Anisotropic mesh adaptation for 3D flows on structured and unstructured grids

This paper presents a mesh optimization methodology in three dimensions, MO M3D. An initial mesh is continually adapted during the solution process wit hout the need for global remeshing. The adaptation procedure uses an interp olation error estimate whose magnitude and direction are controlled by the Hessian, the matrix of second derivatives of the solution. This metric erro r is projected over mesh edges and drives the nodal movement scheme as well as the edge refinement and coarsening strategies. These operations yield h ighly anisotropic grids in which the mesh movement significantly contribute s to the stretching and realignment of the edges along unidirectional featu res of flow problems. The results presented have been chosen to illustrate some important points. First, the method is gauged on problems with exact s olutions, demonstrating good agreement between the error estimate and the t rue error as well as an equidistribution of the error. The cost-effectivene ss of grid adaptation is then addressed by determining the size of an aniso tropic grid that would be equivalent to that of a given non-adapted finer g rid for the same error level. The capture of sharp discontinuities through highly anisotropic grids is illustrated on a transonic flow. Flow in a gas turbine combustor demonstrates how automatically generated meshes can somet imes cause convergence difficulties and how mesh adaptation can cure these ills. Finally, the flow over a wing-nacelle-pylon configuration is studied to further validate the solver-mesh adaptation capabilities by comparing th e numerical results against experiments. (C) 2000 Elsevier Science S.A. All rights reserved.