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

Abstract This paper presents a mesh optimization methodology in three dimensions, MOM3D. An initial mesh is continually adapted during the solution process without the need for global remeshing. The adaptation procedure uses an interpolation error estimate whose magnitude and direction are controlled by the Hessian, the matrix of second derivatives of the solution. This metric error is projected over mesh edges and drives the nodal movement scheme as well as the edge refinement and coarsening strategies. These operations yield highly anisotropic grids in which the mesh movement significantly contributes to the stretching and realignment of the edges along unidirectional features of flow problems. The results presented have been chosen to illustrate some important points. First, the method is gauged on problems with exact solutions, demonstrating good agreement between the error estimate and the true error as well as an equidistribution of the error. The cost-effectiveness of grid adaptation is then addressed by determining the size of an anisotropic grid that would be equivalent to that of a given non-adapted finer grid 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 sometimes 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 the numerical results against experiments.