Singularity consideration in the integral equations for contactless inductive flow tomography

Purpose The contactless inductive flow tomography is a procedure that enables the reconstruction of the global three-dimensional flow structure of an electrically conducting fluid by measuring the flow-induced magnetic flux density outside the melt and by subsequently solving the associated linear i...

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Bibliographic Details
Published in:Compel 2018-10, Vol.37 (4), p.1366-1375
Main Authors: Jacobs, Ralf T., Wondrak, Thomas, Stefani, Frank
Format: Article
Language:English
Subjects:
Accuracy
Computation
Conducting fluids
Continuous casting
Flux density
Forward problem
Integral equations
Integrals
Inverse problems
Investigations
Magnetic fields
Magnetic flux
Magnetism
Mathematical analysis
Reynolds number
Singularity (mathematics)
Three dimensional flow
Tomography
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Summary:Purpose The contactless inductive flow tomography is a procedure that enables the reconstruction of the global three-dimensional flow structure of an electrically conducting fluid by measuring the flow-induced magnetic flux density outside the melt and by subsequently solving the associated linear inverse problem. The purpose of this study is to improve the accuracy of the computation of the forward problem, since the forward solution primarily determines the accuracy of the inversion. Design/methodology/approach The tomography procedure is described by a system of coupled integral equations where the integrals contain a singularity when a source point coincides with a field point. The integrals need to be evaluated to a high degree of precision to establish an accurate foundation for the inversion. The contribution of a singular point to the value of the surface and volume integrals in the system is determined by analysing the behaviour of the fields and integrals in the close proximity of the singularity. Findings A significant improvement of the accuracy is achieved by applying higher order elements and by attributing special attention to the singularities inherent in the integral equations. Originality/value The contribution of a singular point to the value of the surface integrals in the system is dependent upon the geometry of the boundary at the singular point. The computation of the integrals is described in detail and the improper surface and volume integrals are shown to exist. The treatment of the singularities represents a novelty in the contactless inductive flow tomography and is the focal point of this investigation.
ISSN:0332-1649
2054-5606
DOI:10.1108/COMPEL-08-2017-0361