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Local orthogonal mappings and operator formulation for varying cross-sectional ducts.
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
2010 (English)Independent thesis Advanced level (degree of Master (Two Years)), 15 credits / 22,5 HE creditsStudent thesis
Abstract [en]

A method is developed for solving the two dimensional Helmholtz equation in a ductwith varying cross-section region bounded by a curved top and flat bottom, having oneregion inside. To compute the propagation of sound waves in a curved duct with a curvedinternal interface is difficult problem. One method is to transform the wave equation intoa solvable form and making the curved interface plane. To this end a local orthogonaltransformation is developed for the varying cross-sectional duct having one medium inside.This transformation is first used to make the curved top of the waveguide flat andto transform the Helmholtz equation into an initial value problem. Later on the local orthogonaltransformation is developed for a waveguide having two media inside with flattop, a flat bottom and a curved interface. This local orthogonal transformation is used toflatten the interface and also to transform the Helmholtz equation into a simple, solvableordinary differential equation. In this paper we present operator formulation for the partwith flat bottom and curved top including a curved interface. In the ordinary differentialequation with operators in coefficients, obtained after the transformation, all the operationsrelated to the transverse variable are treated as operators while the derivative withrespect to the range variable is kept.

Place, publisher, year, edition, pages
2010. , p. 29
Keywords [en]
Helmholtz equation; Local orthogonal transform; operator equation iii
Identifiers
URN: urn:nbn:se:lnu:diva-6366OAI: oai:DiVA.org:lnu-6366DiVA, id: diva2:325598
Presentation
B2034, Linnaeus University, Växjö, Sweden (English)
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2010-06-18 Created: 2010-06-18 Last updated: 2010-06-18Bibliographically approved

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CiteExportLink to record
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  • apa
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