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We present the modeling of the main facets of turbulence diffusion, i.e., diffusion of momentum, mass, density, and heat, within the smoothed particle hydrodynamics (SPH) method. The treatment is developed considering the large eddy simulation (LES) approach and is specifically founded on the δ-LES-SPH [A. Di Mascio et al., Phys. Fluids 29, 035102 (2017)], a model characterized by a turbulence closure for the continuity equation. The novelties introduced are the modeling of the advection–diffusion equation through turbulent mass diffusivity and the modeling of the internal energy equation through heat eddy diffusivity. Moreover, a calibration for the closure term of the continuity equation is also proposed, based on the physical assumption of equivalence between turbulent mass and density diffusion rates. Three test cases are investigated. The first test regards a two-dimensional (2D) problem with splashing and wave-breaking dynamics, which is used to investigate the proposed calibration for the turbulent density diffusion term. In the second test, a 2D jet in coflow condition without gravity is studied with particular emphasis on the advection–diffusion process. The last test regards the most general condition and reproduces three-dimensional (3D) jets in crossflow conditions, in which attention is given to both the mass and heat advection–diffusion processes. The proposed methodology, which allowed us to accurately reproduce the experimental tests considered, represents a promising approach for future investigation of problems characterized by complex dynamics with turbulence and mixing involved. [ABSTRACT FROM AUTHOR]

In this paper, the large eddy simulation (LES) model introduced in the smoothed particle hydrodynamics (SPH) by Di Mascio et al. [Phys. Fluids 29, 035102 (2017)] and called δ-LES-SPH, is extended to treat multiphase flows. This is achieved by modifying the multiphase δ-SPH by Hammani et al. [Comput. Methods Appl. Mech. Eng. 368, 113189 (2020)] by switching the viscous and density diffusion constants to dynamic variables evaluated as turbulence closure terms. The equation for energy conservation is also written for the presented model. The validation is performed for two-dimensional problems, by comparison with other established SPH solvers, with a finite volume method solver based on the turbulence closure corresponding to that adopted for the Lagrangian scheme, and with experimental data. The first test case investigated is a modified Taylor–Green vortex in which the introduction of macro-bubbles of a lighter fluid phase inside the domain is considered. In the second test case, a more violent problem involving wave breaking and splashing dynamics is analyzed. In the final test, the dynamic of a sloshing problem is reproduced. An analysis of turbulence resolution is conducted by considering modeled and resolved turbulent kinetic energies, as well as viscous dissipation and turbulent viscosity dissipation. [ABSTRACT FROM AUTHOR]

This paper proposes a 2D diffusive weakly-compressible Smoothed Particle Hydrodynamics (SPH) model to simulate wave loads and hydraulic characteristics at perforated breakwaters. The solid boundary technique of the fixed ghost particles (Marrone et al., 2011a), based on interpolation nodes located within the fluid domain, is here extended to a multi-node approach. The proposed modeling is defined by the association of more interpolation nodes to a single solid particle in order to allow interaction with fluid particles located at different positions in the computational domain. The present enforcing is introduced with the aim of overcoming disadvantages in terms of CPU time for heavy SPH simulations in which the choice of the initial spatial resolution of the model is driven by the presence of thin structures immersed in a fluid mass such as the slotted wall of breakwaters. The present solid boundary treatment is firstly validated for a still water tank characterized by two different static levels and for a green water overtopping a fixed deck. Successively, the SPH model is applied to simulate the interaction between regular waves with fully and partially perforated breakwaters. Numerical results are successfully compared with experimental data in terms of dynamic pressures acting on the body profiles of the considered breakwater and wave reflection. [ABSTRACT FROM AUTHOR]

This paper deals with the development of a 2D weakly compressible SPH model to simulate wave pressures acting on vertical and slotted coastal structures. Attention is devoted to investigate the diffusive term in the continuity equation in order to smooth out the high-frequency numerical noise in the pressure field. A hybrid formulation based on two literature diffusive models is proposed. The interaction between regular waves with vertical and perforated breakwaters is analyzed in time, space, and frequency domain. Numerical results are compared with laboratory experiments and other diffusive SPH formulations, varying the magnitude of the adopted diffusive term. On the basis of an error analysis, the results show that the hybrid formulation gives a better agreement with the experimental data for the majority of the investigated cases. Moreover, SPH simulations highlight nonlinear trends of dynamic pressures in correspondence with geometrical singularities, such as the holes of slotted walls, due to strong pressure drops induced by the flow motion. [ABSTRACT FROM AUTHOR]

This work deals with an experimental and numerical study on the horizontal and vertical hydrodynamic forces induced by solitary waves on submerged horizontal circular cylinders. Laboratory tests were performed in the wave flume of the University of Calabria. A battery of pressure transducers was mounted along the external contour of a cylinder placed at half water depth, while four wave gauges were located close to the cylinder and an ultrasonic sensor behind the paddle to measure its displacement. From the numerical viewpoint, a diffusive weakly-compressible SPH model was adopted. To prevent spurious flows near the cylindrical contour, a packing algorithm has been applied to initialize the SPH fluid particles. The acoustic components occurring in the numerical pressure field were filtered through the application of Wavelet Transform. Experimental and numerical analyses were performed in the inertia-dominated regime where these force components are more relevant than the drag and lift ones. The deviation from the fully inertia regime was highlighted in the simulations by the occurrence of a couple of asymmetric vortices behind the cylinder. The good agreement between experimental and SPH forces and kinematics at the cylinder has allowed the numerical calibration of the hydrodynamic coefficients in the Morison and transverse semi-empirical equations by different time-domain methods. For engineering purposes, we propose simple empirical formulas based on the knowledge of wave amplitude to calculate the hydrodynamic coefficients. [ABSTRACT FROM AUTHOR]

A laboratory and numerical investigation on the features of the horizontal and vertical hydrodynamic loads given by a solitary wave on a submerged square barrier is presented. By the experimental viewpoint, the wave forces were deduced from the records of a discrete battery of pressure sensors located along the external surface of the barrier. As regards the numerical viewpoint, simulations were performed through the SPH model presented in Di Mascio et al. (2017), in which the governing equations are written considering a turbulence closure model. The numerical simulations allowed to extend the range of analyzed cases and highlighted the regions around the submerged barrier of higher dissipation occurring during the wave-structure interaction. A good agreement between the experimental and numerical peaks of the horizontal and vertical forces was found. Afterwards, a semi-analytical scheme able to determine the horizontal loads was adopted using the speed drop factor obtained by physical tests and simulations. For practical purposes, attention was finally paid to determine the critical conditions against the sliding of the barrier. • Investigation on solitary wave-induced forces on a submerged square barrier. • The maximum vertical loads have been found relevant for stability analysis. • The speed drop factor has been determined to estimate the horizontal force. • The safety factor against the sliding of the barrier has been analyzed. [ABSTRACT FROM AUTHOR]