Singularity consideration in the integral equations for contactless inductive flow tomography

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 accurate computation of the forward problem which is essential for the inversion represents the focal point of this investigation. 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 contribution of a singular point to the value of the surface and volume integrals in the system is considered in detail. 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. The treatment of the singularities described in this investigation is similar to the procedure applied in the boundary element method. It represents a novelty in the Contactless Inductive Flow Tomography.