Multigrid accelerated projection method on GPU cluster for the simulation of turbulent flows

Abstract

ABSTRACT A graphics processing unit (GPU)-enabled numerical procedure based on the projection method is developed for simulating incompressible turbulent flows. The pressure Poisson equation is efficiently solved using the V-cycle geometric multigrid method. Additionally, the coarse grid aggregation (CGA) technique enhances the multigrid level of multi-GPU simulations, resulting in significant performance improvements. The validity of the proposed method is confirmed through direct numerical simulations of the turbulent lid-driven cavity flows at a Reynolds number of 3200. The computed mean, and turbulence quantities closely match the available measured data, validating the accuracy of the approach. For the cubic cavity under consideration, the optimized minimum grid sizes for multigrid and CGA are determined to be 83 and 323, respectively. An additional speedup of approximately ≈2.3 to ≈2.6 is achieved by employing CGA. In terms of performance, the current implementation demonstrates compatibility with the lattice Boltzmann method while also being three times faster than the explicit weakly compressible scheme. The superior performance of the GPU implementation over CPU is further highlighted, with a remarkable one thousandfold speedup observed between the Nvidia Tesla V100 and a single core of the Intel I7-6900K (8 cores). Specifically, the performance of one Tesla V100 is found to be equivalent to 125 I7-6900K central processing units.