GPU Acceleration of a High-Order Discontinuous Galerkin Incompressible Flow Solver

12/31/2017
by   Ali Karakus, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 16

12/31/2017

A GPU Accelerated Discontinuous Galerkin Incompressible Flow Solver

We present a GPU-accelerated version of a high-order discontinuous Galer...
05/05/2020

High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration

We present a high-order entropy stable discontinuous Galerkin (ESDG) met...
08/04/2020

High order pressure-based semi-implicit IMEX schemes for the 3D Navier-Stokes equations at all Mach numbers

This article aims at developing a high order pressure-based solver for t...
11/27/2019

High Order Semi-Lagrangian Discontinuous Galerkin Method Coupled with Runge-Kutta Exponential Integrators for Nonlinear Vlasov Dynamics

In this paper, we propose a semi-Lagrangian discontinuous Galerkin metho...
12/08/2021

Assessment of high-order IMEX methods for incompressible flow

This paper investigates the competitiveness of semi-implicit Runge-Kutta...
10/14/2021

Tuning Spectral Element Preconditioners for Parallel Scalability on GPUs

The Poisson pressure solve resulting from the spectral element discretiz...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.