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On the benefits of using GPUS to simulate shallow flows with finite volume schemes

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Abstract

In this paper, we focus on the efficient implementation of path conservative Roe type high order finite volume schemes to simulate shallow flows. The motion of a layer of homogeneous non-viscous fluid is supposed to be governed by the shallow-water system, formulated under the form of a conservation law with source terms. The implementation of the scheme is carried out on Graphics Processing Units (GPUs), thus achieving a substantial improvement of the speedup with respect to normal CPUs. Finally, some numerical experiments are presented.

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References

  1. M.J. Castro, J.A. García, J.M. González and C. Parés (2006). A parallel 2d finite volume scheme for solving systems of balance laws with non-conservative products: application to shallow flows. Comp. Meth. Appl. Mech. Eng. 196, 2788–2815.

    Article  Google Scholar 

  2. M.J. Castro, J.A. García, J.M. González and C. Parés (2008). Solving shallow-water systems in 2D domains using finite volume methods and multimedia SSE instructions. J. Comput. App. Math., 221: 16–32.

    Article  MATH  Google Scholar 

  3. M.J. Castro, E.D. Fernández, A.M. Ferreiro, A. García, C. Parés (2009). High order extension of Roe schemes for two dimensional nonconservative hyperbolic systems. J. Sci. Comput. 39, 67–114.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Dal Maso, P.G. LeFloch and F. Murat (1995). Definition and weak stability of nonconservative products. J. Math. Pures Appl. 74: 483–548.

    MathSciNet  MATH  Google Scholar 

  5. J.M. Gallardo, S. Ortega, M. de la Asunción, J.M. Mantas (2010). Two-dimensional compact third-order polynomial reconstructions. Solving nonconservative hyperbolic systems using GPUs. Submitted to J. Sci. Comput.

    Google Scholar 

  6. T.R. Hagen, J.M. Hjelmervik, K.A. Lie, J.R. Natvig, M. Ofstad (2005). Visual simulation of shallow-water waves. Sim. Modelling Pract. and Th. 13, 716–726.

    Article  Google Scholar 

  7. A. Harten, J.M. Hyman (1983). Self-adjusting grid methods for one-dimensional hyperbolic conservation laws. J. Comp. Phys. 50, 235–269.

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Lastra, J.M. Mantas, C. Ureña, M.J. Castro, J.A. García (2009). Simulation of shallow-water systems using graphics processing units. Math. Comp. Simul. 80, 598–618.

    Article  MATH  Google Scholar 

  9. M. de la Asunción, J.M. Mantas, M.J. Castro (2009). Simulation of one-layer shallow water systems on multicore and CUDA architectures. Accepted in J. Supercomputing.

    Google Scholar 

  10. P.G. LeFloch. Shock waves for nonlinear hyperbolic systems in nonconservative form (1989). Institute for Math. and its Appl., Minneapolis, Preprint 593.

    Google Scholar 

  11. S. Noelle, N. Pankratz, G. Puppo, J. Natvig (2006). Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows. J. Comput. Phys. 213, 474–499.

    Article  MathSciNet  MATH  Google Scholar 

  12. http://www.nvidia.com

  13. NVIDIA. CUDA Zone. http://www.nvidia.com/object/cuda_home.html. Accessed November 2009.

  14. C. Parés (2006). Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J. Num. Anal. 44, 300–321.

    Article  MATH  Google Scholar 

  15. Chapman B, Jost G, van der Pas R (2007). Using OpenMP: Portable Shared Memory Parallel Programming, The MIT Press.

  16. J.D. Owens, D. Luebke, N. Govindaraju, M. Harris, J. Krüger, A.E. Lefohn, T. Purcell (2005). A Survey of General-Purpose Computation on Graphics Hardware, Eurographics 2005 State of the Art Report.

  17. J.D. Owens, M. Houston, D. Luebke, S. Green, J.E. Stone, J.C. Phillips (2008). GPU Computing. Proceedings of the IEEE, 96(5): 879–899.

    Article  Google Scholar 

  18. M. Rumpf, R. Strzodka (2006). Graphics Processor Units: New Prospects for Parallel Computing, L. N. in Computational Science and Engineering 51, 89–121.

    Google Scholar 

  19. C.-W. Shu, S. Osher (1998). Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys. 77, 439–71.

    Article  MathSciNet  Google Scholar 

  20. A.I. Volpert (1967). Spaces BV and quasilinear equations, Math. USSR Sbornik, 73 (1967): 255–302.

    MathSciNet  Google Scholar 

  21. G. Walz (1997). Romberg Type Cubature over Arbitrary Triangles. Mannheimer Mathem. Manuskripte Nr.225, Mannhein.

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Authors and Affiliations

  1. Dpto. de Análisis Matemático, Universidad de Málaga, Campus de Teatinos s/n, 29071, Málaga, Spain

    Manuel J. Castro & Sergio Ortega

  2. Dpto. Lenguajes y Sistemas Informáticos. Facultad de Informática, Universidad de Granada, Spain

    Marc de la Asunción & José M. Mantas

Authors
  1. Manuel J. Castro
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  2. Sergio Ortega
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  3. Marc de la Asunción
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  4. José M. Mantas
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Corresponding author

Correspondence to Manuel J. Castro.

Additional information

This research has been partially supported by the Spanish Government Research projects MTM09-11923, TIN2007-29664-E, MTM2008-06349-C03-03, and P06-RNM-01594. The numerical computations have been performed at the Laboratory of Numerical Methods of the University of Málaga.

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Castro, M.J., Ortega, S., de la Asunción, M. et al. On the benefits of using GPUS to simulate shallow flows with finite volume schemes. SeMA 50, 27–44 (2010). https://doi.org/10.1007/BF03322540

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