Grant: Discovery Grants Program - Individual

The objectives of the proposed work are to increase the capabilities of high order spectral element methods for direct numerical simulation of complex flows on high performance computing platforms and to use those methods to discover mechanisms of transition to turbulence in fundamental and applied fluid flows in aeronautics and other applications. The work builds on past developments of computer algorithms on supercomputers that can calculate very complex turbulent flows using adaptive grids of points representing the flow domain, where equations are to be solved using polynomial approximation. Adaptive grids are automatically generated by mathematical analysis to allocate computational resources only where they are needed, which can then allow more complex cases to be tackled. Graphical Processing Units (GPUs) are more powerful processors than traditional Central Processing Units (CPUs) and are better suited to high order (more intense) calculations but are much more difficult to program especially with adaptive grids: distribution of data on massively parallel computing platforms needs to be rebalanced as grids change, to extract the best performance of the platform, yet communication between processors needs to be minimized to maintain efficiency. This work will address GPU programming for adaptive grids in the high order context for the full fluid dynamics equations as well as improvements in high order methods to better resolve complex turbulent flows by investigating wavelets. Wavelets are powerful mathematical functions that can resolve a wide range of scales efficiently. We propose to blend wavelets with our traditional polynomial functions within the same framework for more efficient resolution of multiscale turbulent flows. We will develop efficient adaptive methods with both wavelets and polynomials, accounting for their approximation properties and computational cost. Further, we will develop a new method to introduce immersed and moving bodies in a flow, such as a flap being deployed from an aircraft wing. The method allows for simplified grid generation for curved bodies for example and more complex situations such as interaction of flows with moving parts of an aircraft wing for example. In addition to numerical method development, this project also investigates flows of interest to the aircraft industry in Canada and abroad: for example how aerodynamic flow becomes turbulent on a wing with slats and flaps deployed for take-off from the runway or a wing that has been compromised by ice buildup. The knowledge gained from these investigations will help the aircraft industry design greener aircraft through drag reduction and hence reduced fuel consumption and emissions, as well as lower noise pollution. The goals of this entire project reach beyond those stated in NASA's Computational Fluid Dynamics Vision 2030 map and will significantly improve modeling capabilities.