On numerical techniques in CFD

Abstract

Numerical techniques play an important role in CFD. Some of them are reviewed in this paper. The necessity of using high order difference scheme is demonstrated for the study of high Reynolds number viscous flow. Physical guide lines are provided for the construction of these high order schemes. To avoid unduly ad hoc tremtment in the boundary region the use of compact scheme is recommended because it has a small stencil size compared with the traditional finite difference scheme. Besides preliminary Fourier analysis shows the compact scheme can also yield better space resolution which makes it more suitable to study flow with multiscales e.g. turbulence. Other approaches such as perturbation method and finite spectral method are also emphasized. Typical numerical simulations were carried out. The first deals with Euler equations to show its capabilities to capture flow discontinuity. The second deals with Navier-Stokes equations studying the evolution of a mixing layer, the pertinent structures at different times are shown. Asymmetric break down occurs and also the appearance of small vortices.