Numerical Simulation of Viseous Flow around a Two-Dimensional Finite Flat Plate : A Scheme of Solving Simultaneous Basic Equations at the Same Time

Abstract

Numerical computation of two-dimensional imcompressible flow was conducted around a finite flat plate. A full implicit scheme was used to solve the Navier-Stokes equations and a continuity equation. The three basic equations were descritized by finite difference method and the predictor-corrector method. The subsequent algebraic matrix was solved directly at the same time. The examples of the results were presented for the steady and unsteady cases at a Reynolds number 10^5. The latter case is the flow field around a flat plate in surging motion around a mean advance speed. The steady state solution was compared with the Blasius solution and the numerical solution of the triple-deck theory. The close agreements were obtained. With regard to the unsteady case, the solution is compared with Lin's analysis which assume the small amplitude and the high frequency of the unsteady motion. For the case in which Lin's assumption is valid, the numerical solution was in close agreement with the analysis. From these solutions, the present scheme has the ability to resolve the trailing edge interaction and the unsteady effect. For the unsteady flow, the solutions were also obtained for the large amplitude case and the medium frequency case. In the former, the small nonlinear effect to the averaged velocity was observed, where in the latter the large difference was observed for the fluctuation part.