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Volumn , Issue , 2007, Pages 211-264

How to solve systems of conservation laws numerically using the graphics processor as a high-performance computational engine

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EID: 84889991271     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-68783-2_8     Document Type: Chapter
Times cited : (19)

References (55)
  • 3
    • 0001884854 scopus 로고
    • A two-dimensional finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for compressible flows
    • M. Hafez and K. Oshima, editors
    • P. Arminjon, D. Stanescu, and M.-C. Viallon. A two-dimensional finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for compressible flows. In M. Hafez and K. Oshima, editors, Proceedings of the 6th I nternati onal Symposium on CFD, Lake Tahoe, volume IV, pages 7-14, 1995.
    • (1995) Proceedings of the 6th i Nternati Onal Symposium on CFD, Lake Tahoe , vol.4 , pp. 7-14
    • Arminjon, P.1    Stanescu, D.2    Viallon, M.-C.3
  • 4
    • 4644342716 scopus 로고    scopus 로고
    • A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows
    • E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein, and B. Perthame. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comp., 25:2050-2065, 2004.
    • (2004) SIAM J. Sci. Comp. , vol.25 , pp. 2050-2065
    • Audusse, E.1    Bouchut, F.2    Bristeau, M.-O.3    Klein, R.4    Perthame, B.5
  • 5
    • 0038746749 scopus 로고    scopus 로고
    • A wave propagation method for conservation laws and balance laws with spatially varying flux functions
    • (electronic)
    • Derek S. Bale, Randall J. Leveque, Sorin Mitran, and James A. Rossmanith. A wave propagation method for conservation laws and balance laws with spatially varying flux functions. SIAM J. Sci. Comput., 24(3):955-978 (electronic), 2002.
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.3 , pp. 955-978
    • Bale, D.S.1    Leveque, R.J.2    Mitran, S.3    Rossmanith, J.A.4
  • 7
    • 0033296324 scopus 로고    scopus 로고
    • High-order central schemes for hyperbolic systems of conservation laws
    • (electronic)
    • F. Bianco, G. Puppo, and G. Russo. High-order central schemes for hyperbolic systems of conservation laws. SIAM J. Sci. Comput., 21(1):294-322 (electronic), 1999.
    • (1999) SIAM J. Sci. Comput. , vol.21 , Issue.1 , pp. 294-322
    • Bianco, F.1    Puppo, G.2    Russo, G.3
  • 8
    • 33745457614 scopus 로고
    • A mathematical introduction to fluid mechanics
    • Springer-Verlag, New York, third edition
    • A. J. Chorin and J. E. Marsden. A mathematical introduction to fluid mechanics, volume 4 of Texts in Applied Mathematics. Springer-Verlag, New York, third edition, 1993.
    • (1993) Texts in Applied Mathematics , vol.4
    • Chorin, A.J.1    Marsden, J.E.2
  • 15
    • 85114329546 scopus 로고    scopus 로고
    • Numerical approximation of hyperbolic systems of conservation laws
    • Springer-Verlag, New York
    • E. Godlewski and P.-A. Raviart. Numerical approximation of hyperbolic systems of conservation laws, volume 118 of Applied Mathematical Sciences. Springer-Verlag, New York, 1996.
    • (1996) Applied Mathematical Sciences , vol.118
    • Godlewski, E.1    Raviart, P.-A.2
  • 16
    • 0000935266 scopus 로고
    • A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics
    • S. K. Godunov. A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Mat. Sb. (N.S.), 47 (89):271-306, 1959.
    • (1959) Mat. Sb. (N.S.) , vol.47 , Issue.89 , pp. 271-306
    • Godunov, S.K.1
  • 18
    • 33746590744 scopus 로고    scopus 로고
    • Solving the Euler equations on graphical processing units
    • V.N. Alexandrov, G.D. van Albada, P.M.A. Sloot, and J. Dongarra, editors, Computational Science-ICCS 2006: 6th International Conference, Reading, UK, May 28-31, 2006, Proceedings, Part IV, Springer-Verlag
    • T. R. Hagen, K.-A. Lie, and J. R. Natvig. Solving the Euler equations on graphical processing units. In V.N. Alexandrov, G.D. van Albada, P.M.A. Sloot, and J. Dongarra, editors, Computational Science-ICCS 2006: 6th International Conference, Reading, UK, May 28-31, 2006, Proceedings, Part IV, volume 3994 of Lecture Notes in Computer Science (LNCS), pages 220-227. Springer Verlag, 2006.
