Compact Finite Difference based Framework for Large Scale Simulations of Compressible Turbulent Flows*

This work develops a computational framework modernizing the utilization of compact finite difference methods on large scale high performance computing platforms for simulations of compressible turbulent flows. The framework has two major components — a parallel algorithm to solve the cyclic banded system, and a unified discretization approach for compressible Navier-Stokes equations. The linear solver considers the operations on distributed and shared memory hierarchies assuming a flexible grid partition strategy without all-to-all communication nor iterations. The discretization approach allows all conservative variables to be stored at collocated grid points while fluxes to be assembled at staggered grid points. Computational robustness is gained by implicit dealiasing in nonlinear flux assembly as well as enhanced spectral resolution from staggereing and model based subgrid dissipation. The framework has been demonstrated to scale up to 24576 GPUs, and maintains robust performance on cartesian and curvilinear mesh without the need for numerical filtering.