A GPU Accelerated Discontinuous Galerkin Incompressible Flow Solver
2017
We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of the nonlinear term and implicit treatment of the split
Stokes operators. The
pressure systemis solved with a
conjugate gradient methodtogether with a fully GPU-accelerated multigrid
preconditionerwhich is designed to minimize memory requirements and to increase overall performance. A semi-Lagrangian subcycling
advectionalgorithm is used to shift the computational load per timestep away from the pressure Poisson solve by allowing larger timestep sizes in exchange for an increased number of
advectionsteps. Numerical results confirm we achieve the design order accuracy in time and space. We optimize the performance of the most time-consuming kernels by tuning the fine-grain parallelism, memory utilization, and maximizing bandwidth. To assess overall performance we present an empirically calibrated roofline performance model for a target GPU to explain the achieved efficiency. We demonstrate that, in the most cases, the kernels used in the solver are close to their empirically predicted roofline performance.
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