  The consistency of Moving Particle Semi-implicit (MPS) method in reproducing
the gradient, divergence and Laplacian differential operators is discussed in
the present paper. Its relation to the Smoothed Particle Hydrodynamics (SPH)
method is rigorously established. The application of the MPS method to solve
the Navier-Stokes equations using a fractional step approach is treated,
unveiling inconsistency problems when solving the Poisson equation for the
pressure. A new corrected MPS method incorporating boundary terms is proposed.
Applications to one dimensional boundary value Dirichlet and mixed
Neumann-Dirichlet problems and to two-dimensional free-surface flows are
presented.
