A high-order incompressible Navier-Stokes solver coupled with a parallel multigrid pressure correction technique for GPUs

21 Jun 2016
16:30-17:00
XENIA HOTEL, PORTARIA

A high-order incompressible Navier-Stokes solver coupled with a parallel multigrid pressure correction technique for GPUs

A parallel multigrid pressure correction scheme is developed for the numerical solution of the incompressible Navier-Stokes equations for computing architectures with accelerators. The discrete pressure Poisson equation is solved with high-order compact finite-difference approximations of the momentum equations on a staggered grid arrangement. This procedure is the most computationally intensive part of the algorithm and a parallel iterative method based on multigrid techniques can accelerate the computation for high resolution simulation problems. Partial semi-coarsening strategy and line red-black ordering Gauss-Seidel relaxation are employed to solve the resulting large and sparse linear system for both equal and unequal mesh-size discretizations. The staggered grid leads to cell-centred multigrid techniques application, having an intrinsic difficulty, since the coarse grid points do not form a subset of the fine-grid points as in the vertex-centered case. The parallel algorithm is based on mapping the multigrid computation on a shared memory multicore architecture. Its realization is developed with using cuBLAS basic linear algebra operations and the OpenACC API for the remaining parallel procedures.
The performance investigation demonstrates that the parallel pressure correction solver can achieve an acceleration up to 11x for CPU-GPU computations and up to 4x for multi-CPU only environments, over the sequential CPU implementation for realistic applications.