Accelerating high-order WENO schemes using two heterogeneous GPUs

Document Type : Research Paper

Author

Faculty of Engineering Science, College of Engineering, University of Tehran

Abstract

A double-GPU code is developed to accelerate WENO schemes. The test problem is a compressible viscous flow. The convective terms are discretized using third- to ninth-order WENO schemes and the viscous terms are discretized by the standard fourth-order central scheme. The code written in CUDA programming language is developed by modifying a single-GPU code. The OpenMP library is used for parallel execution of the code on both the GPUs. Data transfer between GPUs which is the main issue in developing the code, is carried out by defining halo points for numerical grids and by using a CUDA built-in function. The code is executed on a PC equipped with two heterogeneous GPUs. The computational times of different schemes are obtained and the speedups with respect to the single-GPU code are reported for different number of grid points. Furthermore, the developed code is analyzed by CUDA profiling tools. The analyze helps to further increase the code performance.

Keywords

[1]H. P. Le, J. L. Cambier, L. K. Cole, GPU-based flow simulation with detailed chemical kinetics, Computer Physics Communications, Vol. 184, No. 3, pp. 596-606, 2013.
[2]A. Khajeh-Saeed, J. Blair Perot, Direct numerical simulation of turbulence using GPU accelerated supercomputers, Journal of Computational Physics, Vol. 235, pp. 241-257, 2013.
[3]B. Tutkun, F. O. Edis, A GPU application for high-order compact finite difference scheme, Computers and Fluids, Vol. 55, pp. 29-35, 2012.
[4]J. A. Ekaterinaris, High-order accurate, low numerical diffusion methods for aerodynamics, Progress in Aerospace Sciences, Vol. 41, No. 3-4, pp. 192-300, 2005.
[5]G. S. Jiang, C. W. Shu, Efficient implementation of weighted ENO schemes, Journal of Computational Physics, Vol. 126, No. 1, pp. 202-228, 1996.
[6]X. D. Liu, S. Osher, T. Chan, Weighted Essentially Non-oscillatory Schemes, Journal of Computational Physics, Vol. 115, No. 1, pp. 200-212, 1994.
[7]V. Esfahanian, K. Hejranfar, H. M. Darian, Implementation of high-order compact finite-difference method to parabolized Navier-Stokes schemes, International Journal for Numerical Methods in Fluids, Vol. 58, No. 6, pp. 659-685, 2008.
[8]K. Heiranfar, V. Esfahanian, H. M. Darian, On the use of high-order accurate solutions of PNS schemes as basic flows for stability analysis of hypersonic axisymmetric flows, Journal of Fluids Engineering, Transactions of the ASME, Vol. 129, No. 10, pp. 1328-1338, 2007.
[9]S. K. Lele, Compact finite difference schemes with spectral-like resolution, Journal of Computational Physics, Vol. 103, No. 1, pp. 16-42, 1992.
[10]H. Mahmoodi Darian, V. Esfahanian, K. Hejranfar, A shock-detecting sensor for filtering of high-order compact finite difference schemes, Journal of Computational Physics, Vol. 230, No. 3, pp. 494-514, 2011.
[11]A. S. Antoniou, K. I. Karantasis, E. D. Polychronopoulos, J. A. Ekaterinaris, Acceleration of a finite-difference WENO scheme for large-scale simulations on many-core architectures, in Proceeding of.
[12]V. Esfahanian, H. M. Darian, S. M. Iman Gohari, Assessment of WENO schemes for numerical simulation of some hyperbolic equations using GPU, Computers and Fluids, Vol. 80, No. 1, pp. 260-268, 2013.
[13]H. M. Darian, V. Esfahanian, Assessment of WENO schemes for multi-dimensional Euler equations using GPU, International Journal for Numerical Methods in Fluids, Vol. 76, No. 12, pp. 961-981, 2014.
[14]S. C. Lo, G. A. Blaisdell, A. S. Lyrintzis, High-order shock capturing schemes for turbulence calculations, International Journal for Numerical Methods in Fluids, Vol. 62, No. 5, pp. 473-498, 2010.
[15]H. C. Yee, N. D. Sandham, M. J. Djomehri, Low-Dissipative High-Order Shock-Capturing Methods Using Characteristic-Based Filters, Journal of Computational Physics, Vol. 150, No. 1, pp. 199-238, 1999.
[16]M. Khoshab, A. A. Dehghan, V. Esfahanian, H. M. Darian, Numerical assessment of a shock-detecting sensor for low dissipative high-order simulation of shock-vortex interactions, International Journal for Numerical Methods in Fluids, Vol. 77, No. 1, pp. 18-42, 2015.
[17]N. Corporation, 2010, NVIDIA CUDA C Programming Guide,
Volume 48, Issue 2
Autumn 2017
Pages 161-170
  • Receive Date: 21 July 2017
  • Revise Date: 31 August 2017
  • Accept Date: 01 September 2017