Openmp and MPI Architectures for Simulating 1D Water Oscillation on Parabolic Domain

  • Authors

    • P. H. Gunawan
    • S. Juliati
    • M. R. Pahlevi
    • D. Adytia
    2019-01-26
    https://doi.org/10.14419/ijet.v8i1.9.26405
  • OpenMP, MPI, shallow water, CPU time, multicore process, Oscillation in paraboloid
  • This paper enlightens the simulation of 1D water oscillation on parabolic domain using shallow water equations on multicore processing. Those equation is approached by using finite volume method staggered grid scheme. This scheme is known as a robust scheme for approximating the shallow water equations. Moreover, the scheme is also straightforward to transform into numerical codes.  In this paper, the parallel architectures multicore processing OpenMP and MPI are used. The results are shown the CPU time of OpenMP and MPI are better than the serial programming when the number of grids is given more than 200 points. Moreover, the speedup of OpenMP is shown 3 times better than MPI with N_x  = 6400 points for both 4 and 8 processors. The maximum of efficiency in the simulation can be achieved around 75% with  N_x  = 6400 points by 4 cores using OpenMP. However, by 8 cores of processors using OpenMP, the maximum of efficiency is obtained around 60%.

     

  • References

    1. [1] Audusse, E., Bouchut, F., Bristeau, M.-O., Klein, R., and Perthame, B. (2004). A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM Journal on Scientific Computing, 25(6):2050– 2065.

      [2] Bouchut, F. (2004). Nonlinear stability of finite Volume Methods for hyperbolic conservation laws: And Well-Balanced schemes for sources. Frontiers in Mathematics. Birkhäuser Verlag, Basel.

      [3] Brodtkorb, A. R., Sætra, M. L., and Altinakar, M. (2012). Efficient shallow water simulations on gpus: Implementation, visualization, verification, and validation. Computers & Fluids, 55:1–12.

      [4] Castillo, D., Ferreiro, A. M., García-Rodríguez, J. A., & Vázquez, C. (2013). Numerical methods to solve PDE models for pricing business companies in different regimes and implementation in GPUs. Applied Mathematics and Computation, 219(24), 11233-11257.

      [5] Cushman-Roisin, B. and Beckers, J.-M. (2011). Introduction to geophysical fluid dynamics: physical and numerical aspects, volume 101. Academic Press.

      [6] De la Asunción, M., Castro, M. J., Mantas, J. M., & Ortega, S. (2016). Numerical simulation of tsunamis generated by landslides on multiple GPUs. Advances in Engineering Software, 99, 59-72.

      [7] De La Asunción, M., Mantas, J. M., & Castro, M. J. (2011). Simulation of one-layer shallow water systems on multicore and CUDA architectures. The Journal of Supercomputing, 58(2), 206-214.

      [8] Delestre, O., Cordier, S., James, F., and Darboux, F. (2008). Simulation of rain-water overland-flow. In 12th International Conference on Hyperbolic Problems, volume 67, pages 537–546. American Mathematical Society.

      [9] Delestre, O., & Lagrée, P. Y. (2013). A wellâ€balanced finite volume scheme for blood flow simulation. International Journal for Numerical Methods in Fluids, 72(2), 177-205.

      [10] Delestre, O. and Marche, F. (2011). A numerical scheme for a viscous shallow water model with friction. Journal of Scientific Computing, 48(1-3):41–51.

      [11] Doyen, D. and Gunawan, P. H. (2014). An explicit staggered finite volume scheme for the shallow water equations. In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, pages 227–235. Springer.

      [12] Gunawan, P. H. (2016). Scientific parallel computing for 1d heat diffusion problem based on openmp. In Information and Communication Technology (ICoICT), 2016 4th International Conference on, pages 1–5. IEEE.

      [13] Gunawan, P. H., and Lhébrard, X. (2015). Hydrostatic relaxation scheme for the 1D shallow water-Exner equations in bedload transport. Computers & Fluids, 121, 44-50.

      [14] Gunawan, P. H., Eymard, R., and Pudjaprasetya, S. R. (2015). Staggered scheme for the Exner–shallow water equations. Computational Geosciences, 19(6), 1197-1206.

      [15] LeVeque, R. J. (2002). Finite volume methods for hyperbolic problems, volume 31. Cambridge university press.

      [16] Stelling, G. S. and Duinmeijer, S. A. (2003). A staggered conservative scheme for every froude number in rapidly varied shallow water flows. International Journal for Numerical Methods in Fluids, 43(12):1329–1354.

      [17] Toro, E. F. (2013). Riemann solvers and numerical methods for fluid dynamics: a practical introduction. Springer Science & Business Media.

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  • How to Cite

    H. Gunawan, P., Juliati, S., R. Pahlevi, M., & Adytia, D. (2019). Openmp and MPI Architectures for Simulating 1D Water Oscillation on Parabolic Domain. International Journal of Engineering & Technology, 8(1.9), 230-236. https://doi.org/10.14419/ijet.v8i1.9.26405