Numerical Simulation of Compressible Viscous Flows around an Arbitrary Shape Body Using the Cartesian Grid System.

Abstract

A new Cartesian grid system approach is proposed for the numerical simulation of two-dimensional compressible viscous flows around an arbitrary shape body. The grid system is constructed of patched blocks which is composed of the nested-spacing regular grid. The numerical procedure is based on the method of lines. For the spatial discretization, the neighboring-point local collocation method is developed and introduced for the grid points near the body, and the 2nd-order central difference method is used for the points far from the body. The 2-stage Runge-Kutta method (RK 2) is used for the time integration scheme. For the unsteady solution the nesting time step technique is combined with RK 2. Numerical results are obtained for subsonic steady and unsteady flows around a circular cylinder and compared with the other results. The results for transonic and supersonic steady flows over NACA 0012 are compared with the GAMM workshop ones. The present approach is confirmed to be applicable for the arbitrary shape body, and the computational cost is about 50% that of the conventional boundary-fitted grid approach.