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Optimization of the Parameters of Smoothed Particle Hydrodynamics Method, Using Evolutionary Algorithms

  • Juan de Anda-Suárez
  • Martín CarpioEmail author
  • Solai Jeyakumar
  • Héctor José Puga-Soberanes
  • Juan F. Mosiño
  • Laura Cruz-Reyes
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 749)

Abstract

Smooth particle hydrodynamics (SPH) is a mesh free numerical method for solving hydrodynamical equations. For its functioning, the method uses; one integer-domain parameter (the total number of particles) and three real domain parameters (smoothing parameters and artificial viscosity). For a given problem (geometry and initial conditions) these parameters can be tuned to reduce the computational cost and improve the accuracy of the solutions. Optimized values of the SPH parameters using the evolutionary algorithms, Differential Evolution (DE) and Boltzmann Univariate Marginal Distribution Algorithm (BUMDA) are obtained for different Sod shock tube test problems. Comparison of the numerical solution of the physical variables with that of the exact solution shows that this optimization strategy can be used to make an initial guess of the SPH parameters based on the initial conditions of the simulation domain. The performance of the two algorithms are statistically compared.

Keywords

Evolutipnary Algorithm Optimization Evolutionary computation Application 

Keywords

Evolutionary algorithms Differential Evolution Smooth Particle Hydrodynamics Riemann solver Parameters tunning Optimization of Algorithms 

References

  1. 1.
    J.J. Monaghan, Smoothed Particle Hydrodynamics, Area, vol. 30 (1992), pp. 543–574Google Scholar
  2. 2.
    N. Xiao, C. Leiting, X. Tao, Real-time incompressible fluid simulation on the GPU. Int. J. Comput. Games Technol. 2015, 12 (2015)Google Scholar
  3. 3.
    A.W. Alshaer, B.D. Rogers, L. Li, Smoothed particle hydrodynamics (SPH) modelling of transient heat transfer in pulsed laser ablation of Al and associated free-surface problems. Comput. Mater. Sci. 127, 161–179 (2017)Google Scholar
  4. 4.
    S.I. Inutsuka, Reformulation of smooth particle hydrodynamics with Riemann solver. J. Comput. Phys. 179, 238–267 (2002)CrossRefzbMATHGoogle Scholar
  5. 5.
    M. Muller, D. Charypar, M. Gross, Particle-based fluid simulation for interactive applications, in Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2003), pp. 154–159Google Scholar
  6. 6.
    G. Fourtakas, B.D. Rogers, Modelling multi-phase liquid-sediment scour and resuspension induced by rapid flows using smoothed particle hydrodynamics (SPH) accelerated with a graphics processing unit (GPU). Adv. Water Resour. 92, 186–199 (2016)Google Scholar
  7. 7.
    I. Markus, O. Jens, S. Barbara, K. Andreas, T. Matthias, SPH Fluids in Computer Graphics (The Eurographics Association, 2014)Google Scholar
  8. 8.
    H. Chen, Z. Jian, S. Hanqiu, W. Enhua, Parallel-optimizing SPH fluid simulation for realistic VR environments. Comput. Anim. Virtual Worlds 26, 43–54 (2015)Google Scholar
  9. 9.
    R.A. Gingold, J.J. Monagahan, Kernel estimates as a basis for general particle methods in hydrodynamics. J. Comput. Phys. 46, 429–453 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    A. Barreiro, A.J.C. Crespo, J.M. Domínguez, M. Gómez-Gesteira, Smoothed particle hydrodynamics for coastal engineering problems. Comput. Struct. 120, 96–106 (2013)CrossRefGoogle Scholar
  11. 11.
    A. Corrado, A.J.C. Crespoc, J.M. Domínguez, M. Gómez-Gesteira, S. Tomohiro, V. Toon, Applicability of smoothed particle hydrodynamics for estimation of sea wave impact on coastal structures. Coast. Eng. 96, 1–12 (2015)CrossRefGoogle Scholar
  12. 12.
    E.L. Fasanella, K.E. Jackson, Impact testing and simulation of a crashworthy composite fuselage section with energy-absorbing seats and dummies. J. Am. Helicopter Soc. 49, 140–148 (2004)Google Scholar
  13. 13.
    D. Guibert, M. de Leffe, G. Oger, J.-C. Piccinali, Efficient parallelisation of 3D SPH schemes, in 7th International SPHERIC Workshop, Prato, Italy, SPHERIC (2012), pp. 259–265Google Scholar
  14. 14.
    M.S. Shadloo, M. Zainali, M. Yildiz, Improved solid boundary treatment method for the solution of flow over an airfoil and square obstacle by SPH method, in 5th International SPHERIC Workshop, Manchester, UK, SPHERIC (2010), pp. 37–41Google Scholar
  15. 15.
    R.A. Gingold, J.J. Monaghan, Smoothed particle hydrodynamics - theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977)CrossRefzbMATHGoogle Scholar
  16. 16.
    J.J. Monaghan, R.A. Gingold, Shock simulation by the particle method SPH. J. Comput. Phys. 52, 374–389 (1983)CrossRefzbMATHGoogle Scholar
  17. 17.
    M. Steinmetz, E. Mueller, Hydrodynamical cosmology: galaxy formation in a cosmological context, metallicities and metallicity gradients. Astron. Ges. Abstract Ser. 281 (1992)Google Scholar
  18. 18.
    V. Springel, The cosmological simulation code GADGET-2, mnras, vol. 364 (2005), pp. 1105–1134Google Scholar
  19. 19.
    Q. Hongfu, G. Weiran, A new SPH equation including variable smoothing lengths aspects and its implementation. Comput. Mech. ISBN: 9783540759997_143 (2009)Google Scholar
  20. 20.
    J.C. Travis, H.D. Brian, X.H. Zhen, P.B. Wang, Aerodynamic shape optimization of a vertical-Axis wind turbine using differential evolution. ISRN Renew. Energy 2012, 16 (2012)Google Scholar
  21. 21.
    T. Rogalsky, R.W. Derksen, Hybridization of differential evolution for aerodynamic design, in Proceedings of the 8th Annual Conference of the Computational Fluid Dynamics Society of Canada (2000), pp. 729–736Google Scholar
  22. 22.
    K.W. Wagner, The complexity of combinatorial problems with succinct input representation. Acta Inf. 23, 325–356 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    J.K. Lenstra, A.H.G. Rinnooy, P. Brucker, Complexity of machine scheduling problems. Ann. Discret. Math. 1, 343–362 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction (Springer, ISBN. 3540616764, 1997)Google Scholar
  25. 25.
    R. Storn, K. Price, Differential Evolution - A Simple and Efficient Adaptive Scheme for Global Optimization Over Continuous Spaces (1995)Google Scholar
  26. 26.
    S.I. Valdez, A. Hernández, S. Botello, A Boltzmann based estimation of distribution algorithm. Inf. Sci. 236, 126–137 (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Juan de Anda-Suárez
    • 1
  • Martín Carpio
    • 1
    Email author
  • Solai Jeyakumar
    • 2
  • Héctor José Puga-Soberanes
    • 1
  • Juan F. Mosiño
    • 1
  • Laura Cruz-Reyes
    • 3
  1. 1.Tecnológico Nacional de México- Instituto Tecnológico de LeónLeónMexico
  2. 2.Departamento de AstronomíaUniversidad de GuanajuatoGuanajuatoMexico
  3. 3.Tecnológico Nacional de México- Instituto Tecnológico de Ciudad MaderoCiudad MaderoMexico

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