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Flow behaviour over a 2D body using the moving particle semi-implicit method with free surface stabilisation

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Abstract

The Moving Particle Semi-implicit (MPS) method is a Lagrangian particle method based on the prediction–correction calculation of the velocity field and the Helmhotz–Hodge decomposition. Initially the predicted velocity is calculated with the viscous and external forces terms and then corrected by the gradient of the pressure which is obtained by the solution of the Poisson Pressure’s equation. The MPS was developed for non-compressible bodies and it is adequate for free surface problems. However, when used to simulate fluid structure interaction problems, like ship resistance, the original formulation of the method can not accurately compute the pressure distribution over the bodies. This paper proposes a modified MPS method for modelling immerse bodies in an free surface flow. It was found that small variations in the source term of the Poisson Pressure’s equation can destabilise simulations. Therefore, a reformulation of the Poisson pressure equation was developed. The results show that the proposed variation produced numerical stabilisation. The free surface particles behave in a good agreement with experimental observations. Also, although pressure fluctuations were still present, satisfactory results were obtained when comparing the drag coefficient with those reported values in the literature.

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References

  1. Caboussat, A., Picasso, M., Rappaz, J.: Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas. J. Comput. Phys. 203(2), 626–649 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Donea, J., Huerta, A.: Finite Element Methods for Flow Problems. Wiley, New York (2003)

    Book  Google Scholar 

  3. Ferziger, J.H., Perić, M.: Computational Methods for Fluid Dynamics, 3rd edn. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  4. García, M., Duque, J., Boulanger, P., Figueroa, P.: Computational steering of CFD simulations using a grid computing environment. Int. J. Interact. Des. Manuf. 9(3), 235–245 (2015). doi:10.1007/s12008-014-0236-1

    Article  Google Scholar 

  5. Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics–theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977)

    Article  MATH  Google Scholar 

  6. Goswami, P., Schlegel, P., Solenthaler, B., Pajarola, R.: Interactive SPH simulation and rendering on the GPU. In: Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 55–64. Eurographics Association (2010)

  7. Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39(1), 201–225 (1981)

    Article  MATH  Google Scholar 

  8. Hwang, S., Khayyer, A., Gotoh, H., Park, J.: Development of a fully lagrangian MPS-base coupled method for simulation of fluid–structure interaction problems. J. Fluids Struct. 50, 497–511 (2014)

    Article  Google Scholar 

  9. Khayyer, A., Gotoh, H.: Development of CMPS method for accurate water-surface tracking in breaking waves. Coast. Eng. J. 50(2), 179–207 (2008)

    Article  Google Scholar 

  10. Khayyer, A., Gotoh, H.: Modified moving particle semi-implicit methods for the prediction of 2d wave impact pressure. Coast. Eng. 56(4), 419–440 (2009)

    Article  Google Scholar 

  11. Khayyer, A., Gotoh, H.: A high order Laplacian model for enhancement and stabilization of pressure calculation by MPS method. Appl. Ocean Res. 32, 124–131 (2010)

    Article  Google Scholar 

  12. Khayyer, A., Gotoh, H.: Enhancement of stability and accuracy of the moving particle semi-implicit method. J. Comput. Phys. 230(8), 3093–3118 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Khayyer, A., Gotoh, H.: A 3D higher order Laplacian model for enhancement and stabilization of pressure calculation in 3D MPS-based simulations. Appl. Ocean Res. 37, 120–126 (2012)

    Article  Google Scholar 

  14. Khayyer, A., Gotoh, H.: Enhancement of performance and stability of MPS mesh-free particle method for multiphase flows characterized by high density ratios. J. Comput. Phys. 242, 211–233 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kondo, M., Koshizuka, S.: Improvement of stability in moving particle semi-implicit method. Int. J. Numer. Methods Fluids 65, 638–654 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Koshizuka, S., Ikeda, H., Oka, Y.: Numerical analysis of fragmentation mechanisms in vapor explosions. Nucl. Eng. Des. 189(1–3), 423–433 (1999). doi:10.1016/S0029-5493(98)00270-2. http://www.sciencedirect.com/science/article/pii/S0029549398002702

  17. Koshizuka, S., Nobe, A., Oka, Y.: Numerical analysis of breaking waves using the moving particle semi-implicit method. Int. J. Numer. Methods Fluids 26(7), 751–769 (1998)

    Article  MATH  Google Scholar 

  18. Koshizuka, S., Oka, Y.: Moving particle semi-implicit method or fragmentation of incomprssible fluid. Nucl. Sci. Eng. 123, 421–434 (1996)

    Google Scholar 

  19. Lee, B., Park, J., Kim, M., Hwang, S.: Step by step improvement of MPS method in simulating violent free-surface motions and impact-loads. Comput. Methods Appl. Mech. Eng. 200(9), 1113–1125 (2011)

