An octree solution to conservation laws over arbitrary regions (OSCAR) with applications to aircraft aerodynamics.

Abstract

An octree-based method is presented for the automatic grid generation and computational solution of flows around complicated geometries. The use of computational fluid dynamics (CFD) for aerodynamic analysis and design is still delayed by three major operations: surface definition, grid generation, and flow solution. Through oscar, a parametric model is used for the aircraft surface definition allowing rapid production of aircraft shapes, an octree forms the framework for an automatic grid generator than can run with minimal user input, and a parallel flow solver is built with Message Passing Interface (MPI) to accelerate the solution of the Euler equations using a Godunov-type finite-volume second-order (MUSCL) method on parallel supercomputers. Octrees are recursive data structures where each tree-node may have eight geometrically-similar children. The octree is used to fill the space around the body; cells which intersect the body are labeled as cut-cells, and they are computed as the input body subtracted from the base Cartesian cell. The flow solver is validated through comparison with an exact subsonic concentric cylinder flow and through comparison to Onera data for the M-6 wing. Another design-oriented benefit of oscar's method is that it decouples the input surface and resultant volume grid, such that the user needs only to be concerned with the actual input geometry and flow conditions. To support more realistic modeling of aircraft flows, embedded boundary conditions are included to handle jet engines and propellors. Additionally, an object-oriented programming system (OOPS) is used to encourage simpler development and extension. Examples include subsonic reconnaissance aircraft, propellor-driven aircraft, a supercritical business-jet, an airliner configuration, and the flow around a set of buildings.