Extreme-scale turbulent mixing: dual-resolution asynchronism on GPUs and science results at very low diffusivity

Efficient mixing in turbulent flow is primarily the result of a coupling between transport of local inhomogeneities by the velocity fluctuations and molecular diffusivity. In some applications, such as salinity in the ocean, the molecular diffusivity can be several hundreds times smaller than the fluid viscosity, leading to fluctuations at scales much harder to resolve than the velocity field itself. Computational algorithms where velocity and scalar fields are computed on grids of different resolutions are thus potentially very useful. Numerical requirements lead to both increased algorithmic complexity arising from the need to transfer velocity information from a coarser grid to a finer grid, as well as opportunities for asynchronism between velocity and scalar operations. In this talk we will discuss algorithmic advances as well as science results from pseudo-spectral GPU codes developed on Frontier (the first Exascale supercomputer in the world). Comparisons will also be made with single-resolution studies in the moderately diffusive regime which is much more accessible to both experiment or computation.