation method

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Abstract

We study the simulation of specular reflection in a level set method implementation for wavefront propagation in high frequency acoustics usingWENO spatial operators. To implementWENO efficiently andmaintain convergence rate, a rectangular grid is used over the physical space. When the physical domain does not conformto 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.

Original languageEnglish (US)
Pages (from-to)509-536
Number of pages28
JournalCommunications in Computational Physics
Volume14
Issue number2
DOIs
StatePublished - Aug 2013

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specular reflection
boundary conditions
propagation
grids
operators
acoustics
approximation
simulation

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

Cite this

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abstract = "We study the simulation of specular reflection in a level set method implementation for wavefront propagation in high frequency acoustics usingWENO spatial operators. To implementWENO efficiently andmaintain convergence rate, a rectangular grid is used over the physical space. When the physical domain does not conformto 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.",
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