A parallel nonlinear multigrid solver for unsteady incompressible flow simulation on multi-GPU cluster

A nonlinear multigrid solver for solutions of unsteady three-dimensional incompressible viscous flow working on multi-GPU cluster is developed. The solver consists of a full approximation scheme (FAS) V-cycle scheme to accelerate the computation, in which the artificial compressibility method based Navier-Stokes solver is used as a smoother. Multi-stream overlapping strategies are designed to assist multi-GPU computations. The numerical procedure is validated by computing 3D laminar and turbulent flows within a lid-driven cubic cavity. The predicted results compare favorably with previous benchmark solutions and measurements, both in mean and turbulent quantities. For the performance of the FAS V-cycle scheme, up to two orders of magnitude speedups are reported, and the relationship between work unit (WU) and total grid number N is O(N^0.3) under the deepest FAS V-cycle. A detailed evaluation of the GPU implementation is carried out employing the Roofline model and the scalability analysis.