Output-based adaptive RANS solutions using higher-order FEM on a multi-element airfoil

Abstract

Higher-order methods in computational fluid dynamics have the potential to provide accurate solutions at lower computational costs than traditional methods. Obtaining accurate flow solutions requires the use of computational meshes that resolve relevant solution features, but generating such meshes a priori is difficult. In this thesis, the effects of adaptivity and discretization order are studied on the solutions of a 2D multi-element high-lift airfoil test case. The flow in this test case is simulated by the RANS equations and Spalart-Allmaras turbulence model. Numerical flow solutions are obtained using both stabilized continuous Galerkin and discontinuous Galerkin finite element frameworks. For both discretizations, a series of increasingly refined adapted meshes are generated using the Metric Optimization via Error Sampling and Synthesis algorithm. The convergence of aerodynamic coefficients, surface pressure, and skin friction on these meshes are studied in order to evaluate the accuracy and cost of the solution. This study is done for several discretization orders, and for both linear and curved meshes. In addition, the characteristics of the adapted meshes for different discretization orders are investigated at a prescribed error level. This analysis provides insight into how the discretization order affects the mesh, along with the resulting solution accuracy and cost. The conclusions of this study indicate that higher-order methods, in particular the p = 2 and p = 3 Continuous Galerkin Variational Multi-Scale with Discontinuous subscales discretizations, provide accurate outputs with an order of magnitude less computational time than p = 1 methods.