Moving particle semi-implicit method

The moving particle semi-implicit (MPS) method is a computational method for the simulation of incompressible free surface flows. It is a macroscopic, deterministic particle method (Lagrangian meshfree method) developed by Koshizuka and Oka (1996).

Method

The MPS method is similar to the SPH (smoothed-particle hydrodynamics) method (Gingold and Monaghan, 1977; Lucy, 1977) in that both methods provide approximations to the strong form of the Partial Differential Equations (PDEs) on the basis of integral interpolants. However, the MPS method applies simplified differential operator models solely based on a local weighted averaging process without taking the gradient of a kernel function. In addition, the solution process of MPS method differs to that of the original SPH method as the solutions to the PDEs are obtained through a semi-implicit prediction-correction process rather than the fully explicit one in original SPH method.

Applications

Through the past years, the MPS method has been applied in a wide range of engineering applications including Nuclear Engineering (e.g. Koshizuka et al., 1999; Koshizuka and Oka, 2001; Xie et al., 2005), Coastal Engineering (e.g. Gotoh et al., 2005; Gotoh and Sakai, 2006), Environmental Hydraulics (e.g. Shakibaeina and Jin, 2009), Ocean Engineering (Shibata and Koshizuka, 2007; Sueyoshi et al., 2008), Structural Engineering (e.g. Chikazawa et al., 2001), Mechanical Engineering (e.g. Heo et al., 2002; Sun et al., 2009), Bioengineering (e.g. Tsubota et al., 2006) and Chemical Engineering (e.g. Sun et al., 2009).

Improvements

Improved versions of MPS method have been proposed for enhancement of numerical stability (e.g. Koshizuka et al., 1998; Zhang et al., 2005; Ataie-Ashtiani and Farhadi, 2006;Shakibaeina and Jin, 2009 ), momentum conservation (e.g. Hamiltonian MPS by Suzuki et al., 2007; Corrected MPS by Khayyer and Gotoh, 2008), mechanical energy conservation (e.g. Hamiltonian MPS by Suzuki et al., 2007) and pressure calculation (e.g. Khayyer and Gotoh, 2009, Kondo and Koshizuka, 2010, Khayyer and Gotoh, 2010).

References

1) B. Ataie-Ashtiani and L. Farhadi, “A stable moving particle semi-implicit method for free surface flows,” Fluid Dynamics Research 38, 241–256, 2006.

2) Y. Chikazawa, S. Koshizuka, and Y. Oka, “A particle method for elastic and visco-plastic structures and fluid-structure interactions,” Comput. Mech. 27, pp. 97–106, 2001.

3) R.A. Gingold and J.J. Monaghan, “Smoothed particle hydrodynamics: theory and application to non-spherical stars,” Mon. Not. R. Astron. Soc., Vol 181, pp. 375–89, 1977.

4) H. Gotoh and T. Sakai, “Key issues in the particle method for computation of wave breaking,” Coastal Engineering, Vol 53, No 2–3, pp. 171–179, 2006.

5) H. Gotoh, H. Ikari, T. Memita and T. Sakai, “Lagrangian particle method for simulation of wave overtopping on a vertical seawall,” Coast. Eng. J., Vol 47, No 2–3, pp. 157–181, 2005.

6) S. Heo, S. Koshizuka and Y. Oka, “Numerical analysis of boiling on high heat-flux and high subcooling condition using MPS-MAFL,” International Journal of Heat and Mass Transfer, Vol 45, pp. 2633–2642, 2002.

7) A. Khayyer and H. Gotoh, “Development of CMPS method for accurate water-surface tracking in breaking waves,” Coast. Eng. J., Vol 50, No 2, pp. 179–207, 2008.

8) A. Khayyer and H. Gotoh, “Modified Moving Particle Semi-implicit methods for the prediction of 2D wave impact pressure,” Coastal Engineering, Vol 56, pp. 419–440, 2009.

9) A. Khayyer and H. Gotoh, "A higher order Laplacian model for enhancement and stabilization of pressure calculation by the MPS method," Applied Ocean Research, 2010 (in press).