    • (2006) Lecture Notes in Computer Science (LNCS) , vol.3994 , pp. 220-227
    • Hagen, T.R.1    Lie, K.-A.2    Natvig, J.R.3
  • 19
    • 40749159424 scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • A. Harten. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys., 49(3):357-393, 1983.
    • (1983) J. Comput. Phys. , vol.49 , Issue.3 , pp. 357-393
    • Harten, A.1
  • 20
    • 0000876320 scopus 로고
    • On upstream differencing and Godunov-type schemes for hyperbolic conservation laws
    • A. Harten, P. D. Lax, and B. van Leer. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev., 25(1):35-61, 1983.
    • (1983) SIAM Rev. , vol.25 , Issue.1 , pp. 35-61
    • Harten, A.1    Lax, P.D.2    Van Leer, B.3
  • 21
    • 84889981811 scopus 로고    scopus 로고
    • Finite volumes for complex applications III
    • Laboratoire d'Analyse, Topologie et Probabilit́es CNRS, Marseille, Papers from the 3rd Symposium held in Porquerolles, June 24-28, 2002
    • R. Herbin and D. Kr̈oner, editors. Finite volumes for complex applications III. Laboratoire d'Analyse, Topologie et Probabilit́es CNRS, Marseille, 2002. Problems and perspectives, Papers from the 3rd Symposium held in Porquerolles, June 24-28, 2002.
    • (2002) Problems and Perspectives
    • Herbin, R.1    Kr̈oner, D.2
  • 22
    • 85067915698 scopus 로고    scopus 로고
    • Front tracking for hyperbolic conservation laws
    • Springer-Verlag, New York
    • H. Holden and N. H. Risebro. Front tracking for hyperbolic conservation laws, volume 152 of Applied Mathematical Sciences. Springer-Verlag, New York, 2002.
    • (2002) Applied Mathematical Sciences , vol.152
    • Holden, H.1    Risebro, N.H.2
  • 23
    • 0032206542 scopus 로고    scopus 로고
    • Nonoscillatory central schemes for multidimensional hyperbolic conservation laws
    • G.-S. Jiang and E. Tadmor. Nonoscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput., 19(6):1892-1917, 1998
    • (1998) SIAM J. Sci. Comput. , vol.19 , Issue.6 , pp. 1892-1917
    • Jiang, G.-S.1    Tadmor, E.2
  • 24
    • 0000220623 scopus 로고
    • First order quasilinear equations with several independent variables
    • S. N. Kruzkov. First order quasilinear equations with several independent variables. Mat. Sb. (N.S.), 81 (123):228-255, 1970.
    • (1970) Mat. Sb. (N.S.) , vol.81 , Issue.123 , pp. 228-255
    • Kruzkov, S.N.1
  • 25
    • 0036288577 scopus 로고    scopus 로고
    • Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations
    • (electronic)
    • A. Kurganov, S. Noelle, and G. Petrova. Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput., 23(3):707-740 (electronic), 2001.
    • (2001) SIAM J. Sci. Comput. , vol.23 , Issue.3 , pp. 707-740
    • Kurganov, A.1    Noelle, S.2    Petrova, G.3
  • 26
    • 0000356257 scopus 로고    scopus 로고
    • New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations
    • A. Kurganov and E. Tadmor. New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations. J. Comp. Phys., 160:720-742, 2000.
    • (2000) J. Comp. Phys. , vol.160 , pp. 720-742
    • Kurganov, A.1    Tadmor, E.2
  • 27
    • 0036333838 scopus 로고    scopus 로고
    • Central-upwind schemes for the Saint-Venant system
    • Alexander Kurganov and Doron Levy. Central-upwind schemes for the Saint-Venant system. M2AN Math. Model. Numer. Anal., 36(3):397-425, 2002.
