Enhancement of pressure calculation in projection-based particle methods by incorporation of background mesh scheme

Particle methods, or Lagrangian mesh-free methods, are well known as potentially robust computational methods for a wide range of applications in science and engineering, including ocean engineering. Despite their potential robustness, a challenge in the application of particle methods corresponds to the presence of unphysical pressure noise. This study presents a simple and straightforward approach for enhancement of pressure calculation in projection-based particle methods, in the context of MPS (Moving Particle Semi-implicit) method. One of the causes for the presence of unphysical pressure noise in projection-based particle methods corresponds to the use of Eulerian kernels (with a fixed radius of influence or smoothing length) with a purely Lagrangian description of motions in the presence of particle perturbations, leading to spatial discontinuities in the source term of Poisson Pressure Equation (PPE). To enhance continuity, accuracy and smoothness of calculated source term of PPE, a so-called Background Mesh (BM) scheme is proposed to provide spatial connectivity and continuity in between calculated source terms at moving particle positions. The scheme is validated through several benchmark tests including a simple uniform flow, a dam-breaking flow and violent sloshing flows. Incorporation of BM scheme is shown to be effective in enhancing the pressure calculation in projection-based particle methods with only a slight increase in computational cost.