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).
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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 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).
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).
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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).
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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.
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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.