    • (2002) M2AN Math. Model. Numer. Anal. , vol.36 , Issue.3 , pp. 397-425
    • Kurganov, A.1    Levy, D.2
  • 28
    • 0003362166 scopus 로고
    • Fluid mechanics
    • Translated from the Russian by J. B. Sykes and W. H. Reid, Pergamon Press, London
    • L. D. Landau and E. M. Lifshitz. Fluid mechanics. Translated from the Russian by J. B. Sykes and W. H. Reid. Course of Theoretical Physics, Vol. 6. Pergamon Press, London, 1959.
    • (1959) Course of Theoretical Physics , vol.6
    • Landau, L.D.1    Lifshitz, E.M.2
  • 29
    • 84980078953 scopus 로고
    • Weak solutions of nonlinear hyperbolic equations and their numerical computation
    • P. D. Lax. Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math., 7:159-193, 1954.
    • (1954) Comm. Pure Appl. Math. , vol.7 , pp. 159-193
    • Lax, P.D.1
  • 32
    • 0001315315 scopus 로고    scopus 로고
    • Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
    • R. J. LeVeque. Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm. J. Comput. Phys, 146:346-365, 1998.
    • (1998) J. Comput. Phys , vol.146 , pp. 346-365
    • Leveque, R.J.1
  • 34
    • 0035075926 scopus 로고    scopus 로고
    • Compact central WENO schemes for multidimensional conservation laws
    • D. Levy, G. Puppo, and G. Russo. Compact central WENO schemes for multidimensional conservation laws. SIAM J. Sci. Comput., 22(2):656-672, 2000.
    • (2000) SIAM J. Sci. Comput. , vol.22 , Issue.2 , pp. 656-672
    • Levy, D.1    Puppo, G.2    Russo, G.3
  • 35
    • 0142101586 scopus 로고    scopus 로고
    • An improved quadrature rule for the flux-computation in staggered central difference schemes in multidimensions
    • K.-A. Lie and S. Noelle. An improved quadrature rule for the flux-computation in staggered central difference schemes in multidimensions. J. Sci. Comput., 18(1):69-81, 2003.
    • (2003) J. Sci. Comput. , vol.18 , Issue.1 , pp. 69-81
    • Lie, K.-A.1    Noelle, S.2
  • 36
    • 0041428206 scopus 로고    scopus 로고
    • On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws
    • K.-A. Lie and S. Noelle. On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. SIAM J. Sci. Comput., 24(4):1157-1174, 2003.
    • (2003) SIAM J. Sci. Comput. , vol.24 , Issue.4 , pp. 1157-1174
    • Lie, K.-A.1    Noelle, S.2
  • 37
    • 0000088242 scopus 로고    scopus 로고
    • Composite schemes for conservation laws
    • R. Liska and B. Wendroff. Composite schemes for conservation laws. SIAM J. Numer. Anal., 35(6):2250-2271, 1998.
    • (1998) SIAM J. Numer. Anal. , vol.35 , Issue.6 , pp. 2250-2271
    • Liska, R.1    Wendroff, B.2
  • 38
    • 0032336616 scopus 로고    scopus 로고
    • Third order nonoscillatory central scheme for hyperbolic conservation laws
    • X.-D. Liu and E. Tadmor. Third order nonoscillatory central scheme for hyperbolic conservation laws. Numer. Math., 79(3):397-425, 1998.
    • (1998) Numer. Math. , vol.79 , Issue.3 , pp. 397-425
    • Liu, X.-D.1    Tadmor, E.2
  • 39
    • 17444372778 scopus 로고    scopus 로고
    • Real-time 3d fluid simulation on GPU with complex obstacles
    • IEEE Computer Society
    • Y. Liu, X. Liu, and E. Wu. Real-time 3d fluid simulation on GPU with complex obstacles. In Proceedings of Paci fic Graphics 2004, pages 247-256. IEEE Computer Society, 2004.
    • (2004) Proceedings of Paci Fic Graphics , vol.2004 , pp. 247-256
    • Liu, Y.1    Liu, X.2    Wu, E.3
  • 40
    • 28144455569 scopus 로고
    • Nonoscillatory central differencing for hyperbolic conservation laws
    • H. Nessyahu and E. Tadmor. Nonoscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys., 87(2):408-463, 1990.
