### 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 language | English (US) |
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Pages (from-to) | 509-536 |

Number of pages | 28 |

Journal | Communications in Computational Physics |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - Aug 2013 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

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**Numerical boundary conditions for specular reflection in a level-sets-based wavefront propagation method.** / Martinelli, Sheri L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Numerical boundary conditions for specular reflection in a level-sets-based wavefront propagation method

AU - Martinelli, Sheri L.

PY - 2013/8

Y1 - 2013/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84872191944&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872191944&partnerID=8YFLogxK

U2 - 10.4208/cicp.130312.301012a

DO - 10.4208/cicp.130312.301012a

M3 - Article

AN - SCOPUS:84872191944

VL - 14

SP - 509

EP - 536

JO - Communications in Computational Physics

JF - Communications in Computational Physics

SN - 1815-2406

IS - 2

ER -