Eulerian methods for high frequency acoustics

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

The high frequency approximation to the wave equation yields an eikonal equation for the wave phase and a transport equation for the amplitude. Unfortunately, straightforward computation of the eikonal equation poses a challenge in that solutions may be multivalued which affects the convergence of a numerical scheme. Traditional numerical schemes invoke ray tracing methods to solve the eikonal equation in a Lagrangian frame of reference. Ray tracing performs well in many cases and handles the multivalued solution inherently. However, in long range simulations or simulations with complicated boundary conditions, ray solutions may perform poorly as rays are very sensitive to small perturbations in initial conditions. In the past few decades, several methods for solving the eikonal equation in a fixed (Eulerian) frame of reference have been devised. As with any computational method, each has its own advantages and disadvantages, but it is useful to be aware of alternatives since many problems in physical acoustics may benefit from having phase solutions computed on a fixed grid. We present a brief review of recent Eulerian approaches and discuss the merits and open issues with each.

Original languageEnglish (US)
Article number045001
JournalProceedings of Meetings on Acoustics
Volume26
Issue number1
DOIs
StatePublished - May 23 2016
Event171st Meeting of the Acoustical Society of America 2016 - Salt Lake City, United States
Duration: May 23 2016May 27 2016

Fingerprint

eikonal equation
acoustics
ray tracing
rays
wave equations
simulation
grids
boundary conditions
perturbation
approximation

All Science Journal Classification (ASJC) codes

  • Acoustics and Ultrasonics

Cite this

@article{8ca3797a1f6c49ffb976edc6e88ad217,
title = "Eulerian methods for high frequency acoustics",
abstract = "The high frequency approximation to the wave equation yields an eikonal equation for the wave phase and a transport equation for the amplitude. Unfortunately, straightforward computation of the eikonal equation poses a challenge in that solutions may be multivalued which affects the convergence of a numerical scheme. Traditional numerical schemes invoke ray tracing methods to solve the eikonal equation in a Lagrangian frame of reference. Ray tracing performs well in many cases and handles the multivalued solution inherently. However, in long range simulations or simulations with complicated boundary conditions, ray solutions may perform poorly as rays are very sensitive to small perturbations in initial conditions. In the past few decades, several methods for solving the eikonal equation in a fixed (Eulerian) frame of reference have been devised. As with any computational method, each has its own advantages and disadvantages, but it is useful to be aware of alternatives since many problems in physical acoustics may benefit from having phase solutions computed on a fixed grid. We present a brief review of recent Eulerian approaches and discuss the merits and open issues with each.",
author = "Martinelli, {Sheri L.}",
year = "2016",
month = "5",
day = "23",
doi = "10.1121/2.0000242",
language = "English (US)",
volume = "26",
journal = "Proceedings of Meetings on Acoustics",
issn = "1939-800X",
publisher = "Acoustical Society of America",
number = "1",

}

Eulerian methods for high frequency acoustics. / Martinelli, Sheri L.

In: Proceedings of Meetings on Acoustics, Vol. 26, No. 1, 045001, 23.05.2016.

Research output: Contribution to journalConference article

TY - JOUR

T1 - Eulerian methods for high frequency acoustics

AU - Martinelli, Sheri L.

PY - 2016/5/23

Y1 - 2016/5/23

N2 - The high frequency approximation to the wave equation yields an eikonal equation for the wave phase and a transport equation for the amplitude. Unfortunately, straightforward computation of the eikonal equation poses a challenge in that solutions may be multivalued which affects the convergence of a numerical scheme. Traditional numerical schemes invoke ray tracing methods to solve the eikonal equation in a Lagrangian frame of reference. Ray tracing performs well in many cases and handles the multivalued solution inherently. However, in long range simulations or simulations with complicated boundary conditions, ray solutions may perform poorly as rays are very sensitive to small perturbations in initial conditions. In the past few decades, several methods for solving the eikonal equation in a fixed (Eulerian) frame of reference have been devised. As with any computational method, each has its own advantages and disadvantages, but it is useful to be aware of alternatives since many problems in physical acoustics may benefit from having phase solutions computed on a fixed grid. We present a brief review of recent Eulerian approaches and discuss the merits and open issues with each.

AB - The high frequency approximation to the wave equation yields an eikonal equation for the wave phase and a transport equation for the amplitude. Unfortunately, straightforward computation of the eikonal equation poses a challenge in that solutions may be multivalued which affects the convergence of a numerical scheme. Traditional numerical schemes invoke ray tracing methods to solve the eikonal equation in a Lagrangian frame of reference. Ray tracing performs well in many cases and handles the multivalued solution inherently. However, in long range simulations or simulations with complicated boundary conditions, ray solutions may perform poorly as rays are very sensitive to small perturbations in initial conditions. In the past few decades, several methods for solving the eikonal equation in a fixed (Eulerian) frame of reference have been devised. As with any computational method, each has its own advantages and disadvantages, but it is useful to be aware of alternatives since many problems in physical acoustics may benefit from having phase solutions computed on a fixed grid. We present a brief review of recent Eulerian approaches and discuss the merits and open issues with each.

UR - http://www.scopus.com/inward/record.url?scp=85010966345&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010966345&partnerID=8YFLogxK

U2 - 10.1121/2.0000242

DO - 10.1121/2.0000242

M3 - Conference article

VL - 26

JO - Proceedings of Meetings on Acoustics

JF - Proceedings of Meetings on Acoustics

SN - 1939-800X

IS - 1

M1 - 045001

ER -