Analysis of wall boundary in moving particle semi-implicit method and a novel model of fluid-wall interaction

Wall boundary modelling is one of the key factors that affect the accuracy of the moving particle semi-implicit (MPS) method. In most implementations of the MPS method, wall boundaries are modelled by discrete wall particles and corresponding phantom particles. In this work, a systematic analysis is performed to demonstrate that the discretised representation of wall boundaries can numerically cause unphysical 'frictional force' and 'bouncing movement' to nearby fluid particles. This can significantly influence the accuracy of the MPS method. To address these issues, a new fluid-wall interaction model is proposed which replaces the discrete wall particles with a continuous, smooth mathematical description of the particle number density. With the new fluid-wall interaction model, solid boundaries are modelled to retain their physical shapes. Numerical examples demonstrate that the new method generates more accurate and physical results than the original MPS method. In addition to the improved results, the new method also features reduced complexity of MPS modelling and more efficient computation. The method is also envisioned to be applicable to problems with arbitrarily shaped boundaries.