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Boundary layer in unsteady two-dimensional Navier-Stokes equations. (English) Zbl 0928.76071
Fujita, H. (ed.) et al., Recent developments in domain decomposition methods and flow problems. Dedicated to Professor Hideo Kawarada on the occasion of his 60th birthday. Tokyo: Gakkotosho. GAKUTO Int. Ser., Math. Sci. Appl. 11, 171-180 (1998).
Summary: We consider the unsteady two-dimensional Navier-Stokes solutions having a stagnation point. The problem was investigated by $$(*)$$ S. Childress et al. [J. Fluid Mech. 203, 1-22 (1989; Zbl 0674.76013)]. They showed numerically that sufficiently small viscosity produces finite-time blow-up. Here we examine this phenomenon by two methods: finite difference method and spectral method. Both results of these two methods are much the same, but different from $$(*)$$. We obtain no finite-time blow-up under the same initial conditions as in $$(*)$$, and even for smaller viscosity. Difference of our simulations is mainly in formulation of the problem. In this paper, the algorithm using finite difference scheme and some numerical results are shown.
For the entire collection see [Zbl 0903.00022].

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 76D10 Boundary-layer theory, separation and reattachment, higher-order effects