High-Order Methods and Boundary Conditions for Simulating Subsonic Flows

The direct numerical simulation of the aeroacoustics of subsonic flows is widely recognized as being crucial to the detailed understanding of the underlying physics. It is also extremely challenging to computational technique due to the relatively small energy of the radiated field, the wide range of spatial and temporal scales, and the fundamental importance of unsteady flow features. In this work we report on our progress in building and testing a highly accurate solver for the compressible Navier-Stokes equations in the subsonic, high Reynolds number regime. Our focus is on optimizing various parameters in our high-order, Hermitebased spatio-temporal discretizations and in our domain truncation methods. We will discuss new theoretical results as well as ongoing numerical experiments ranging from simple one-dimensional simulations of the viscous Burgers and Navier-Stokes equations to fully nonlinear experiments with two-dimensional flows.