Moving particle semi-implicit method
Encyclopedia
The moving particle semi-implicit (MPS) method is a computational method for the simulation of incompressible
Incompressible flow
In fluid mechanics or more generally continuum mechanics, incompressible flow refers to flow in which the material density is constant within an infinitesimal volume that moves with the velocity of the fluid...

 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
Differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation, accepting a function and returning another .This article considers only linear operators,...

 models solely based on a local weighted averaging process without taking the gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

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).

External links

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