Numerical simulation of the problem on the two-dimensional reconstruction of axisymmetric flow velocity profiles

In this paper we consider a numerical method for the axisymmetric flow velocity profile reconstruction and for the pointwise error estimation of reconstruction in the case of fluid or gas flow in circular cross-section transport channels. Our approach is based on applying special ultrasonic flowmeters and on solving an Abel-type integral equation whose right-hand side is assumed to be given with errors at a finite number of measurement points. In order to formulate the problem as well-posed according to Tikhonov, we use the natural a priori information on a velocity vector distribution. It is assumed that the exact solution of the Abel-type equation is a monotonic convex bounded function. In this case, it is possible to determine the error of an approximate solution. We propose a sufficiently simple algorithm for solving the problem; this algorithm is applicable when the number of experimental data is arbitrary.