Результаты поиска по 'Galerkin–Petrov method':
Найдено статей: 3
  1. Vinogradova P.V., Zarubin A.G., Samusenko A.M.
    Galerkin–Petrov method for one-dimensional parabolic equations of higher order in domain with a moving boundary
    Computer Research and Modeling, 2013, v. 5, no. 1, pp. 3-10

    In the current paper, we study a Galerkin–Petrov method for a parabolic equations of higher order in domain with a moving boundary. Asymptotic estimates for the convergence rate of approximate solutions are obtained.

    Keywords: initial boundary value problem, parabolic equation, Galerkin–Petrov method, convergence, convergence rate.
    Views (last year): 2.
  2. Petrov I.B., Miryaha V.A., Sannikov A.V., Shevtsov A.V.
    Computational modeling of a meteor entering atmosphere dense layers using elastoplastic approximation
    Computer Research and Modeling, 2013, v. 5, no. 6, pp. 957-967

    The article contains results of modeling a meteor entering dense atmosphere layers using Galerkin’s method and smoother particle hydrodynamics. Numerical simulations were run using experimental data gathered for the Chelyabinsk meteor while varying the meteor material characteristics and its orientation when entering the atmosphere.

    Keywords: meteor, atmosphere dense layers, Galerkin’s method, smoothed particle hydrodynamics.
    Views (last year): 2. Citations: 3 (RSCI).
  3. Potapov I.I., Potapov D.I.
    Model of steady river flow in the cross section of a curved channel
    Computer Research and Modeling, 2024, v. 16, no. 5, pp. 1163-1178

    Modeling of channel processes in the study of coastal channel deformations requires the calculation of hydrodynamic flow parameters that take into account the existence of secondary transverse currents formed at channel curvature. Three-dimensional modeling of such processes is currently possible only for small model channels; for real river flows, reduced-dimensional models are needed. At the same time, the reduction of the problem from a three-dimensional model of the river flow movement to a two-dimensional flow model in the cross-section assumes that the hydrodynamic flow under consideration is quasi-stationary and the hypotheses about the asymptotic behavior of the flow along the flow coordinate of the cross-section are fulfilled for it. Taking into account these restrictions, a mathematical model of the problem of the a stationary turbulent calm river flow movement in a channel cross-section is formulated. The problem is formulated in a mixed formulation of velocity — “vortex – stream function”. As additional conditions for problem reducing, it is necessary to specify boundary conditions on the flow free surface for the velocity field, determined in the normal and tangential direction to the cross-section axis. It is assumed that the values of these velocities should be determined from the solution of auxiliary problems or obtained from field or experimental measurement data.

    To solve the formulated problem, the finite element method in the Petrov – Galerkin formulation is used. Discrete analogue of the problem is obtained and an algorithm for solving it is proposed. Numerical studies have shown that, in general, the results obtained are in good agreement with known experimental data. The authors associate the obtained errors with the need to more accurately determine the circulation velocities field at crosssection of the flow by selecting and calibrating a more appropriate model for calculating turbulent viscosity and boundary conditions at the free boundary of the cross-section.

    Keywords: river flow, open channel, riverbed bend, cross-section, finite element method.

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