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

Zhang, N., Yan, S. ORCID: 0000-0001-8968-6616, Ma, Q. ORCID: 0000-0001-5579-6454 & Zheng, X. (2021). A QSFDI based Laplacian discretisation for modelling wave-structure interaction using ISPH. Applied Ocean Research, 117, article number 102954. doi: 10.1016/j.apor.2021.102954


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.

Publication Type: Article
Additional Information: © 2021. This article has been published in Applied Ocean Research by Elsevier, doi: This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Publisher Keywords: ISPH, QSFDI, Laplacian Operator, PPE, Wave-structure interaction
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Science & Technology > Engineering
SWORD Depositor:
[thumbnail of An enhanced ISPH method based on Quadric SFDI for Laplacian Discretization review.pdf]
Text - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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