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Multicore/Multi-GPU Accelerated Simulations of Multiphase Compressible Flows Using Wavelet Adapted Grids

Published: 01 March 2011 Publication History
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  • Abstract

    We present a computational method of coupling average interpolating wavelets with high-order finite volume schemes and its implementation on heterogeneous computer architectures for the simulation of multiphase compressible flows. The method is implemented to take advantage of the parallel computing capabilities of emerging heterogeneous multicore/multi-GPU architectures. A highly efficient parallel implementation is achieved by introducing the concept of wavelet blocks, exploiting the task-based parallelism for CPU cores, and by managing asynchronously an array of GPUs by means of OpenCL. We investigate the comparative accuracy of the GPU and CPU based simulations and analyze their discrepancy for two-dimensional simulations of shock-bubble interaction and Richtmeyer-Meshkov instability. The results indicate that the accuracy of the GPU/CPU heterogeneous solver is competitive with the one that uses exclusively the CPU cores. We report the performance improvements by employing up to 12 cores and 6 GPUs compared to the single-core execution. For the simulation of the shock-bubble interaction at Mach 3 with two million grid points, we observe a 100-fold speedup for the heterogeneous part and an overall speedup of 34.

    References

    [1]
    J. M. Alam, N. K.-R. Kevlahan, and O. V. Vasilyev, Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations, J. Computat. Phys., 214 (2006), pp. 829-857.
    [2]
    D. A. Bader, V. Agarwal, and S. Kang, Computing discrete transforms on the Cell Broadband Engine, Parallel Computing, 35 (2009), pp. 119-137.
    [3]
    A. Bagabir and D. Drikakis, Mach number effects on shock-bubble interaction, Shock Waves, 11 (2001), pp. 209-218.
    [4]
    M. Bergdorf and P. Koumoutsakos, A Lagrangian particle-wavelet method, Multiscale Model. Simul., 5 (2006), pp. 980-995.
    [5]
    M. J. Berger and J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53 (1984), pp. 484-512.
    [6]
    M. Bernaschi, L. Rossi, R. Benzi, M. Sbragaglia, and S. Succi, Graphics processing unit implementation of lattice Boltzmann models for flowing soft systems, Phys. Rev. E, 80 (2009), 066707.
    [7]
    R. D. Blumofe and C. E. Leiserson, Scheduling multithreaded computations by work stealing, J. ACM, 46 (1999), pp. 720-748.
    [8]
    T. Brandvik and G. Pullan, Acceleration of a $3$D Euler solver using commodity graphics hardware, in Proceedings of the 46th AIAA Aerospace Sciences Meeting, American Institute of Aeronautics and Astronautics, Reston, VA, 2008, AIAA-2008-607.
    [9]
    M. Brouillette, The Richtmyer-Meshkov instability, Ann. Rev. Fluid Mech., 34 (2002), pp. 445-468.
    [10]
    S. Browne, J. Dongarra, N. Garner, G. Ho, and P. Mucci, A portable programming interface for performance evaluation on modern processors, Int. J. High Perform. Comput. Appl., 14 (2000), pp. 189-204.
    [11]
    I. L. Chern, J. Glimm, O. McBryan, B. Plohr, and S. Yaniv, Front tracking for gas-dynamics, J. Comput. Phys., 62 (1986), pp. 83-110.
    [12]
    A. Cohen, I. Daubechies, and J. C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), pp. 485-560.
    [13]
    M. O. Domingues, S. M. Gomes, O. Roussel, and K. Schneider, An adaptive multiresolution scheme with local time stepping for evolutionary PDEs, J. Comput. Phys., 227 (2008), pp. 3758-3780.
    [14]
    M. O. Domingues, S. M. Gomes, O. Roussel, and K. Schneider, Space-time adaptive multiresolution methods for hyperbolic conservation laws: Applications to compressible Euler equations, Appl. Numer. Math., 59 (2009), pp. 2303-2321.
    [15]
    D. L. Donoho, Smooth wavelet decompositions with blocky coefficient kernels, in Recent Advances in Wavelet Analysis, Academic Press, New York, 1993, pp. 259-308.
    [16]
    B. Einfeldt, On Godunov-type methods for gas dynamics, SIAM J. Numer. Anal., 25 (1988), pp. 294-318.
    [17]
    E. Elsen, P. LeGresley, and E. Darve, Large calculation of the flow over a hypersonic vehicle using a GPU, J. Comput. Phys., 227 (2008), pp. 10148-10161.
    [18]
    P. N. Glaskowsky, NVIDIA's Fermi: The First Complete GPU Computing Architecture, Tech. report, NVIDIA, Santa Clara, CA, 2009.
    [19]
    J. W. Grove, Applications of front tracking to the simulation of shock refractions and unstable mixing, Appl. Numer. Math., 14 (1994), pp. 213-237.
    [20]
    J. F. Haas and B. Sturtevant, Interaction of weak shock-waves with cylindrical and spherical gas inhomogeneities, J. Fluid Mech., 181 (1987), pp. 41-76.
    [21]
    T. R. Hagen, K. A. Lie, and J. R. Natvig, Solving the Euler equations on graphics processing units, Computational Science - ICCS 2006, 3994 (2006), pp. 220-227.
    [22]
    A. Harten, Adaptive multiresolution schemes for shock computations, J. Comput. Phys., 115 (1994), pp. 319-338.
    [23]
    B. Hejazialhosseini, D. Rossinelli, M. Bergdorf, and P. Koumoutsakos, High order finite volume methods on wavelet-adapted grids with local time-stepping on multicore architectures for the simulation of shock-bubble interactions, J. Comput. Phys., 229 (2010), pp. 8364-8383.