    • (1990) J. Comput. Phys. , vol.87 , Issue.2 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 41
    • 32644433341 scopus 로고    scopus 로고
    • Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
    • S. Noelle, N. Pankratz, G. Puppo, and J. R. Natvig. Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows. J. Comput. Phys., 213(2):474-499, 2006.
    • (2006) J. Comput. Phys. , vol.213 , Issue.2 , pp. 474-499
    • Noelle, S.1    Pankratz, N.2    Puppo, G.3    Natvig, J.R.4
  • 44
    • 0003588880 scopus 로고
    • Difference methods for initial-value problems. Second edition
    • Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney
    • R. D. Richtmyer and K. W. Morton. Difference methods for initial-value problems. Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4. Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967.
    • (1967) Interscience Tracts in Pure and Applied Mathematics , Issue.4
    • Richtmyer, R.D.1    Morton, K.W.2
  • 45
    • 84875253961 scopus 로고    scopus 로고
    • Addison Wesley Longman Publishing Co., Inc.
    • R Shading Language. Addison Wesley Longman Publishing Co., Inc., 2004.
    • (2004) R Shading Language
    • Rost, R.J.1
  • 46
    • 84880477362 scopus 로고    scopus 로고
    • Graphics processor units: New prospects for parallel computing
    • A.M. Bruaset and A. Tveito, editors Numerical Solution of Partial Differential Equations on Parallel Computers, Springer Verlag
    • M. Rumpf and R. Strzodka. Graphics processor units: new prospects for parallel computing. In A.M. Bruaset and A. Tveito, editors, Numerical Solution of Partial Differential Equations on Parallel Computers, volume 51 of Lecture Notes in Computational Science and Engineering, pages 89-134. Springer Verlag, 2006.
    • (2006) Lecture Notes in Computational Science and Engineering , vol.51 , pp. 89-134
    • Rumpf, M.1    Strzodka, R.2
  • 47
    • 0000564951 scopus 로고
    • Total-variation-diminishing time discretisations
    • C.-W. Shu. Total-variation-diminishing time discretisations. SIAM J. Sci. Stat. Comput., 9:1073-1084, 1988.
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , pp. 1073-1084
    • Shu, C.-W.1
  • 48
    • 0000034725 scopus 로고    scopus 로고
    • Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Advanced numerical approximation of nonlinear hyperbolic equations (Cetraro 1997)
    • Springer, Berlin
    • C.-W. Shu. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In Advanced numerical approximation of nonlinear hyperbolic equations (Cetraro, 1997), volume 1697 of Lecture Notes in Math., pages 325-432. Springer, Berlin, 1998.
    • (1998) Lecture Notes in Math. , vol.1697 , pp. 325-432
    • Shu, C.-W.1
  • 49
    • 13844270719 scopus 로고    scopus 로고
    • Finite-volume WENO schemes for three-dimensional conservation laws
    • V. A. Titarev and E. F. Toro. Finite-volume WENO schemes for three-dimensional conservation laws. J. Comput. Phys., 201(1):238-260, 2004.
    • (2004) J. Comput. Phys. , vol.201 , Issue.1 , pp. 238-260
    • Titarev, V.A.1    Toro, E.F.2
  • 54
    • 0004181419 scopus 로고
    • Wiley-Interscience [John Wiley & Sons], New York, Pure and Applied Mathematics
    • G. B. Whitham. Linear and nonlinear waves. Wiley-Interscience [John Wiley & Sons], New York, 1974. Pure and Applied Mathematics.
    • (1974) Linear and Nonlinear Waves
    • Whitham, G.B.1
  • 55
    • 10644272216 scopus 로고    scopus 로고
    • An improved study of real-time fluid simulation on GPU
    • E. Wu, Y. Liu, and X. Liu. An improved study of real-time fluid simulation on GPU. J. of Computer Animation and Virtual World, 15(3-4):139-146, 2004.
    • (2004) J. of Computer Animation and Virtual World , vol.15 , Issue.3-4 , pp. 139-146
    • Wu, E.1    Liu, Y.2    Liu, X.3


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