Moving particle semi-implicit method

Moving Particle Semi-implicit Method 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 and Sakai; 2006), Structural Engineering (e.g. Koshizuka et al., 2001), Nuclear Engineering (Koshizuka and Oka, 2001), Mechanical Engineering, (e.g. Heo et al., 2002), Bioengineering (e.g. Tsubota et al., 2006) and Chemical Engineering (e.g. Sun et al., 2009). Improved versions of MPS method has been proposed for enhancement of 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).