Development of Moving Particle Explicit (MPE) method for incompressible flows

Abstract

A new particle method is proposed for computing incompressible flows. Using Moving Particle Semi-implicit (MPS) and Smoothed Particle Hydrodynamics (SPH) approaches, a new Moving Particle Explicit (MPE) method is developed. The concept, like the MPS method, is based on the weighted averaging scheme. Introducing a directional particle number density, the derivation of spatial discretization is performed without imposing any simplification. As a consequence, the formulation becomes more generic and covers the MPS scheme. The solution algorithm is similar to the weakly compressible SPH method. Considering slight compressibility for an incompressible flow, the continuity equation for compressible flow together with an equation of state is used to decouple the velocity and pressure of the Navier–Stokes equations. Consequently, the method becomes fully explicit, and the problems related to solving a set of equations in an implicit procedure are removed. Easy application of the solution algorithm, in comparison with the MPS method, as well as the generic discretization scheme, makes the MPE method more efficient for simulating incompressible flows. The proposed method is validated using a Poiseuille flow and two dam break problems; furthermore, a submerged hydraulic jump is investigated to evaluate the method’s capability in simulating open boundary problems. In all cases, good agreement between numerical results and analytical/experimental data is observed.