Salvatore Marrone

In the present work, we address some aspects related to the numerical solution of the Poisson equation within the framework of the Smoothed Particle Hydrodynamics (SPH). In this case, the Poisson equation is solved using nonlocal, kernel‐based discretizations of the differential operators (i.e., gradient, divergence, and Laplacian operators) defined on scattered particle sets without topological connections. This paper clarifies two distinct sources of pressure artifacts that are often conflated in the SPH literature: (i) checkerboard‐like spurious pressure modes caused by discrete operator incompatibility and pressure‐velocity decoupling, and (ii) loss of accuracy due to particle disorder and kernel support truncation near boundaries. We propose diagnostics and procedures that separate these mechanisms and use representative benchmark tests to compare common SPH Poisson/Laplacian formulations in terms of robustness, convergence, and sensitivity to disorder and boundary deficiency. The resulting perspective reconciles conflicting claims and provides a theoretical guidance for practical applications.

This work presents a coupled Finite Volume-Smoothed Particle Hydrodynamics (FV-SPH) approach for simulating free-surface flows around a vertical surface-piercing cylinder. The proposed method combines the strengths of the Eulerian and Lagrangian frameworks, as the Finite Volume (FV) solver effectively resolves viscous effects and boundary-layer dynamics. In contrast, the Smoothed Particle Hydrodynamics (SPH) method accurately captures large free-surface deformations and breaking. We achieve coupling via an overlapping domain decomposition with smooth blending across FV-SPH interfaces, enabling inclusion of FV forcing within the SPH regions. We introduce a new algorithm for consistent free-surface transfer and adaptive particle injection at open boundaries. The method is validated against experimental data from a fixed, bottom-mounted free-surface-piercing cylinder in an incoming stream, for Froude numbers of 0.6 and 0.73. Results show good agreement across wake features, free-surface elevation, and depth-averaged velocity fields, confirming that the FV-SPH coupling provides a robust and efficient framework for free-surface problems with strong interactions between viscous and interface phenomena.

The aim of the present work is the investigation of an adaptive particle refinement (APR) approach that enables large variations in particle size even in the presence of a free surface. In the smoothed particle hydrodynamics (SPH) literature, the existing APR or similar multi-resolution techniques can be categorized into three main approaches, essentially driven by the discrete differential operators selected. When a conservative formulation is retained, either variable smoothing-length techniques or buffer regions are generally employed. By contrast, in formulations using accurate but non-conservative SPH operators, large variations of the particle size are achievable without requesting any specific treatment. However, because of the difficulties of such formulations in addressing the free surface, they have so far been restricted to internal flows. Recently, a regularized high-order diffusive (RHOD)-SPH approach has been derived in the context of single resolution. In this approach an accurate formulation is used inside the bulk of the fluid, whereas a conservative one is preferred in the free-surface region. In the present paper, the ingredients required in the RHOD-SPH approach are extended to APR. Specifically, the Riemann-based diffusive terms and particle shifting technique are generalized to deal with particles of different sizes. A particle-splitting procedure is employed to enlarge the range of applications of the approach. The formulation is validated on six different test cases, with comparisons to both single-resolution and reference results.

In the present work, we derive a novel high-order weakly compressible smoothed particle hydrodynamics scheme based on an accurate approximation of the pressure gradient and on the use of numerical Riemann fluxes. Specifically, a switch between non-conservative and conservative formulations of the pressure gradient is adopted close to the free surface, in order to fulfill the dynamic free-surface boundary condition and, at the same time, prevent the onset of the tensile instability in inner regions of the fluid domain. The numerical diffusion is obtained using Riemann solvers, with reconstruction/limitation of the left and right states derived from the Monotonic Upstream-centered Scheme for Conservation Laws technique. These allow for a high-order convergence rate of the diffusive terms that, for increasing spatial resolutions, results in a low numerical dissipation without tuning parameters. Regular particle distributions, which are crucial for the model accuracy, are obtained thanks to recent improvements in Particle Shifting Techniques. These are taken into account within the constitutive equations through a quasi-Lagrangian formalism. The energy balance of such a non-conservative formulation is derived, and an in-depth analysis of the term contributing to numerical dissipation is performed. The numerical investigation is carried out on several problems, illustrating the advantages of the present scheme with respect to conservative formulations. Since the proposed formulation does not intrinsically guarantee momenta conservation, the latter are monitored showing that the overall errors are generally small.

In recent years, forest fires and maritime accidents have occurred frequently, which have had a bad impact on human production and life. Thus, the development of seaplanes is an increasingly urgent demand. It is important to study the taxiing process of seaplanes for the development of seaplanes, which is a strong nonlinear fluid-structure interaction problem. In this paper, the Smoothed Particle Hydrodynamics (SPH) method based on the Lagrangian framework is utilized to simulate the taxiing process of seaplanes, and the SPH results are compared with those of the Finite Volume Method (FVM) based on the Eulerian method. The results show that the SPH method can not only give the same accuracy as the FVM but also have a strong ability to capture the splashing waves in the taxiing process, which is quite meaningful for the subsequent study of the effect of a splash on other parts of the seaplane.