    [24]
    R. L. Holmes, J. W. Grove, and D. H. Sharp, Numerical investigation of Richtmyer-Meshkov instability using front tracking, J. Fluid Mech., 301 (1995), pp. 51-64.
    [25]
    M. Hopf and T. Ertl, Hardware accelerated wavelet transformations, in Proceedings of EG/IEEE TCVG Symposium on Visualization, IEEE, Washington, DC, 2000, pp. 93-103.
    [26]
    X. Y. Hu, B. C. Khoo, N. A. Adams, and F. L. Huang, A conservative interface method for compressible flows, J. Comput. Phys., 219 (2006), pp. 553-578.
    [27]
    T. Ishihara, T. Gotoh, and Y. Kaneda, Study of high-Reynolds number isotropic turbulence by direct numerical simulation, Ann. Rev. Fluid Mech., 41 (2009), pp. 165-180.
    [28]
    G. S. Jiang and C. W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), pp. 202-228.
    [29]
    I. C. Kampolis, X. S. Trompoukis, V. G. Asouti, and K. C. Giannakoglou, CFD-based analysis and two-level aerodynamic optimization on graphics processing units, Comput. Methods Appl. Mech. Engrg., 199 (2010), pp. 712-722.
    [30]
    N. K.-R. Kevlahan and O. V. Vasilyev, An adaptive wavelet collocation method for fluid-structure interaction at high Reynolds numbers, SIAM J. Sci. Comput., 26 (2005), pp. 1894-1915.
    [31]
    R. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, UK, 2002.
    [32]
    J. Liandrat and P. Tchamitchian, Resolution of the $1$D regularized Burgers equation using a spatial wavelet approximation, Tech. report 90-83, 1CASE, NASA Contractor Report 18748880, 1990.
    [33]
    X. D. Liu, S. Osher, and T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys., 115 (1994), pp. 200-212.
    [34]
    E. E. Meshkov, Instability of a shock wave accelerated interface between two gases, NASA Tech. Trans., 1970.
    [35]
    F. Miniati and P. Colella, Block structured adaptive mesh and time refinement for hybrid, hyperbolic plus n-body systems, J. Comput. Phys., 227 (2007), pp. 400-430.
    [36]
    A. Munshi, The OpenCL specification, version 1.0, Khronos Group Std., Beaverton, OR, 2009.
    [37]
    Nvidia, NVIDIA CUDA Compute Unified Device Architecture: Programming guide, NVIDIA, Santa Clara, CA, 2007.
    [38]
    A. Prosperetti and G. Tryggvason, eds., Computational Methods for Multiphase Flow, Cambridge University Press, Cambridge, UK, 2007, Ch. 3.
    [39]
    L. Qianlong and O. V. Vasilyev, A Brinkman penalization method for compressible flows in complex geometries, J. Comput. Phys., 227 (2007), pp. 946-966.
    [40]
    J. J. Quirk and S. Karni, On the dynamics of a shock-bubble interaction, J. Fluid Mech., 318 (1996), pp. 129-163.
    [41]
    R. D. Richtmyer, Taylor instability in shock acceleration of compressible fluids, Commun. Pure Appl. Math., 13 (1960), pp. 297-319.
    [42]
    D. Rossinelli, M. Bergdorf, G.-H. Cottet, and P. Koumoutsakos, GPU accelerated simulations of bluff body flows using vortex particle methods, J. Comput. Phys., 229 (2010), pp. 3316-3333.
    [43]
    D. Rossinelli, M. Bergdorf, B. Hejazialhosseini, and P. Koumoutsakos, Wavelet-based adaptive solvers on multi-core architectures for the simulation of complex systems, in Euro-Par '09: Proceedings of the 15th International Euro-Par Conference on Parallel Processing, Springer-Verlag, Berlin, Heidelberg, 2009, pp. 721-734.
    [44]
    O. Roussel, K. Schneider, A. Tsigulin, and H. Bockhorn, A conservative fully adaptive multiresolution algorithm for parabolic PDEs, J. Comput. Phys., 188 (2003), pp. 493-523.
    [45]
    R. Saurel and R. Abgrall, A simple method for compressible multifluid flows, SIAM J. Sci. Comput., 21 (1999), pp. 1115-1145.
    [46]
    C. E. Scheidegger, J. L. D. Comba, R. D. da Cunha, and N. Corporation, Practical CFD simulations on programmable graphics hardware using SMAC, Computer Graphics Forum, 24 (2005), pp. 715-728.
    [47]
    K. Schneider and O. V. Vasilyev, Wavelet methods in computational fluid dynamics, Ann. Rev. Fluid Mech., 42 (2010), pp. 473-503.
    [48]
    C. Tenllado, J. Setoain, M. Prieto, L. Pinuel, and F. Tirado, Parallel implementation of the $2$D discrete wavelet transform on graphics processing units: Filter bank versus lifting, IEEE Trans. Parallel Distributed Systems, 19 (2008), pp. 299-310.
    [49]
    E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag, Berlin, 1999.
    [50]
    S. Williams, A. Waterman, and D. Patterson, Roofline: An insightful visual performance model for multicore architectures, Commun. ACM, 52 (2009), pp. 65-76.
    [51]
    J. H. Williamson, Low-storage Runge-Kutta schemes, J. Comput. Phys., 35 (1980), pp. 48-56.

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    Published In

    cover image SIAM Journal on Scientific Computing
    SIAM Journal on Scientific Computing  Volume 33, Issue 2
    April 2011
    579 pages

    Publisher

    Society for Industrial and Applied Mathematics

    United States

    Publication History

    Published: 01 March 2011

    Author Tags

    1. GPU
    2. adaptive grid
    3. compressible flow
    4. multicore architectures
    5. multiphase
    6. multiresolution
    7. wavelets

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