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.
Key WordsHigh order accurate scheme Euler equations Navier-Stokes equations
Unable to display preview. Download preview PDF.
- 1.Zhang Hanxin, Guo Chao, Zong Wengang. Problems about grid and high order schemes.Acta Mechanica Sinica, 1999, 31(4): 398–405 (in Chinese)Google Scholar
- 2.Zhang Hanxin et al. On the construction of high order accuracy difference schemes.Acta Aerodynamica Sinica, 1998, 16(1): 14–23Google Scholar
- 4.Zhang Hanxin, Zhuang Fenggan. NND schemes and their applications to numerical simulation of two and three dimensional flows.Advances in Applied Mechanics, 1992, 29Google Scholar
- 6.Fu Dexun, Ma Yanwen. High Resolution Schemes. In: Hafez M, Oshima K, eds. Computational Fluid Dynamics Review. Wiley, 1995. 234–250Google Scholar
- 7.Wang Qiang. Stability analysis and numerical simulation of compressible plane mixing layers. Ph.D. Dissertation. Institute of Mechanics, CAS, 1999Google Scholar
- 8.Wang Jianping. Finite spectral method based on non-periodic fourier transform.Computers and Fluids, 1998, 27(5–6): 639–644Google Scholar
- 9.Chen Guoqian, Gao Zhi. A Compact Fourth Order Upwind Finite Difference Scheme for Convection Diffusion Equation.Journal of Computational Mathematics, 1992, (Aug): 345–357 (in Chinese)Google Scholar
- 10.Li Q. High accuracy difference scheme for solving gas dynamic equations. In: Second Asia Workshop on Computational Fluid Dynamics, Tokyo, 1996Google Scholar
- 11.Fu Dexun, Ma Yanwen, Zhang Linbo. Direct numerical simulation of incompressible mixing layer, transition and turbulence.Science in China, Series A, 2000, 43(4): 421–429Google Scholar