The paper presents a high-order consistent ISPH fluid model for accurate simulation of ocean engineering problems. The high-order consistent discretization schemes on differential operators are derived through consideration of Taylor-series expansion until second-order differential terms. The derived consistent discretization schemes are applied to the calculations of Laplacian term of pressure in PPE and pressure gradient term in the momentum equation. To enhance and ensure the accuracy, stability and conservation property of the model, the enhanced schemes developed by our research team, namely HS, ECS and DS schemes, are also incorporated. The proposed high-order consistent ISPH fluid model is validated through reproduction of a set of numerical examples.
Lagrangian meshfree computational methods, or the so-called particle methods such as SPH (Smoothed Particle Hydrodynamics; Gingold and Monaghan, 1977) or ISPH (Incompressible SPH; Shao and Lo, 2003), have recently been attracting a lot of interest in various engineering fields. Thanks to their Lagrangian meshfree description of motion, the particle methods possess great advantages, e.g. being free from calculation of advection term and stable/natural tracking of complex moving boundaries. In the field of ocean engineering, one can easily find a number of existing applications of particle methods towards violent free surface fluid flow and its interaction with rigid/deformable structures as comprehensively reviewed in Luo et al. (2021) and Gotoh et al. (2021).
In the context of SPH method, consistency has been considered as one of the key challenges (SPHERIC Grand Challenges; Vacondio et al., 2020) and much effort has been devoted to enhancement of consistency of particle-based differential operator discretization schemes (e.g. Khayyer et al., 2011; Fatehi and Manzari, 2011; Duan et al., 2021). The application of high-order consistent discretization schemes for differential operators would reduce the so-called "discretization error" (Quinlan et al., 2006) and result in enhancement of accuracy.
In the context of ISPH method, first-order consistency correction on the pressure gradient model has been widely used and its enhanced effects have been presented in the literature (e.g. Lind et al., 2012; Khayyer et al., 2017a; Zheng et al., 2017). On the other hand, there have been few ISPH studies for development of second-order operator schemes or high-order Laplacian ones, although these topics have been attracting a lot of interest in other branches of projection-based particle methods, MPS or CPM (Consistent Particle Method) (e.g. Gao et al., 2021; Luo et al., 2022).
