Comptes Rendus
GPU computing for shallow water flow simulation based on finite volume schemes
Comptes Rendus. Mécanique, Volume 339 (2011) no. 2-3, pp. 165-184.

This article is a review of the work that we are carrying out to efficiently simulate shallow water flows. In this paper, we focus on the efficient implementation of path-conservative Roe type high-order finite volume schemes to simulate shallow flows that are supposed to be governed by the one-layer or two-layer shallow water systems, 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.

Published online:
DOI: 10.1016/j.crme.2010.12.004
Keywords: Computer science, GPUs, Finite volume methods, Shallow water, High-order schemes

Manuel J. Castro 1; Sergio Ortega 1; Marc de la Asunción 2; José M. Mantas 2; José M. Gallardo 1

1 Dpto. de Análisis Matemático, Universidad de Málaga, Campus de Teatinos s/n, 29080 Malaga, Spain
2 Dpto. de Lenguajes y Sistemas Informáticos, Universidad de Granada, C./Periodista Daniel Saucedo Aranda s/n, 18071 Granada, Spain
     author = {Manuel J. Castro and Sergio Ortega and Marc de la Asunci\'on and Jos\'e M. Mantas and Jos\'e M. Gallardo},
     title = {GPU computing for shallow water flow simulation based on finite volume schemes},
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Manuel J. Castro; Sergio Ortega; Marc de la Asunción; José M. Mantas; José M. Gallardo. GPU computing for shallow water flow simulation based on finite volume schemes. Comptes Rendus. Mécanique, Volume 339 (2011) no. 2-3, pp. 165-184. doi : 10.1016/j.crme.2010.12.004.

[1] M.J. Castro; J.A. García-Rodríguez; J.M. González-Vida; C. Parés A parallel 2D finite volume scheme for solving systems of balance laws with nonconservative products: Application to shallow flows, Comput. Meth. Appl. Mech. Eng., Volume 195 (2006), pp. 2788-2815

[2] M.J. Castro; J.A. García-Rodríguez; J.M. González-Vida; C. Parés Solving shallow-water systems in 2D domains using finite volume methods and multimedia SSE instructions, J. Comput. Appl. Math., Volume 221 (2008), pp. 16-32

[3] M. Rumpf; R. Strzodka Graphics processor units: New prospects for parallel computing, Lecture Notes Comput. Sci. Eng., Volume 51 (2006), pp. 89-121

[4] J.D. Owens; M. Houston; D. Luebke; S. Green; J.E. Stone; J.C. Phillips GPU computing, Proceedings of the IEEE, Volume 96 (2008), pp. 879-899

[5] T.R. Hagen; J.M. Hjelmervik; K.-A. Lie; J.R. Natvig; M.O. Henriksen Visual simulation of shallow-water waves, Simul. Model. Pract. Theory, Volume 13 (2005), pp. 716-726

[6] M. Lastra; J.M. Mantas; C. Ureña; M.J. Castro; J.A. García-Rodríguez Simulation of shallow-water systems using graphics processing units, Math. Comput. Simul., Volume 80 (2009), pp. 598-618

[7] Wen-Yew Liang; Tung-Ju Hsieh; Muhammad Satria; Yang-Lang Chang; Jyh-Perng Fang; Chih-Chia Chen; Chin-Chuan Han A GPU-based simulation of tsunami propagation and inundation, Lecture Notes in Computer Science, Volume 5574 (2009), pp. 593-603

[8] (NVIDIA, CUDA home page)

[9] M. de la Asunción; J.M. Mantas; M.J. Castro Simulation of one-layer shallow water systems on multicore and CUDA architectures, J. Supercomput. (2009) | DOI

[10] M. de la Asunción, J.M. Mantas, M.J. Castro, Programming CUDA-based GPUs to simulate two-layer shallow water flows, Euro-Par 2010, Ischia, Italy.

[11] M.J. Castro; S. Ortega; M. de la Asunción; J.M. Mantas On the benefits of using GPUs to simulate shallow flows with finite volume schemes, Boletín de la Sociedad Española de Matemática Aplicada, Volume 50 (2010), pp. 27-44

[12] A.R. Brodtkorb, T.R. Hagen, K.-A. Lie, J.R. Natvig, Simulation and visualization of the Saint-Venant system using GPUs, Computing and Visualization in Science, Special issue on Hot Topics in Computational Engineering (2010), , in press. | DOI

[13] M.J. Castro; E.D. Fernández; A.M. Ferreiro; A. García; C. Parés High order extension of Roe schemes for two-dimensional nonconservative hyperbolic systems, J. Sci. Comput., Volume 39 (2009), pp. 67-114

[14] G. Dal Maso; P.G. LeFloch; F. Murat Definition and weak stability of nonconservative products, J. Math. Pures Appl., Volume 74 (1995), pp. 483-548

[15] A.I. Volpert Spaces BV quasilinear equations, Math. USSR Sbornik, Volume 73 (1967), pp. 255-302

[16] A. Harten; J.M. Hyman Self-adjusting grid methods for one-dimensional hyperbolic conservation laws, J. Comp. Phys., Volume 50 (1983), pp. 235-269

[17] M.J. Castro; P.G. LeFloch; M.L. Muñoz; C. Parés Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes, Jour. Comp. Phys., Volume 3227 (2008), pp. 8107-8129

[18] C. Parés; M.L. Muñoz Ruíz On some difficulties of the numerical approximation of nonconservative hyperbolic systems, Boletín SEMA, Volume 47 (2009), pp. 23-52

[19] T.Y. Hou; P.G. LeFloch Why nonconservative schemes converge to wrong solutions: error analysis, Math. Comput., Volume 62 (1994), pp. 497-530

[20] M.L. Muñoz, C. Parés, On the convergence and well-balanced property of path-conservative numerical schemes for systems of balance laws, J. Sci. Comp. (2010), , in press. | DOI

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

[22] G. Walz, Romberg type cubature over arbitrary triangles, Mannheimer Mathem, Manuskripte Nr. 225, Mannhein, 1997.

[23] C.-W. Shu; S. Osher Efficient implementation of essentially non-oscillatory shock capturing schemes, J. Comput. Phys., Volume 77 (1998), pp. 439-471

[24] J.M. Gallardo, S. Ortega, M. de la Asunción, J.M. Mantas, Two-dimensional compact third-order polynomial reconstructions. Solving nonconservative hyperbolic systems using GPUs, J. Sci. Comput. (2010), submitted for publication.

[25] (NVIDIA, NVIDIA CUDA Programming Guide Version 3.0, 2010)

[26] (Eigen 2.0.15)

[27] B. Chapman; G. Jost; R. van der Pas Using OpenMP: Portable Shared Memory Parallel Programing, The MIT Press, 2007

[28] (EISPACK)

[29] E.D. Fernández Nieto, M.J. Castro, C. Parés, IFCP Riemann solver for the two-layer shallow-water system, J. Sci. Comput. (2010), submitted for publication.

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