    Article  MATH  Google Scholar 

  20. Li, S., Liu, W.: Meshfree and particle methods and their applications. Appl. Mech. Rev. 55(1), 1–34 (2002)

    Article  Google Scholar 

  21. Li, S., Liu, W.K.: Meshfree Particle Methods. Springer, Berlin (2004)

    MATH  Google Scholar 

  22. Lucy, L.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82(12), 1013–1024 (1977)

    Article  Google Scholar 

  23. Maronnier, V., Picasso, M., Rappaz, J.: Numerical simulation of free surface flows. J. Comput. Phys. 155(2), 439–455 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Martin, J.C., Moyce, W.J.: Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 244(882), 312–324 (1952). doi:10.1098/rsta.1952.0006

    Google Scholar 

  25. Monaghan, J.J.: Simulating free surface flows with SPH. J. Comput. Phys. 110, 399–406 (1994)

    Article  MATH  Google Scholar 

  26. Müller, M., Charypar, D., Gross, M.: Particle-based fluid simulation for interactive applications. In: Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 154–159. Eurographics Association (2003)

  27. Price, D.J.: Splash: an interactive visualisation tool for smoothed particle hydrodynamics simulations. Publ. Astron. Soc. Aust. 24(03), 159–173 (2007)

    Article  Google Scholar 

  28. Shakibaeinia, A., Jin, Y.C.: A weakly compressible MPS method for modeling of open-boundary free-surface flow. Int. J. Numer. Methods Fluids 63(10), 1208–1232 (2010)

    MathSciNet  MATH  Google Scholar 

  29. Shibata, K., Koshizuka, S.: Numerical analysis of shipping water impact on a deck using a particle method. Ocean Eng. 34, 585–593 (2007)

    Article  Google Scholar 

  30. Shibata, K., Koshizuka, S., Tanizawa, K.: Three-dimensional numerical analysis of shipping water onto a moving ship using a particle method. J. Mar. Sci. Technol. 14, 214–227 (2009)

    Article  Google Scholar 

  31. Sueyoshi, M., Kashiwagi, M., Naito, S.: Numerical simulation of wave-induced nonlinear motions of a two dimensional floating body by the moving particle semi-implicit method. J. Mar. Sci. Technol. 13, 85–94 (2008)

    Article  Google Scholar 

  32. Tamai, T., Koshizuka, S.: Least squares moving particle semi-implicit method. Comput. Part. Mech. 1(3), 277–305 (2014)

    Article  Google Scholar 

  33. Tanaka, M., Masunaga, T.: Stabilization and smoothing pressure in MPS method by quasi-compressibility. J. Comput. Phys. 229(11), 4279–4290 (2010)

    Article  MATH  Google Scholar 

  34. Tsubota, K.I., Wada, S., Kamada, H., Kitagawa, Y., Lima, R., Yamaguchi, T.: A particle method for blood flow simulation: application to flowing red blood cells and platelets. J. Earth Simul. 5, 2–7 (2006)

    Google Scholar 

  35. Venugopal, V., Varyanib, K.S., Barltrop, N.D.: Wave force coefficients for horizontally submerged rectangular cylinders. Ocean Eng. 30, 1669–1704 (2006)

    Article  Google Scholar 

  36. Wang, Q., Zheng, Y., Chen, C., Tadahiro, F., Chiba, N.: Efficient rendering of breaking waves using MPS method. J. Zhejiang Univ. Sci. A 7(6), 1018–1025 (2006). doi:10.1631/jzus.2006.A1018

  37. Wenisch, P., Treeck, C.V., Borrmann, A., Rank, E., Wenisch, O.: Computational steering on distributed systems: indoor comfort simulations as a case study of interactive CFD on supercomputers. Int. J. Parallel Emerg. Distrib. Syst. 22(4), 275–291 (2007)

    Article  MathSciNet  Google Scholar 

  38. Zhang, F., Hu, L., Wu, J., Shen, X.: A SPH-based method for interactive fluids simulation on the multi-GPU. In: Proceedings of the 10th International Conference on Virtual Reality Continuum and its Applications in Industry, pp. 423–426. ACM (2011)

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  1. Departamento de Ingeniería Mecánica, Universidad EAFIT, Medellín, Colombia

    Carlos A. Perez & Manuel J. Garcia

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  1. Carlos A. Perez
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  2. Manuel J. Garcia
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Correspondence to Carlos A. Perez.

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Perez, C.A., Garcia, M.J. Flow behaviour over a 2D body using the moving particle semi-implicit method with free surface stabilisation. Int J Interact Des Manuf 11, 633–640 (2017). https://doi.org/10.1007/s12008-016-0338-z

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  • DOI: https://doi.org/10.1007/s12008-016-0338-z

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