Extreme-scale computing and studies of intermittency, mixing of passive scalars and stratified flows in turbulence

Abstract

Turbulent flows are known for the intermittent occurrence of intense strain rates and local rotation, and for its ability to provide efficient mixing. This thesis focuses on pursuing fundamental advances in physical understanding, using high-resolution Direct Numerical Simulations based on a Fourier pseudo-spectral approach. The computations are very demanding, while ever-larger simulations are required for studies of intermittency, where high Reynolds number and good small-scale resolution are important.

A new batched asynchronous algorithm capable of extremely large problem sizes has been developed for dense node heterogeneous architecture machines like Summit. Optimizing data copies between CPU and GPU and communication over the network while overlapping data copies and computations are key to achieving good performance. Processing data residing on the larger CPU memory in batches on the GPU helps avoids limitations on problem size. Favorable performance is obtained up to a world-leading problem size of 18432^3 (over 6 trillion grid points) on 3072 Summit nodes. A more portable implementation using OpenMP is pursued to target 32768^3 problem size on the exascale machine Frontier expected in early 2022.

Hero-sized simulations are often relatively short in time, which raises concerns regarding sampling and statistical independence. A Multiple Resolution Independent Simulations approach (MRIS) is developed to address this issue, via multiple short simulation segments evolving from lower-resolution datasets distributed over a longer physical time span. Using this approach, the effects of small-scale intermittency are studied through statistics of local averages of dissipation rate and enstrophy. The dissipation rate is further studied from a multifractal viewpoint. The MRIS approach is also used to study passive scalar intermittency and test for refined similarity hypothesis, through statistics of scalar dissipation rate at high Reynolds number. Lastly, density stratified flows are studied under both stable and unstable stratification, with anisotropy development studied through the Reynolds-stress budget.