The '''moving particle semi-implicit (MPS)''' method is a computational method for the simulation of [[incompressible flow|incompressible]] [[free surface flow]]s. 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 ([[Smoothedsmoothed-particle Particle Hydrodynamicshydrodynamics]]) 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 average|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.
