A Direct Numerical Simulation of an iced Natural Laminar Flow NLF-0414 airfoil is carried out using a high-order spectral element method for low chord Reynolds numbers (O(10^5)). This study aims to advance the state-of-the-art for accurate computational modeling of transition, iced airfoil aerodynamics, and irregular surface spectral element method Direct Numerical Simulation. Ice accretion over an aircraft, ranging from light to severe, changes the aerodynamic profile of the airfoil and alters the overall performance. The literature presents simulations that have been carried out with a range of turbulence models which fail to accurately capture the complex physics of these flows. The iced profiles being studied, Run 606 and 622-2D, were obtained from a Technical Publication by NASA on iced airfoils including the NLF-0414, and were selected as they are relatively lightly iced profiles of the NLF-0414. The largest bottleneck with the current advancement in High Performance Computing is the computation time required for Direct Numerical Simulation. Results such as lift, drag, pressure, and skin friction coefficients, for a clean NLF-0414 and two lightly iced NLF-0414 airfoils at chord Reynolds numbers of Rec = 1 x 10^5 and Rec = 2 x 10^5 are visualized and discussed, showing the degradation of the natural laminar flow due to ice accretion. Turbulence statistics are calculated to study the effective contributions of turbulent fluctuations in the flow to further understand the flow physics near transition. The detailed study of these six cases has led us to 1) further understand the complexities of the transition process on iced airfoils, 2) observe and explain the sometimes unexpected changes in aerodynamic performance due to varying iced geometries, and 3) establish a methodology for spectral element method Direct Numerical Simulations.

Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs) with finite difference methods for the Helmholtz equation. These ABCs are based on exact representations of the outgoing waves by means of farfield expansions. The finite difference methods, which are constructed from a deferred-correction (DC) technique, approximate the Helmholtz equation and the ABCs to any desired order. As a result, high order numerical methods with an overall order of convergence equal to the order of the DC schemes are obtained. A detailed construction of these DC finite difference schemes is presented. Details and results from an extension to heterogeneous media are also included. Additionally, a rigorous proof of the consistency of the DC schemes with the Helmholtz equation and the ABCs in polar coordinates is also given. The results of several numerical experiments corroborate the high order convergence of the proposed method. A novel local high order ABC for elastic waves based on farfield expansions is constructed and preliminary results applying it to elastic scattering problems are presented.