Flow behaviour over a 2D body using the moving particle semi-implicit method with free surface stabilisation

The Moving Particle Semi-implicit (MPS) method is a Lagrangian particle method based on the prediction–correction calculation of the velocity field and the Helmhotz–Hodge decomposition. Initially the predicted velocity is calculated with the viscous and external forces terms and then corrected by the gradient of the pressure which is obtained by the solution of the Poisson Pressure’s equation. The MPS was developed for non-compressible bodies and it is adequate for free surface problems. However, when used to simulate fluid structure interaction problems, like ship resistance, the original formulation of the method can not accurately compute the pressure distribution over the bodies. This paper proposes a modified MPS method for modelling immerse bodies in an free surface flow. It was found that small variations in the source term of the Poisson Pressure’s equation can destabilise simulations. Therefore, a reformulation of the Poisson pressure equation was developed. The results show that the proposed variation produced numerical stabilisation. The free surface particles behave in a good agreement with experimental observations. Also, although pressure fluctuations were still present, satisfactory results were obtained when comparing the drag coefficient with those reported values in the literature.