Development of an efficient multigrid code for 3-D Navier-Stokes equations

Abstract

A multigrid acceleration technique has been developed to solve the three-dimensional Navier-Stokes equations efficiently. An explicit multistage Runge-Kutta type of time-stepping scheme is used as the basic algorithm in conjunction with the multigrid scheme. Solutions for flow over a finite wing have been obtained on extremely fine meshes in order to achieve grid convergence of the solutions. Present solutions indicate that the number of multigrid cycles required to achieve a given level of convergence does not increase with the number of mesh points employed, making it a very attractive scheme for fine meshes.