A scalable multi-GPU method for semi-implicit fractional-step integration of incompressible Navier-Stokes equations

Abstract: A new flow solver scalable on multiple Graphics Processing Units (GPUs) for direct numerical simulation of wall-bounded incompressible flow is presented. This solver utilizes a previously reported work (J. Comp. Physics, vol. 352 (2018), pp.246-264) which proposes a semi-implicit fractional-step method on a single GPU. Extension of this work to accommodate multiple GPUs becomes inefficient when global transpose is used in the Alternating Direction Implicit (ADI) and Fourier-transform-based direct methods. A new strategy for designing an efficient multi-GPU solver is described to completely remove global transpose and achieve high scalability. Parallel Diagonal Dominant (PDD) and Parallel Partition (PPT) methods are implemented for GPUs to obtain good scaling and preserve accuracy. An overall efficiency of 0.89 is shown. Turbulent flat-plate boundary layer is simulated on 607M grid points using 4 Tesla P100 GPUs.