A QSFDI based Laplacian discretisation for modelling wave-structure interaction using ISPH

Abstract

The incompressible Smoothed Particle Hydrodynamics (ISPH) is one of the most popular Lagrangian particle methods for modelling wave-structure interactions. It solves the unsteady Navier-Stokes and continuity equations using the projection method, in which solving the pressure Poisson's equation (PPE) plays a critical role. To discretise the Laplacian operator, the quadric semi-analytical finite difference interpolation scheme (QSFDI) has been developed recently and the relevant patch test has demonstrated its superiority over existing schemes at a similar accuracy level in terms of the convergence and robustness. In this paper, the QSFDI is adopted by the ISPH for discretising the Laplacian operator in the PPE. The developed scheme (ISPH_QSFDI) is then applied to various cases with wave propagations and wave impacts on structures. For the purpose of comparison, other Laplacian discretisation schemes, including the classic scheme widely adopted by the ISPH, the CSPM and the CSPH2Γ, have also been considered. Except the Laplacian discretisation, other numerical implementations of the ISPH are kept the same as the classic ISPH. The convergence, accuracy and robustness of these schemes are analysed with reference to either analytical solutions or experimental data. The results demonstrate that the present ISPH_QSFDI leads to more accurate results with the same number of particles and costs less computational time to achieve a specific accuracy, compared with other schemes, although the convergence rate of the ISPH_QSFDI seems to be one-order lower than the theoretical patch test primarily due to the fact that linear schemes are used for the discretisation of the right-hand side of the PPE, the gradient/divergence estimation and the treatment of the boundary conditions.