Time-Dependent Viscous Incompressible Flow past a Finite Flat Plate

摘要

The flow is started suddenly with a constant velocity and is parallel with the plate. This simple flow configuration is used to compare the accuracy and the speed of various numerical methods and to examine the effect of the far field boundary conditions and the variable mesh size on the flow. The governing Navier-Stokes equations are expressed in terms of vorticity and stream function. The (parabolic) vorticity equation is approximated by two finite difference methods. The (elliptic) stream function equation is approximated by two relaxation schemes. The details of the flow field around the flat plate are computed for Reynolds number equal to 4 and 993. One of the interesting results is that the velocity at the outer edge of the boundary layer exceeds that of the free stream and the maximum velocity overshoot is 9.5% at Re = 4 and 5.4% at Re - 993. The implicit alternating direction method is two to three times faster than the explicit method. (Author)