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  • FD2013 2927 72 -72

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    [email protected]

    [email protected]

    [email protected]

    . ( 31 ) D2Q13L2

    .

    .

    CUDA .

    . CUDA .

    . :

    . 2

    3 .

    DVBE . 1 ( FDM )

    Lattice Boltzmann Method (LBM) 1

    Lattice Gas Automata (LGA) 2

    Discrete Velocity Boltzmann Equation (DVBE) 3

  • FD2013 2927 72-72

    DVBE( . FEM( )FVM ) . [ 3 ]

    5 4 .

    . ) ( . WENO TVD MUSCL

    DVBE .

    . [. 6-1 ]-

    [. 31-7 ] [ 333]

    31) D2Q13L2 . . 6 (

    . 7 . MUSCL

    .

    .

    . [31] [. 34 ]

    [.35 ] [.36 ]

    . [.35 ]( CPU 131 )

    . .

    CUDA .

    . 7

    SolutionWeak 4

    Partial Differential Equation (PDE) 5

    Circular Function 6

    Structured 7

  • FD2013 2927 72-72

    1

    D2Q13L2 . [31-3] .

    .

    D2Q13L2 . 7-2

    (3 ) . :

    (3)

    e 9 c 8 ) D pe

    D=2. ( . 3

    DVBE - [.3 ]( BGK )

    . 3

    ) ( .

    ) . . ( 31

    d . )( D2Q13

    Rest Energy 8

    Effective Peculiar Velocity 9

  • FD2013 2927 72-72

    4

    . :

    ()

    BGK

    .

    . . D2Q13

    . (1 0 ) 31 6 :

    (1)

    . )( D2Q13L2

    D2Q13L2 ( ) D2Q13 ( ).

    : ( 4 )

    (4)

    ( 4. ) 3 v( 4 ) ][ D2Q13 . 31

    .

    . 7-7

    Maple 10

    )( ()

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    5

    . DVBE

    . 33MUSCL

    : DVBE

    (5)

    k kk

    f GF

    t

    . kG kF k kf :

    (6) Fk=fkekx Gk=fkeky

    . kye xke . 4 .

    (i,j) (5) - :

    (7) 4

    , ,

    , ,

    1,

    1( )

    k i j

    k k l k i j

    li j

    fF y G x

    t A

    . l .

    y x A. f G F .

    . 1

    (5 ) : ( 1 ) .

    (8)

    centered Scheme for Conservation Laws-Monotone Upstream 11

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    6

    MUSCL :

    (9)

    : 3 s

    (31) 2

    2 2

    2

    s

    .

    . k,i,j .

    .

    CFL ( ) .

    .

    . : .

    [ .31-3 ] .

    :

    (33)

    13 2

    1 1

    iv

    i v

    f

    13 2

    1 1

    iv i

    i v

    u f e

    213 2

    2

    1 1 2

    iiv i

    i v

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    2| |

    2

    ue E

    ( 1)p e

    . e p

    . 7-9 . :

    .

    12 Van Albada Limiter

  • FD2013 2927 72-72

    7

    . ( ) DFC .

    .

    . -

    . . .

    . [ .313 . ]

    . 7-4

    GPU CPU .

    .

    . . 6

    4 . [37] .

    6 . 4

    1 1884 NACA0012 )(6 5 . )(6 [38] . . [38] . . [38 ]

  • FD2013 2927 72-72

    8

    . .

    . .

    1 1884 NACA0012 . 5

    )( 1 1884 NACA0012 )( . 6 [35 ] 1 1884 NACA0012

    . 9 CUDA nVidia 116

    . C CUDA C /

    CUDA .[1]

    . CUDA

    CUDA GTX 480 . 7

    )( )(

  • FD2013 2927 72-72

    9

    nVidia GTX 480 . 7

    .

    [.34 ] .

    . 9-2

    8 .

    nVidia GTX 480 . 8

    . 4

    31 ) D2Q13L2.

    ( CUDA .

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  • FD2013 2927 72-72

    31

    [1]- R. BENZI, S. SUCCI AND M. VERGASSOLA, The lattice Boltzmann equation: theory and

    application, Phys. Rep., 222 (1992),145197.

