A Unigrid Multi-Model Full Potential and Euler Formulation for Transonic Flows

Marius Paraschivoiu
Department of Mechanical and Industrial Engineering
University Toronto
Toronto, Canada M5S 3G8

Xiao-Chuan Cai
Dept. of Comp. Sci., University of Colorado
Boulder, CO 80309
USA


Abstract

In this paper we present a unigrid multi-model formulation for transonic flow calculations based on solving, in sequence, the full potential equation and the the Euler equations. The goal is to minimize the overall computation time to simulate steady flows by using a more computational efficient physical model in the early iteration steps. The proposed method is based on two steps. In the first step, the full potential equation is solved to obtain a intermediate solution which is ``improved'', in the second step, by solving the Euler equations. The full potential equation and the Euler equations are discretized on the same unstructured mesh to avoid new coarse grid generation and to simplify the transfer, between the two models. The resulting nonlinear systems are solved by a Newton-Krylov algorithm. To demonstrate the feasibility of this multi-model formulation, we present computational results for a three-dimensional transonic flows around a nonlifting wing created from a NACA0012 airfoil.