Advances in Homotopy Continuation Methods in Computational Fluid Dynamics

Progress in the development of a homotopy continuation method to globalize the spatiallydiscretized steady flow equations in computational fluid dynamics (CFD) is presented. The algorithm contains many new features developed specifically for application to the large sparse highly parallelized systems encountered in modern CFD. A second-difference dissipation operator common in finite-difference CFD algorithms is used as the homotopy function. Performance is investigated for compressible subsonic and transonic flow over an ONERA M6 wing geometry. Performance of the homotopy algorithm is demonstrated to be comparable to or better than the well-established pseudo-transient continuation method for all inviscid and laminar cases investigated. The algorithm also shows comparable performance to pseudo-transient continuation for turbulent flows (using Reynolds-averaging).