You can manage bookmarks using lists, please log in to your user account for this.
Media type:
E-Article
Title:
Singularity consideration in the integral equations for contactless inductive flow tomography
Contributor:
Jacobs, Ralf T.;
Wondrak, Thomas;
Stefani, Frank
Published:
Emerald, 2018
Published in:
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 37 (2018) 4, Seite 1366-1375
Description:
<jats:sec>
<jats:title content-type="abstract-subheading">Purpose</jats:title>
<jats:p>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.</jats:p>
</jats:sec>
<jats:sec>
<jats:title content-type="abstract-subheading">Design/methodology/approach</jats:title>
<jats:p>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.</jats:p>
</jats:sec>
<jats:sec>
<jats:title content-type="abstract-subheading">Findings</jats:title>
<jats:p>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.</jats:p>
</jats:sec>
<jats:sec>
<jats:title content-type="abstract-subheading">Originality/value</jats:title>
<jats:p>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.</jats:p>
</jats:sec>