A Robust hp-Adaptation Method for Discontinuous Galerkin Discretizations Applied to Aerodynamic Flows.

Abstract

Quantitatively accurate results from realistic Computational Fluid Dynamics (CFD) simulations are often accompanied by high computational expense. Higher-order methods are good candidates for providing accurate solutions at reduced cost. However, these methods are still not robust for industrial applications.

This thesis presents a solution advancement method that improves robustness of discontinuous Galerkin (DG) discretizations in the iteration to steady-state. The method includes physical realizability constraints in the solution path and provides the solver with the ability of circumventing non-physical regions of the solution space that can occur during the solution transient.

Affordable accurate solutions for challenging problems are obtained via output-based $hp$-adaptation. The adaptation method proposed in this thesis directly targets output error by locally choosing between subdividing an element or raising the approximation order. The decision is made by finding the refinement option that maximizes a merit function that involves output sensitivity and computational cost. Results in two and three dimensions show savings of up to an order of magnitude in terms of number of degrees of freedom and at least a factor of two in terms of computational time when compared to uniform refinement.