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Accelerated GPU simulation of compressible flow by the discontinuous evolution Galerkin method

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Abstract

The aim of the present paper is to report on our recent results for GPU accelerated simulations of compressible flows. For numerical simulation the adaptive discontinuous Galerkin method with the multidimensional bicharacteristic based evolution Galerkin operator has been used. For time discretization we have applied the explicit third order Runge-Kutta method. Evaluation of the genuinely multidimensional evolution operator has been accelerated using the GPU implementation. We have obtained a speedup up to 30 (in comparison to a single CPU core) for the calculation of the evolution Galerkin operator on a typical discretization mesh consisting of 16384 mesh cells.

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References

  1. A.Hundertmark, M.Lukáčová-Medvid’ová, F.Prill, J. Sci. Comp. 48, 227 (2011)

    Article  MATH  Google Scholar 

  2. M.Lukáčová-Medvid’ová, K.W.Morton, G.Warnecke, SIAM J. Sci. Comp. 26, 1 (2004)

    Article  Google Scholar 

  3. M.Lukáčová-Medvid’ová, S.Noelle, M.Kraft, J. Comput. Phys. 221, 122 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. T.Preis, P.Virnau, P.Wolfgang, J.J.Schneider, J. Comput. Phys. 228, 4468 (2009)

    Article  ADS  MATH  Google Scholar 

  5. B.J.Block, P.Virnau, T.Preis, Comp. Phys. Communic. 1810, 1549 (2010)

    Article  ADS  Google Scholar 

  6. M.Weigel, Phys. Rev. E 84, 036709 (2011)

    Article  ADS  Google Scholar 

  7. J.A.Anderson, Ch.D.Lorenz, A.Travesset, J. Comput. Phys. 227, 5342 (2008)

    Article  ADS  MATH  Google Scholar 

  8. J.A.van Meel, A.Arnold, D.Frenkel, S.F.Portegies Zwart, R.G.Belleman, Mol. Sim. 34, 259 (2008)

    Article  Google Scholar 

  9. P.H.Colberg, F.Höfling, Comp. Phys. Comm. 182, 1120 (2011)

    Article  ADS  Google Scholar 

  10. D.Reith, L.Mirny, P.Virnau, Prog. Theor. Phys. Suppl. 191, 135 (2011)

    Article  ADS  Google Scholar 

  11. D.Reith, A.Milchev, P.Virnau, K.Binder, EPL 95, 28003 (2011)

    Article  ADS  Google Scholar 

  12. T.Preis, P.Virnau, W.Paul, J.J.Schneider, New J. Physics 11, 093024 (2009)

    Article  ADS  Google Scholar 

  13. A.R.Brodtkorb, T.R.Hagen, K.-A.Lie, J.R.Natvig, Comput. Visual. Sci. 13, 341 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. M.J.Castro, S.Ortega, M.AsunciónJ.M.de la Mantas, Bol. Soc. Esp. Mat. Apl. 50, 27 (2010)

    MATH  Google Scholar 

  15. T.R.Hagen, M.O.Henriksen, J.M.Hjelmervik, K.-A.Lie, How to solve systems of conservation laws numerically using the graphics processor as a high-performance computational engine. Geometric modelling, numerical simulation, and optimization: applied mathematics at SINTEF (Springer, Berlin, 2007), 211

  16. W.Xian, A.Takayuki, Parallel Computing 37, 521 (2011)

    MathSciNet  Google Scholar 

  17. J.Appleyard, D.Drikakis, Computers Fluids 46, 101 (2011)

    Article  MATH  Google Scholar 

  18. F.X.Giraldo, M.Restelli, M.Lauter, SIAM J. Sci. Comp. 32, 3394 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. A.Müller, J.Behrens, F.X.Giraldo, V.Wirth, J. Comput. Phys. (2011), submitted

  20. J.M.Straka, R.B.Wilhelmson, L.J.Wicker, J.R.Anderson, Droegemeier, Int. J. Numer. Fl. 17, 1 (1993)

    Article  MathSciNet  Google Scholar 

  21. M.Lukáčová-Medvid’ová, A.Müller, F.X.Giraldo, V.Wirth, L.Yelash, in preparation

  22. F.X.Giraldo, M.Restelli, SIAM J. Sci. Comput. 31, 2231 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. A.Müller, J.Behrens, F.X.Giraldo, V.Wirth, Proceedings of the V European Conference on Computational Fluid Dynamics ECCOMAS CFD 2010 (2010), 1

  24. F.X.Giraldo, T.Wartburton, Int. J. Numer. Meth. Fl. 56, 899 (2008)

    Article  MATH  Google Scholar 

  25. M.Lukáčová-Medvid’ová, K.W.Morton, G.Warnecke, Math. Comp. 69, 1355 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. F.X.Giraldo, M.Restelli, J. Comput. Phys. 227, 3849 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. A.Robert, J. Atmos. Sci. 50, 865 (1993)

    Article  Google Scholar 

  28. J.Behrens, N.Rakowsky, W.Hiller, D.Handorf, M.Lauter, J.Papke, K.Dethloff, Ocean Model 10, 171 (2005)

    Article  ADS  Google Scholar 

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Correspondence to B. J. Block, M. Lukáčová-Medvid’ová, P. Virnau or L. Yelash.

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Block, B.J., Lukáčová-Medvid’ová, M., Virnau, P. et al. Accelerated GPU simulation of compressible flow by the discontinuous evolution Galerkin method. Eur. Phys. J. Spec. Top. 210, 119–132 (2012). https://doi.org/10.1140/epjst/e2012-01641-0

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  • DOI: https://doi.org/10.1140/epjst/e2012-01641-0

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