Development of an Upwind Relaxation Multigrid Method for Computing three-Dimensional, Viscous Internal Flows

摘要

The development of an efficient, implicit multigrid strategy for solving the three-dimensional, compressible Navier-Stokes equations is presented in this work. Emphasis is placed on the rapid computation of high Reynolds number flows within configurations characteristic of aircraft propulsion systems. In this context, a planar Gauss-Seidel implicit operator based on a robust, approxiamte linearization of the AUSMV low-diffusion flux-vector splitting scheme is used as a smoother for a convergence acceleration - storage concepts. Four test cases are considered Mach 0.3 turbulent flow through a contoured diffuser, laminar transonic flow through a proto-type "quiet" wind tunnel geometry, Mach 2.89 turbulent flow over a blended cylinder-cone geometry, and Mach 10 laminar flow through a sidewall-compression SCramjet inlet. The grid sizes for the simulations range from approximately 0.5M nodes to over 2.9M nodes. For all test cases, the effects of grid refinement and choice of cycling strategy on convergence rates are examined, and comparisons between multigrid and single-grid approaches are presented.