Projection-based particle methods, including Incompressible SPH (ISPH) and MPS methods, are founded on Helmholtz decomposition of an intermediate velocity vector field into a solenoidal (divergence-free) one and an irrotational (curl-free) one. These methods  potentially result in accurate solutions to the continuity and Navier-Stokes equations, especially in terms of pressure calculation and volume conservation. In particular, the prediction-correction feature of projection-based particle methods provides the opportunity for numerical error minimization through the application of, for instance, error mitigating functions in the source term of the Poisson Pressure Equation (PPE) [1, 2]. This paper aims at illustrating a concise summary of the latest achievements made in the field of projection-based particle methods, as well as some future perspectives.

The latest achievements made in the field of projection-based particle methods correspond to enhancements of stability, accuracy, boundary conditions, energy conservation and enhanced simulations of multiphase flows, fluid-structure interactions, etc. In this extended abstract, these achievements will be briefly illustrated. More detailed explanations will be presented in the full paper.