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

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.

[1]  A. I. Vol'pert.  THE SPACES BV AND QUASILINEAR EQUATIONS , 1967 .

[2]  Martin Rumpf,et al.  Graphics Processor Units: New Prospects for Parallel Computing , 2006 .

[3]  Ricardo Baeza Yates,et al.  Lenguajes y Sistemas Informáticos , 2002 .

[4]  M. J. Castro,et al.  Solving shallow-water systems in 2D domains using Finite Volume methods and multimedia SSE instructions , 2008 .

[5]  Miguel Lastra,et al.  Simulation of shallow-water systems using graphics processing units , 2009, Math. Comput. Simul..

[6]  P. Floch.  Shock Waves for Nonlinear Hyperbolic Systems in Nonconservative Form , 1989 .

[7]  John D. Owens,et al.  GPU Computing , 2008, Proceedings of the IEEE.

[8]  Ami Harten,et al.  Self adjusting grid methods for one-dimensional hyperbolic conservation laws☆ , 1983 .

[9]  Jostein R. Natvig,et al.  Visual simulation of shallow-water waves , 2005, Simul. Model. Pract. Theory.

[10]  Jostein R. Natvig,et al.  Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows , 2006, J. Comput. Phys..

[11]  Barbara Chapman,et al.  Using OpenMP - portable shared memory parallel programming , 2007, Scientific and engineering computation.

[12]  C. Parés.  Numerical methods for nonconservative hyperbolic systems: a theoretical framework. , 2006 .

[13]  M. J. Castro,et al.  A parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products: Application to shallow flows , 2006 .

[14]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[15]  José Miguel Mantas,et al.  Simulation of one-layer shallow water systems on multicore and CUDA architectures , 2010, The Journal of Supercomputing.

[16]  Jens H. Krüger,et al.  A Survey of General‐Purpose Computation on Graphics Hardware , 2007, Eurographics.

[17]  Christer Sjöström,et al.  State-of-the-art report , 1997 .

[18]  José Miguel Mantas,et al.  Two-Dimensional Compact Third-Order Polynomial Reconstructions. Solving Nonconservative Hyperbolic Systems Using GPUs , 2011, J. Sci. Comput..

[19]  Manuel Jesús Castro Díaz,et al.  High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems , 2009, J. Sci. Comput..

[20]  Guido Walz.  Romberg Type Cubature over Arbitrary Triangles , 1997 .

[21]  G. D. Maso,et al.  Definition and weak stability of nonconservative products , 1995 .