Embedded mesh solutions of the Euler equation using a multiple-grid method

Abstract

New developments make it now possible to obtain solutions to Euler equations for many problems on the basis of acceptable computing times. The possibility of an extension of these methods to more difficult flows and increasingly complex geometries can depend on obtaining suitable grid structures. Thus, an attractive approach to complex geometries involves the recasting of the problem into the framework of a multiple-grid structure. The discrete equations represented on the grid are solved as a simultaneous system. In the present investigation, this is accomplished with the aid of Ni's multiple-grid algorithm. The multiple-grid structure provided in this study represents the first step towards a completely general modular approach to the solution of the complete compressible flow problem. In the presented cases, a fine mesh resolution is obtained within the embedded mesh regions, while preserving the global coarse mesh convergence rates.