Numerical study of stagnation-point flows of incompressible fluid
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The nonstationary stagnation-point flows of incompressible viscous fluid are studied by a finite difference method. By some ansatz, the two-dimensional equations are reduced to a one-dimensional equation and the three-dimensional ones are reduced to a coupled equations in one-dimension. We perform numerical experiments with various initial values to find the following results. In two dimensions, we find the formation and development of the boundary layers, while no blow-up is observed. In three dimensions, blow-ups are found if both of the initial values are sufficiently large. Some modified equations are also discussed and compared with the original equations. Different roles of the convection, stretching terms are also discussed.
Key wordsNavier-Stokes equations finite difference method boundary layer blow-up
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