Numerical Solution for the Time-Dependent Two-Dimensional Viscous Flows past Obstacle : Part 1, Duct Flow with an Oscillating Plate

抄録

In the analyses of unsteady two-dimensional incompressible laminar flows past an obstacle by means of the vorticity transport equation and Poisson's equation of stream function, a condition [numerical formula] must be satisfied along a closed curve round the obstacle. First, the condition is derived from the one-valued pressure condition, and the relation between the condition and the boundary values of stream function is discussed. Next, for the duct flow with an obstacle, a finite-difference method is proposed for obtaining the solution to satisfy the condition. Them a numerical example that a flat plate in the parallel walled duct is initially at rest on the center line and then oscillates transversely is solved, and flow behavior leaving the plate and the time-variation of lift and drag forces of the plate are shown.