A parallel multigrid solver for incompressible flows on computing architectures with acceleratorsA parallel multigrid solver for incompressible flows on computing architectures with accelerators Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2018-03-162017enAn efficient parallel multigrid pressure correction algorithm is proposed for the solution of the incompressible Navier–Stokes equations on computing architectures with acceleration devices. The pressure correction procedure is based on the numerical solution of a Poisson-type problem, which is discretized using a fourth-order finite difference compact scheme. Since this is the most time-consuming part of the solver, we propose a parallel pressure correction algorithm using an iterative method based on a block cyclic reduction solution method combined with a multigrid technique. The grid points are numbered with respect to the red–black ordering scheme for the parallel Gauss–Seidel smoother. These parallelization techniques allow the execution of the entire simulation computations on the acceleration device, minimizing memory communication costs. The realization is developed using the OpenACC API, and the numerical method is demonstrated for the solution of two classical incompressible flow test problems. The first is the two-dimensional lid-driven cavity problem over equal mesh sizes while the other is the Stokes boundary layer, which is a decent benchmark problem for unequal mesh spacing. The effect of several multigrid components on modern and legacy acceleration architectures is examined. Eventually the performance investigation demonstrates that the proposed parallel multigrid solver achieves an acceleration of more than 10× over the sequential solver and more than 4× over multi-core CPU only realizations for all tested accelerators.http://creativecommons.org/licenses/by/4.0/Journal of Supercomputing73114931-4956 Mandikas Vasileios Μανδικας Βασιλειος Mathioudakis Emmanouil Μαθιουδακης Εμμανουηλ Springer Verlag BCR Block cyclic reduction Compact finite difference schemes Computing accelerators GMG Geometric multigrid techniques Incompressible Navier–Stokes equations Zebra line Gauss–Seidel relaxation