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N. V. Burmasheva, E. Yu. Prosviryakov

A CLASS OF EXACT SOLUTIONS WITH SPATIAL ACCELERATION FOR THE DESCRIPTION OF VISCOUS INCOMPRESSIBLE FLUID FLOWS IN THE FIELD OF MASS FORCES

DOI: 10.17804/2410-9908.2021.1.006-025

The article presents a new class of exact solutions to the system of Navier–Stokes equations, which allows one to take into account the nonlinear distribution of the pressure field and the influence of external volumetric forces, as well as the possibility of horizontal fluid outflow/inflow when modeling its vertical motion. This class is a generalization of the Lin–Sidorov–Aristov class, which assumes the linear distribution of two projections of the fluid flow velocity vector along a part of the coordinates and the independence of the third projection of the velocity vector from these coordinates.

Keywords: class of exact solutions, Navier–Stokes equation, overdetermined system, field of mass (volumetric) forces

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Н. В. Бурмашева, Е. Ю. Просвиряков

КЛАСС ТОЧНЫХ РЕШЕНИЙ С ПРОСТРАНСТВЕННЫМ УСКОРЕНИЕМ ДЛЯ ОПИСАНИЯ ТЕЧЕНИЙ ВЯЗКОЙ НЕСЖИМАЕМОЙ ЖИДКОСТИ В ПОЛЕ МАССОВЫХ СИЛ

В статье представлен новый класс точных решений системы уравнений Навье–Стокса, позволяющий учитывать нелинейное распределение поля давления и влияние внешних объемных сил, а также принимать во внимание возможность горизонтального оттока/притока жидкости при моделировании ее движения в вертикальном направлении. Данный класс является обобщением класса Линя–Сидорова–Аристова, предполагающего линейное распределение двух проекций вектора скорости течения жидкости по части координат и независимость от этих координат третьей проекции вектора скорости.

Ключевые слова: класс точных решений, уравнение Навье–Стокса, переопределенная система, поле массовых (объемных) сил

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Burmasheva N. V., Prosviryakov E. Yu. A Class of Exact Solutions with Spatial Acceleration for the Description of Viscous Incompressible Fluid Flows in the Field of Mass Forces [Electronic resource] // Diagnostics, Resource and Mechanics of materials and structures. - 2021. - Iss. 1. - P. 6-25. -
DOI: 10.17804/2410-9908.2021.1.006-025. -
URL: http://dream-journal.org/issues/2021-1/2021-1_310.html
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