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As a mesh-free approach, the incompressible Smoothed Particle Hydrodynamics (ISPH) method has been often used for simulating wave-structure interaction problems. In the conventional ISPH method, the pressure-projection phase of solving the pressure Poisson's equation (PPE) is the most time-consuming. In recent years, the machine learning (ML) techniques has gradually shown their potential in accelerating the computational fluid dynamics. In this paper, the graph neural network (GNN) supported ISPH method (ISPH_GNN), in which the GNN replaces solving the PPE for the fluid pressure in the conventional ISPH, is adopted for numerical simulations of wave-floater interactions. To the best of the authors' knowledge, this is the first work to study the wave-floater interactions by using GNN supported ISPH method. More importantly, this paper demonstrates that the GNN trained only on data for simpler wave-only cases (i.e. no structure in the wave fields) can be satisfactorily applied to the cases for wave-floater interactions. More specifically, the paper will show this by using the ISPH_GNN with such trained GNN model to simulate various different cases, including the decay tests of a box, a floating box subjected to a wave, the interaction between wave and a moored floating breakwater and the violent green water impact on a floating structure. In most of the cases, the numerical results are validated by comparing with experimental data. Agreement between them is surprisingly satisfactory, being as good as those obtained by the conventional ISPH. The paper will also show that the ISPH_GNN requires much less computational time (97 times less for the cases concerned) than the conventional ISPH for estimating pressure involved in wave-floater interactions. This reveals a great potential that one can train the GNN using the datasets for simpler cases and then use the ISPH_GNN to simulate wave-floater interaction problems. • The first work to study the wave-floater interactions by using the graph neural network (GNN) supported ISPH method. • The GNN trained only on data for simpler wave-only cases can be applied to more complex cases for wave-floater interactions. • The ISPH_GNN can give satisfactory results for the relatively complex cases involving wave-floater interactions. • The ISPH_GNN takes much less computation time than the conventional ISPH for estimating pressure. [ABSTRACT FROM AUTHOR]

As a popular method for modeling violent free surface flow, the incompressible Smoothed Particle Hydrodynamics (ISPH) based on the Lagrangian formulation has attracted a great attention worldwide. The Lagrangian ISPH solves the unsteady Navier-Stokes and continuity equations using the projection method, in which the pressure is obtained by solving the pressure Poisson's equation (PPE) that is the most time-consuming part in the ISPH procedure. In this paper, the Convolutional Neural Network (CNN) is combined with ISPH and used to predict the fluid pressure instead of solving the PPE directly. Although limited attempts of using CNN for solving the PPE in Eulerian formulation (referred to as the Eulerian CNN framework) in mesh-based methods are found in the public domain, the present model is the first ISPH model supported by CNN in a Lagrangian formulation. The proposed model overcome several challenges associated with combining CNN with ISPH, including selecting the input parameters, formulating the objective functions, producing the training dataset and dealing with boundary conditions. Two classic free surface problems, i.e. the dam breaking and the wave propagation, are simulated to evaluate the performance of the present model. Quantitative assessments of the numerical error in terms of both the free surface profile and the pressure field are carried out. The assessments show that the new model does not only give results with satisfactory accuracy, but also requires much less computation time for estimating pressure if the number of particles is large, e.g., 100 thousands particles that is usually required in the practical ISPH simulation for free surface flow. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]