Turbulence at the Exascale: particle tracking and asynchronous GPU algorithm for low-diffusivity turbulent mixing.

Recent advances in GPU algorithm development targeting the world's first Exascale computer (Frontier) are making new milestones for direct numerical simulation of fluid turbulence with many trillions of grid points in a simplified domain achievable in the very near future. In this talk we present further work focusing on two fundamental turbulence phenomena: namely the dispersion of fluid or particulate material at high Reynolds numbers, and the mixing of transported substances with very low molecular diffusivity (such as salinity in the ocean). The first problem requires a particle-tracking capability that is accurate, scalable, and capable of supporting larger particle counts with little increase in cost. This objective is met by cubic spline interpolation combined with ghost layers on the GPU, and a dynamic local decomposition for the particles which greatly reduces the communication costs. In the second, the challenge of low-diffusivity scalars requiring finer resolution than the velocity field is met very economically by a dual-resolution, dual-communicator scheme where both velocity and scalar fields are computed by pseudo-spectral methods asynchronously.