Local orthogonal transformation and one-way methods for acoustic waveguides

A numerical method is developed for solving the two-dimensional Helmholtz equation in a region bounded by a flat top and a curved bottom. A local orthogonal transformation is first used to flatten the curved bottom of the waveguide. The one-way re-formulation based on the Dirichlet-to-Neumann map is...

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Bibliographic Details
Published inWave motion Vol. 34; no. 2; pp. 193 - 207
Main Authors Lu, Ya Yan, Huang, Jinyang, McLaughlin, Joyce R.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.07.2001
Elsevier
Subjects
Acoustic instruments, equipment, and techniques
Acoustical measurements and instrumentation
Acoustics
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Two dimensional equation
Boundary value problem
Wave propagation
Eigenfunction
Initial value problem
Helmholtz equation
Numerical method
Riccati equation
Acoustic waveguide
Implementation
Orthogonal transformation
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Summary:A numerical method is developed for solving the two-dimensional Helmholtz equation in a region bounded by a flat top and a curved bottom. A local orthogonal transformation is first used to flatten the curved bottom of the waveguide. The one-way re-formulation based on the Dirichlet-to-Neumann map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator Riccati equation uses a large range step method for discretizing the range variable and a truncated local eigenfunction expansion for approximating the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides.
ISSN:0165-2125
1878-433X
DOI:10.1016/S0165-2125(00)00083-4