An accelerated iterative linear solver with GPUs for CFD calculations of unstructured grids

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Abstract

Computational Fluid Dynamics (CFD) utilizes numerical solutions of Partial Differential Equations (PDE) on discretized volumes. These sets of discretized volumes, grids, can often contain tens of millions, or billions of volumes. The analysis time of these large unstructured grids can take weeks to months to complete even on large computer clusters. For CFD solvers utilizing the Finite Volume Method (FVM) with implicit time stepping or a segregated pressure solver, a large portion of the computation time is spent solving a large linear system with a sparse coefficient matrix. In an effort to improve the performance of these CFD codes, in effect decreasing the time to solution of engineering problems, a conjugate gradient solver for a Finite Volume Method Solver Graphics Processing Units (GPU) was implemented to solve a model Poisson's equation. Utilizing the improved memory throughput of NVIDIA's Tesla K20 GPU a 2.5 times improvement was observed compared to a parallel CPU implementation on all 10 cores of an Intel Xeon E5-2670 v2. The parallel CPU implementation was constructed using the open source CFD toolbox, Open-FOAM.

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Williams, J., Sarofeen, C., Shan, H., & Conley, M. (2016). An accelerated iterative linear solver with GPUs for CFD calculations of unstructured grids. In Procedia Computer Science (Vol. 80, pp. 1291–1300). Elsevier B.V. https://doi.org/10.1016/j.procs.2016.05.504

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