Конференции ИВТ СО РАН

MIT-2009
Международная конференция "Математические и информационные технологии"
(VIII конференция "Вычислительные и информационные технологии в науке, технике и образовании")

Копаоник, Сербия, 27 - 31 августа 2009 года;
Будва, Черногория, 31 августа - 5 сентября 2009 года

Тезисы докладов

Математическое моделирование распространения нелинейных волн в изогнутом трубопроводе

Ткаченко О.П.

Вычислительный центр ДВО РАН (Хабаровск)

A mathematical model describing the dynamics of nonlinear waves in cylindrical pipeline similar to the dynamics of gravitational waves was constucted. For this problem is derived the Korteweg-de Vries equation.

The problem of internal waves in the pipe used original asymptotic expansion of solution by the radial coordinate, where eliminated the infinity of the 1/r in the equations [1].

For the study of strongly nonlinear wave processes in weakly bent pipeline was constructed mathematical model of co-oscillating movement of the pipe and fluid. It is shown that in a bent pipe can exist soliton-like waves. The conditions for the existence of these waves and the influence of the curvature of the axis of the pipeline on their amplitude, speed and form an envelope was investigated.

In the study of equations of the mathematical model of oscillatory motions of the pipe and liquids used methods of decomposition of their solutions in the asymptotic series by small parameters. For the numerical solution of simplified equations with a small parameter at the highest derivative used methods zoom variables and the splicing of numerical solutions.

We derived an asymptotical analysis of nonlinear waves in a bent pipeline, subject to the same order of small parameters describing nonlinearity, dispersion and curvature of the centreline of the pipe. We show that propagating waves with these parameters should describe the precise two-waves non-linear equations to perform basic conservation laws.

1. Rukavishnikov V.A., Tkachenko O.P. The Korteweg-de Vries Equation in a Cylindrical Pipe // Computational Mathematics and Mathematical Physics, 2008, Vol. 48, No. 1, pp. 139–146.

Примечание. Тезисы докладов публикуются в авторской редакции

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