Solution-Based Adaptivity as a Paradigm for Computational Fluid Dynamics

Abstract

This is the final report for the DOE Early Career award. Through innovation in error estimation and solution-based adaptation methods we strive to dramatically improve the efficiency and robustness of computational science and engineering simulations. By solution-based error estimation and adaptation we refer to techniques for estimating numerical error and efficiently reducing it through targeted discretization changes. In such a setting, high-order methods play a key role, though they are just one mechanism for efficient accuracy improvement. Other mechanisms include well known mesh size and stretching optimization, as well as less-practiced mesh motion and basis optimization. With additional work on the latter, we are integrating these techniques into one adaptive suite that maximizes efficiency and robustness of Computational Fluid Dynamics (CFD) calculations.