Multiple-grid solution of the three-dimensional Edler and Navier-Stokes equations

Abstract

A procedure for the accelerated solution of the three-dimensional, compressible Navier-Stokes and Euler equations is described. The convergence of an explicit fine-grid scheme is enhanced through the use of a multiple-grid technique on a collection of coarser grids. The coarse-grid scheme is itself fully explicit and is independent of such details of the fine-grid problem as the formulation of viscous or damping terms and the specification of boundary conditions. Furthermore, this multiple-grid technique may be used, without modification, with a variety of fine-grid algorithms. Results are presented for the flow through a cascade of finite-span, swept blades. The Euler equations are solved for both subcritical and shocked, supercritical flows. The Navier-Stokes computations include laminar and turbulent, attached and separated flows. The procedure is vectorized for use on a CDC Cyber 205 computer and an algorithm version suitable for use on a multiple instruction ↣ultiple data computer is mentioned.