In person (MC 5417) and online talk (for Zoom Link please contact ddelreyfernandez@uwaterloo.ca)

## Speaker

Professor Catherine Mavriplis, University of Ottawa Department of Mechanical Engineering

## Title

h-p Adaptive High Order Methods and Direct Numerical Simulation of Transitioning Flows

## Abstract

High order spectral element methods are now routinely used for high resolution studies of complex fluid dynamics, such as direct numerical simulation of engineering flows. However, these methods remain expensive and are hampered by structured grid topologies. Massively parallel implementations and the increasing power of high performance computing platforms have steadily increased their efficiency. Adaptive mesh refinement can also bring significant savings of computational resources and ease the task of finding suitable grids. While the high order computations and the discontinuous Galerkin approach are ideal for parallel computing, on both CPUs and GPUS, the dynamic nature of the adaptive gridding poses significant challenges.

I will present our parallel adaptive discontinuous Galerkin method, where both h-refinement (splitting of elements) and p-refinement (elemental polynomial order increase) are used, guided by * a posteriori* error estimators. To address load imbalance and interprocessor communication, we use a Hilbert (space filling) curve ordering of elements to maintain locality in connectivity information for the adapted grid. The MPI implementation was tested on up to 16,384 CPUs for a wave equation solver. The implementation showed excellent scaling performance on up to 1 million elements. On GPUs, care must be taken to minimize branching and to maximize loading on each GPU, while avoiding race conditions and minimizing latency. We demonstrate excellent scaling properties on up to 64 GPUs for the hp-adaptive wave equation solver

I will also present high order spectral element simulations of flow past a high lift 30P30N wing using the non-adaptive Nek5000 code. We show two Reynolds number results, one where Görtler vortices appear on top of the main airfoil and, at a slightly higher one, where these are replaced by streaky structures (shown here).