High Order Methods for Direct Numerical Simulation of Incompressible Flows and Applications to Transition to Turbulence

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The objectives of this Discovery Grant are: A) to advance the state of the art of adaptive high order spectral Discontinuous Galerkin methods for the Direct Numerical Simulation of incompressible flows in the transition to turbulence regime; B) to use high order methods to discover new mechanisms in the transition process for complex geometries and, where possible, practical applications such as a laminar morphing wing of Bombardier Aerospace; C) to advance the state of the art in blood viscosity modeling and modeling of blood flow in realistic microcirculation geometries incorporating the effect of Red Blood Cell aggregation; and D) to develop a methodology to 3D print complex laminar and transitional flow structures for research and educational purposes. The work builds on a series of achievements under the last Discovery Grant: namely, the development of a high order h-p adaptive Discontinuous Galerkin method for the incompressible Navier-Stokes equations and its parallel implementation in a hybrid Open MP / MPI approach; development of detailed high Reynolds number (Re) simulations of complex flows with the spectral element Nek5000 open source code, for example at Re=600,000 for the morphing wing; discovery of stability and control mechanisms for the wall jet and models of aircraft wing leading edges; and quantification and characterization of Red Blood Cell aggregation and its effect on blood viscosity in microcirculation. The impact of this work will be felt worldwide, mostly in research arenas that contribute to engineering industry, including aerospace and automotive, to a cleaner environment through leaner fuel consumption and emissions, and to medicine. While over 250 users work with the open source spectral element Nek5000 code, many of these are attempting such complex flows that they need adaptive grids to achieve the proper resolution. The development of h-p adaptive methods will greatly benefit this community. The impact of the fluid dynamics stability and simulation work will benefit the fundamental understanding of such flows and help to elucidate transition and turbulence mechanisms, notoriously difficult to crack. The blood viscosity modeling and blood flow simulations will impact not only biofluid mechanical property understanding but also, potentially in the future, treatment of pathological diseases that affect blood microcirculation, such as diabetes. In the training and education realm, the impact will be on several graduate students and postdoctoral researchers as well as many undergraduate students, first through their direct participation in the research and research skills training, but also through coursework which will be enhanced by the research. The 3D printed methodology will also allow students to better understand fluid mechanics through a previously unexplored tangible and manipulatable approach to fluids.