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


  • N.N. Nikolaeva Lomonosov Moscow State University
  • A.G. Yagola Lomonosov Moscow State University
  • S.V. Ruchkin National Research University of Electronic Technology (MIET)
  • M.N. Rychagov National Research University of Electronic Technology (MIET)


ультразвуковые измерения потоков, интегральное уравнение типа Абеля, реконструкция симметричных профилей скорости, оценка погрешности, численные методы


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.

Author Biographies

N.N. Nikolaeva

A.G. Yagola

S.V. Ruchkin

M.N. Rychagov


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How to Cite

Николаева Н.Н., Ягола А.Г., Ручкин С.В., Рычагов М.Н. Numerical Simulation of the Problem on the Two-Dimensional Reconstruction of Axisymmetric Flow Velocity Profiles // Numerical methods and programming. 2004. 6. 9-16



Section 1. Numerical methods and applications

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