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The Moving Particle Semi-implicit (MPS) method is a macroscopic, deterministic particle method (Lagrangian meshfree method) developed by Koshizuka and Oka (1996) initially for the simulation of incompressible free-surface fluid flows. 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. Through the past years, the MPS method has been applied in a wide range of engineering applications including Coastal Engineering (e.g. Gotoh et al., 2005; Gotoh and Sakai, 2006), Structural Engineering (e.g. Chikazawa et al., 2001), Nuclear Engineering (Koshizuka and Oka, 2001), Mechanical Engineering, (e.g. Heo et al., 2002), Bioengineering (e.g. Tsubota et al., 2001) and Chemical Engineering (e.g. Sun et al., 2009). Improved versions of MPS method have been proposed for enhancement of numerical stability (e.g. Koshizuka et al., 1998; Ataie-Ashtiani and Farhadi, 2006), 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).
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, 45(3), 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, 56(4), pp. 419-440, 2009.
9) 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.
10) S. Koshizuka, S. and Y. Oka, “Application of Moving Particle Semi-implicit Method to Nuclear Reactor Safety,” Comput. Fluid Dyn. J. 9, 366-375, 2001.
11) 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.
12) L.B. Lucy, “A numerical approach to the testing of the fission hypothesis,” Astron. J., Vol 82, pp. 1013-1024, 1977.
13) 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.
14) 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.
Links
1) Laboratory of Professor Seiichi Koshizuka at the University of Tokyo, Japan
2) Laboratory of Professor Hitoshi Gotoh at Kyoto University, Japan