Output-Driven Anisotropic Mesh Adaptation for Viscous Flows Using Discrete Choice Optimization

Abstract

This paper presents a mesh adaptation scheme for direct minimization of output error using a selection process for choosing the optimal refinement option from a discrete set of choices. The scheme is geared for viscous aerodynamic flows, in which solution anisotropy makes certain refinement options more efficient compared to others. No attempt is made, however, to measure the solution anisotropy directly or to incorporate it into the scheme. Rather, mesh anisotropy arises naturally from the minimization of a cost function that incorporates both an output error estimate and a count of the additional degrees of freedom for each refinement option. The method is applied to output-based adaptive simulations of the laminar and Reynolds-averaged compressible Navier-Stokes equations on body-fitted meshes in two and three dimensions. Two-dimensional results for laminar flows show a factor of 2-3 reduction in the degrees of freedom on the final adapted meshes when the discrete choice optimization is used compared to pure isotropic adaptation. Preliminary results on a wing-body configuration show that these savings improve in three dimensions and for higher Reynolds-number flows.