10) M. Kondo and S. Koshizuka, "Improvement of stability in moving particle semi-implicit method", Int. J. Numer. Meth. Fluid, 2010 (in press).

11) S. Koshizuka and Y. Oka, “Moving particle semi-implicit method for fragmentation of incompressible fluid,” Nuclear Science and Engineering, Vol 123, pp. 421–434, 1996.

12) S. Koshizuka, S. and Y. Oka, “Application of Moving Particle Semi-implicit Method to Nuclear Reactor Safety,” Comput. Fluid Dyn. J., Vol 9, pp. 366–375, 2001.

13) S. Koshizuka, H. Ikeda and Y. Oka, “Numerical analysis of fragmentation mechanisms in vapor explosions,” Nuclear Engineering and Design, Vol 189, pp. 423–433, 1999.

14) S. Koshizuka, A. Nobe and Y. Oka, “Numerical Analysis of Breaking Waves Using the Moving Particle Semi-implicit Method,” Int. J. Numer. Meth. Fluid, Vol 26, pp. 751–769, 1998.

15) L.B. Lucy, “A numerical approach to the testing of the fission hypothesis,” Astron. J., Vol 82, pp. 1013–1024, 1977.

16) K. Shibata and S. Koshizuka, “Numerical analysis of shipping water impact on a deck using a particle method,” Ocean Engineering, Vol 34, pp. 585–593, 2007.

17) A. Shakibaeinia and Y.C. Jin “A mesh-free particle model for simulation of mobile-bed dam break.” Advances in Water Resources, 34 (6):794-807 (DOI: 10.1016/j.advwatres.2011.04.011).

18) A. Shakibaeinia and Y.C. Jin “A weakly compressible MPS method for simulation open-boundary free-surface flow.” Int. J. Numer. Methods Fluids, 63 (10):1208–1232 (Published Online: 7 Aug 2009 DOI: 10.1002/fld.2132).

19) A. Shakibaeinia and Y.C. Jin “Lagrangian Modeling of flow over spillways using moving particle semi-implicit method.” Proc. 33rd IAHR Congress, Vancouver, Canada, 2009, 1809-1816.

20) M. Sueyoshi, M. Kashiwagi and S. Naito, “Numerical simulation of wave-induced nonlinear motions of a two-dimensional floating body by the moving particle semi-implicit method,” Journal of Marine Science and Technology, Vol 13, pp. 85–94, 2008.

21) Z. Sun, G. Xi and X. Chen, “A numerical study of stir mixing of liquids with particle method,” Chemical Engineering Science, Vol 64, pp. 341–350, 2009.

22) Z. Sun, G. Xi and X. Chen, “Mechanism study of deformation and mass transfer for binary droplet collisions with particle method,” Phys. Fluids, Vol 21, 032106, 2009.

23) K. Tsubota, S. Wada, H. Kamada, Y. Kitagawa, R. Lima and T. Yamaguchi, “A Particle Method for Blood Flow Simulation – Application to Flowing Red Blood Cells and Platelets–,” Journal of the Earth Simulator, Vol 5, pp. 2–7, 2006.

24) H. Xie, S. Koshizuka and Y. Oka, “Simulation of drop deposition process in annular mist flow using three-dimensional particle method,” Nuclear Engineering and Design, Vol 235, pp. 1687–1697, 2005.

25) S. Zhang, K. Morita, K. Fukuda and N. Shirakawa, “An improved MPS method for numerical simulations of convective heat transfer problems,” Int. J. Numer. Meth. Fluid, 51, 31–47, 2005.

External links

• Laboratory of Professor Seiichi Koshizuka at the University of Tokyo, Japan
• Laboratory of Professor Hitoshi Gotoh at Kyoto University, Japan
• MPS-RYUJIN by Fuji Technical Research
• Prometech Next-Generation Moving Particle Analysis Solution
• MPARS (Mesh-free Particle Simulator) software by A. Shakibaeinia
• An excellent review paper on meshfree and particle methods (S. Li and W.K. Liu, Meshfree and particle methods and their applications, Appl Mech Rev, Vol 55, pp. 1–34, 2002)