A GPU Accelerated Discontinuous Galerkin Incompressible Flow Solver

TL;DR

This paper introduces a GPU-accelerated high-order discontinuous Galerkin solver for incompressible Navier-Stokes equations, achieving high efficiency through optimized kernels, advanced preconditioning, and a semi-Lagrangian advection scheme.

Contribution

The paper presents a novel GPU-accelerated discontinuous Galerkin solver with a fully GPU-optimized pressure solve and a semi-Lagrangian advection method for improved performance.

Findings

Achieves design order accuracy in time and space.

Most kernels operate near their roofline performance.

Significant performance gains from GPU optimization techniques.

Abstract

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 system is solved with a conjugate gradient method together with a fully GPU-accelerated multigrid preconditioner which is designed to minimize memory requirements and to increase overall performance. A semi-Lagrangian subcycling advection algorithm 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 advection steps. 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.