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In this paper, the hydrodynamic behaviors of a typical convex object during water entry are numerically investigated using a meshfree particle method, smoothed particle hydrodynamics (SPH). In order to consider the practical air-cushion effects during water–entry process, a multiphase model with interface force is incorporated to the SPH method to maintain sharp water–air interface. Three numerical examples including bubble rising, water impact on a flate plate and water entry of a wedge are firstly simulated to validate the effectiveness of the multiphase SPH method in predicting the slamming forces and trajectories of falling objects. Water entry of free falling convex objects with different shapes and sizes is then simulated using the validated numerical method for comparative studies. Two slamming processes, including the convex slamming and the structure slamming, are observed in simulations, with double-jetting pattern occurring after the structure slamming. The air-cushion effects are well captured with slamming-induced vortexes clearly shown in the simulation snapshots. Quantitatively, significant drop in pressure peak value is observed when the dimensionless width of the convex is larger than 0.2. Among various shapes of convexes, the square shaped convex experiences the minimal local pressure peak value.

We propose a model of a density-dependent compressible–incompressible fluid, which is intended as a simplified version of models based on mixture theory as, for instance, those arising in the study of biofilms, tumor growth and vasculogenesis. Though our model is, in some sense, close to the density-dependent incompressible Euler equations, it presents some differences that require a different approach from an analytical point of view. In this paper, we establish a result of local existence and uniqueness of solutions in Sobolev spaces to our model, using the Leray projector. Besides, we show the convergence of both a continuous version of the Chorin–Temam projection method, viewed as a singular perturbation approximation, and the artificial compressibility method.

The axial and radial distributions of static pressures and vertical particle velocities of conical spouted beds have been simulated and compared with experimental data. Simulation results show that, among all factors investigated, the Actual Pressure Gradient (the APG term) in conical spouted beds, introduced as the default gravity term plus an empirical axial solid phase source term, has the most significant influence on static pressure profiles, followed by the restitution coefficient and frictional viscosity, while other factors almost have no effect. Apart from the solid bulk viscosity, almost all other factors affect the radial distribution of the axial particle velocity, although the influence of the APG term is less significant. For complex systems such as conical spouted beds where a fluidized spout region and a defluidized annulus region co-exist, the new term introduced in this work can improve the CFD simulation. Furthermore, for other systems with the Actual Pressure Gradient different from either fluidized beds or packed beds, the new approach can also be applied.

Depth-integrated wave models are widely used for simulating large-scale propagation of landslide tsunamis, with the generation of tsunami being simulated separately by various generation models to provide the required initial conditions. For a given problem, the selection of a proper tsunami generation model is an important aspect for tsunami hazard analysis. The generation of tsunamis by submarine or subaerial landslides is a transient multiphase process which involves important fine-scale physics. Depth-integrated generation models, while relatively easy to use, cannot simulate these fine-scale physics. Depth-resolved generation models can overcome the shortcomings of depth-integrated generation models but are computationally demanding. This paper first reviews existing depth-integrated generation models to show the need for depth-resolved generation models. Four classes of depth-resolved generation models are reviewed: computational fluid dynamics (CFD) models, approaches coupling CFD and discrete element method, multiphase flow models, and meshless particle models. Multiphase flow models, which are relatively new, can consider complex interactions between landslide materials and its surrounding fluids. Meshless particle models are appealing for simulating landslide tsunamis because of their convenience to deal with the violent motion of the water surface and ability to run on graphics processing units. The main strengths, weaknesses, and future research directions of the reviewed models are briefly discussed. The literature reviewed, which is by no means complete, aims to provide researchers updated and practical guidelines on numerical modeling techniques for simulating the generation process of landslide tsunamis.