AIAA -86-0103 Calculation of Inviscid Transonic Flow over a Complete Aircraft

We present preliminary results for the calculation of inviscid transonic flow over a complete aircraft. These results have been obtained by a novel approach that combines a new procedure for mesh generation with a new finite element method for solving the Euler equations. Introduction A principal goal of computational aerodynamics has been the calculation of transonic flow over a complete aircraft. Great strides have been made in this direction with major improvements in both the flow solution algorithms and mesh generation techniques. During the last five years, in particular, a variety of methods for solving the complete Euler equations of inviscid flow have been presented, and have been extended to progressively more complex configurations 1,2,3,4,5. While complete aircraft were treated without too much difficulty by the earlier panel methods for subsonic flow, the goal of solving the full nonlinear equations of compressible flow for a complete aircraft has proved less easy to reach, and has been paced by the difficulties of mesh generation. A finite element solution of the potential flow equation for a complete aircraft has been obtained by Bristeau, Glowinski, Periaux, Perrier, Pironneau and Poirier 6. We present here a new finite element method for solving the complete Euler equations of three dimensional compressible flow on a tetrahedral mesh. The method has no requirement of structure in the mesh, and we show preliminary results for the prediction of transonic flow past a complete aircraft, including flow through the engines. Most of the methods hitherto proposed for calculating transonic flow, either by solving the potential equation or by solving the Euler equations, have been based on the use of rectangular cells to discretise the flow equations. This is essentially equivalent to the introduction of curvilinear coordinates and leads to a high degree structure in the mesh. For geometrically simple shapes such as airfoil sections and wings this does not pose a problem. Indeed the curvilinear structure in such meshes has usually been exploited in the solution algorithm. It may help to determine the sweep direction, for example, or allow factorization of the iteration operator for ADI schemes, or in the case of multigrid methods facilitate the interpolation between different grid levels. For multiply connected regions such as the domain around a multi-element airfoil, and for complicated three dimensional regions, the structure imposed by rectangular cells becomes very restrictive. Methods based on the use of several different mesh blocks, each …