Abstract
With the aid of the development of supercomputers, flow Field simulations using the compressible Navier-Stokes equations have become feasible. It is recently reported that a numerical solution of viscous transonic flow field over a practical wing model is obtained about one hour using 200, 000 grid points on a supercomputer. Such progress of Computational Fluid Dynamics is also owing to the development of numerical methods.
In this paper, the recent development of finite-difference methods for solving the compressible Navier-Stokes equations is discussed. First, the concept of the generalized coordinater is described, which is important to apply computational techniques to arbitrary geometries. Next, the contemporary upwind difference techniques are introduced to obtain high-resolution oscillation-free schemes which give the sharp profiles of shock waves. Finally, the implicit procedures for the finite-difference equations are reviewed. The AF (Approximate Factorization) schemes and the 'unfactored' schemes using relaxation algorithms are considered.
The development of Computational Fluid Dynamics will make it possible to simulate the three-dimensional complicated and unsteady phenomena. Numerical simulation will take the place of wind-tunnel test in part.
