Comparison Of High Order And Low Order Methods For Large Eddy Simulation Of A Compressible Shear Layer PDF Download

Turbulent flows occur in a wide variety of engineering applications from flow around an aircraft to internal combustion engines. However for most applications, the computational cost of a direct numerical simulation (DNS) is prohibitive because of the large range of scales of motion. Large eddy simulation (LES) is a more cost effective method where only the large scales of motion are resolved and the smaller scales are modeled. High-order methods, such as the spectral element method (SEM) and the discontinuous Galerkin method (DG), are well suited LES applications because their dissipation and dispersion properties. One limitation of high-order methods is that their polynomial basis cause unphysical oscillations when high-gradient features are under-resolved. For wall-bounded flows, even LES is too expensive for most applications because a large number of elements are needed near the wall to resolve the boundary layer. Wall-modeled LES (WMLES) addresses this challenge by modeling the near wall region while using an LES level of accuracy away from the wall. Traditionally, wall-models use an analytical model to compute the a modeled shear stress on the wall and enforce it as a boundary condition. While shear stress wall-models have shown success, they creates an unphysical solution in the near-wall region. Additionally, these methods are primarily designed for low-order methods and have not been integrated with the advantages of high-order methods. In this thesis, I discuss the development of a solution enrichment method for the spectral element method that augments the polynomial solution with a problem specific non-polynomial enrichment function. This method enhances the ability of SEM to model the targeted feature without unphysical oscillations. The framework is designed to be easily implemented in existing solvers to make it more easily usable for industrial applications and the method is implemented in the open-source solver Nek5000. The enrichment framework is then used to develop a turbulent wall-model for WMLES that maintains a physical solution and turbulent fluctuations throughout the domain. The wall-model enriches the polynomial solution representation with a law-of-the-wall enrichment function so that the large gradients in the near-wall region can be captured with large elements without oscillations. In comparison to traditional shear stress wall-models, the enrichment wall-model is able to better capture the mean velocity profile with larger elements.