Geodesic
Numerical simulation of the problem on the two-dimensional reconstruction of axisymmetric flow velocity profiles
Numerical methods and programming, Tome 6 (2005) no. 1, pp. 9-16.

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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.
Keywords: ultrasonic flowmeters, Abel-type integral equation, symmetric flow velocity profile reconstruction
Mots-clés : error estimation. 
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     author = {N. N. Nikolaeva and S. V. Ruchkin and M. N. Rychagov and A. G. Yagola},
     title = {Numerical simulation of the problem on the two-dimensional reconstruction of axisymmetric flow velocity profiles},
     journal = {Numerical methods and programming},
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     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2005_6_1_a1/}
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N. N. Nikolaeva; S. V. Ruchkin; M. N. Rychagov; A. G. Yagola. Numerical simulation of the problem on the two-dimensional reconstruction of axisymmetric flow velocity profiles. Numerical methods and programming, Tome 6 (2005) no. 1, pp. 9-16. http://geodesic.mathdoc.fr/item/VMP_2005_6_1_a1/