    [2]- F. NANNELLI AND S. SUCCI, The lattice Boltzmann equation in irregular lattices, J. Stat.

    Phys., 68 (1992), 401407.

    [3]- X. Y. HE AND L. S. LUO, Theory of the lattice Boltzmann method: from Boltzmann equation to

    the lattice Boltzmann equation, Phys. Rev. E., 56 (1997), 68116817.

    [4]- X. Y. HE AND L. S. LUO, A priori derivation of the lattice Boltzmann equation, Phys. Rev. E.,

    55 (1997), R6333R6336.

    [5]- X. Y. HE, S. Y. CHEN AND G. D. DOOLEN, A novel thermal model for the lattice Boltzmann

    method in incompressible limit, J. Comput. Phys., 146 (1998), 282300.

    [6]- H. W. ZHENG, C. SHU, Y. T. CHEW AND J. QIU, A platform for developing new lattice

    Boltzmann models, Int. J. Mod. Phys. C., 16 (2005), 6184.

    [7]- G. W. YAN, Y. S. CHEN AND S. X. HU, Simple lattice Boltzmann model for simulating flows

    with shock wave, Phys. Rev. E., 59 (1999), 454459.

    [8]- W. P. SHI, S. Y. WEI AND R. W. MEI, Finite-difference-based lattice Boltzmann method for

    inviscid compressible flows, Numer. Heat. Tr. B-Fund., 40 (2001), 121.

    [9]- T. KATAOKA AND M. TSUTAHARA, Lattice Boltzmann method for the compressible Euler

    equations, Phys. Rev. E., 69 (2004), 056702-1.

    [10]- T. KATAOKA AND M. TSUTAHARA, Lattice Boltzmann method for the compressible

    Navier-Stokes equations with flexible specific-heat ratio, Phys. Rev. E., 69 (2004), 035701-1.

    [11]- K. QU, C. SHU AND Y. T. CHEW, Simulation of shock-wave propagation with finite volume

    lattice Boltzmann method, Int. J. Mod. Phys. C., 18 (2007), 447-454.

    [12]- K. QU, C. SHU AND Y. T. CHEW, Alternative method to construct equilibrium distribution

    functions in Lattice-Boltzmann method simulation of inviscid compressible flows at high Mach

    number, Phys. Rev. E., 75 (2007), 036706.

    [13]- P. Bailey, J. Myre, S. D. Walsh, D. J. Lilja, and M. O. Saar, Accelerating lattice Boltzmann

    fluid flow simulations using graphics processors, International Conference on Parallel Processing

    (ICPP 2009), Vienna, Austria, 2009.

    [14]- X. Ren, Y. Tang, G. Wang, T. Tang, X. Fang, Optimization and Implementation of LBM

    benchmark on Multithreaded GPU, International Conference on Data Storage and Data Engineering,

    2010.

    [15]- T. Pohl, M. Kowarschik, J. Wilke, K. Iglberger, and U. Rude, Optimization and Profiling of

    the Cache Performance of Parallel Lattice Boltzmann Codes, Parallel Processing Letters, 13(4), pp

    549560, 2003.

    [16] C. Korner, T. Pohl, U. Rude, N. Thurey, and T. Zeiser, Parallel Lattice Boltzmann Methods for

    CFD Applications, Numerical Solution of Partial Differential Equations on Parallel Computers, Springer-Verlag, 2006.

    [17]- K. QU, C. SHU AND Y. T. CHEW, Lattice Boltzmann and finite volume simulation of inviscid

    compressible flows with curved boundary, Adv. Appl. Math. Mech., Vol. 2, No. 5, (2010), pp. 573-

    586

    [18]- Anderson, J. D., Modern compressible flow, Mc Graw-Hill, 1990

    [19]- Hafez, M., Wahba, E., Simulations of viscous transonic flows over lifting airfoils and wings,

    Computers and Fluids, 36 (2007), 3952

    [20]- nVidia CUDATM C Programming Guide, Version 3.2, 2010.