Large-Scale Simulations of Complex Turbulent Flows: Modulation of Turbulent Boundary Layer Separation and Optimization of Discontinuous Galerkin Methods for Next-Generation HPC Platforms

Abstract

The separation of spatially evolving turbulent boundary layer flow near regions of adverse pressure gradients has been the subject of numerous studies in the context of flow control. Although many studies have demonstrated the efficacy of passive flow control devices, such as vortex generators (VGs), in reducing the size of the separated region, the interactions between the salient flow structures produced by the VG and those of the separated flow are not fully understood. Here, wall-resolved large-eddy simulation of a model problem of flow over a backward-facing ramp is studied with a submerged, wall-mounted cube being used as a canonical VG. In particular, the turbulent transport that results in the modulation of the separated flow over the ramp is investigated by varying the size, location of the VG, and the spanwise spacing between multiple VGs, which in turn are expected to modify the interactions between the VG-induced flow structures and those of the separated region. The horseshoe vortices produced by the cube entrain the freestream turbulent flow towards the plane of symmetry. These localized regions of high vorticity correspond to turbulent kinetic energy production regions, which effectively transfer energy from the freestream to the near-wall regions. Numerical simulations indicate that: (i) the gradients and the fluctuations, scale with the size of the cube and thus lead to more effective modulation for large cubes, (ii) for a given cube height the different upstream cube positions affect the behavior of the horseshoe vortex---when placed too close to the leading edge, the horseshoe vortex is not sufficiently strong to affect the large-scale structures of the separated region, and when placed too far, the dispersed core of the streamwise vortex is unable to modulate the flow over the ramp, (iii) if the spanwise spacing between neighboring VGs is too small, the counter-rotating vortices are not sufficiently strong to affect the large-scale structures of the separated region, and if the spacing is too large, the flow modulation is similar to that of an isolated VG.

Turbulent boundary layer flows are inherently multiscale, and numerical simulations of such systems often require high spatial and temporal resolution to capture the unsteady flow dynamics accurately. While the innovations in computer hardware and distributed computing have enabled advances in the modeling of such large-scale systems, computations of many practical problems of interest are infeasible, even on the largest supercomputers. The need for high accuracy and the evolving heterogeneous architecture of the next-generation high-performance computing centers has impelled interest in the development of high-order methods. While the new class of recovery-assisted discontinuous Galerkin (RADG) methods can provide arbitrary high-orders of accuracy, the large number of degrees of freedom increases costs associated with the arithmetic operations performed and the amount of data transferred on-node. The purpose of the second part of this thesis is to explore optimization strategies to improve the parallel efficiency of RADG. A cache data-tiling strategy is investigated for polynomial orders 1 through 6, which enhances the arithmetic intensity of RADG to make better utilization of on-node floating-point capability. In addition, a power-aware compute framework is suggested by analyzing the power-performance trade-offs when changing from double to single-precision floating-point types---energy savings of 5 W per node are observed---which suggests that a transprecision framework will likely offer better power-performance balance on modern HPC platforms.