Anisotropic hp-Adaptation Framework for Functional Prediction

Abstract

This paper presents a method for concurrent mesh and polynomial-order adaptation with the objective of direct minimization of output error using a selection process for choosing the optimal refinement option from a discrete set of choices that includes directional spatial resolution and approximation order increment. The scheme is geared toward compressible viscous aerodynamic flows, in which various solution features make certain refinement options more efficient than others. No attempt is made, however, to measure the solution anisotropy or smoothness directly or to incorporate it into the scheme. Rather, mesh anisotropy and approximation order distribution arise naturally from the optimization of a merit function that incorporates both an output sensitivity and a measure of solution cost on the new mesh. The method is applied to output-based adaptive simulations of laminar and Reynolds-averaged compressible Navier-Stokes equations on body-fitted meshes in two and three dimensions. Two-dimensional results show significant reductions in the degrees of freedom and computational time to achieve output convergence when discrete choice optimization is used compared to uniform or refinement. Three-dimensional results show that the presented method is an affordable way of achieving output convergence on difficult cases such as the third AIAA Drag Prediction Workshop W1 configuration.