Numerical Study of the Exact Solution of the Navier-Stokes Equation Describing Free-Boundary Fluid Flow
E. N. Zhuravleva
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: течение вязкой несжимаемой жидкости, уравнения Навье -- Стокса, течения со свободными границами, инвариантные и частично инвариантные решения, численные решения, incompressible viscous fluid, Navier-Stokes equations, free-boundary flows, invariant and partially invariant solutions, numerical solutions
Abstract
This paper presents a numerical study of the partially invariant solutions of the Navier-Stokes equations for the plane case which describes unsteady flow in a layer bounded by a straight solid wall and a free boundary parallel to it. It is found that for different values of the initial flow velocity, there may be the establishment a steady state with a decrease or an increase in the initial layer thickness can be established or the layer thickness can be increased infinitely due to liquid inflow from infinity.
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