Matteo Antuono

Particle packing algorithm for SPH schemes

AbstractUsing some intrinsic features of the Smoothed Particle Hydrodynamics schemes(SPH), an innovative algorithm for the initialization of the particle distribution hasbeen defined. The proposed particle packing algorithm allows a drastic reductionof the numerical noise due to particle resettlement during the early stages of theflow evolution. Moreover, thanks to its structure, it can be easily derived startingfrom whatever SPH scheme and applies under the hypotheses that the fluid isweakly-compressible or incompressible as well. A broad range of numerical testcases proved this tool to be fast, robust and reliable also for complex geometricalconfigurations.Key words: Meshless methods, Smoothed Particle Hydrodynamics, Particleinitialization, Lagrangian Systems.IntroductionIn the Smoothed Particle Hydrodynamics scheme (SPH) the matter of howinitialize the particle positions plays a relevant role. If particles are not initiallyset in “equilibrium” positions, they may resettle giving rise to spurious motionswhich can strongly a ect the fluid evolution.Here, the acceptation of the word “equilibrium” deserves a clarification.We refer to an equilibrium configuration as the set of particle positions which,under static conditions, does not lead to particle resettlement. As proved in thefollowing, the spurious particle motion is caused by inaccuracies in the SPHrepresentation of the pressure gradient. Specifically, these inaccuracies largelyincrease when the particle distribution is anisotropic and disordered. At worst, the

Numerical diffusive terms in weakly-compressible SPH schemes

Abstract A discussion on the use of numerical diffusive terms in SPH models is proposed. Such terms are, generally, added in the continuity equation, in order to reduce the spurious numerical noise that affects the density and pressure fields in weakly-compressible SPH schemes. Specific focus has been given to the theoretical analysis of the diffusive term structure, highlighting the main benefits and drawbacks of the most widespread formulations. Finally, specific test cases have been used to compare such formulations and to confirm the theoretical findings.

An accurate SPH modeling of viscous flows around bodies at low and moderate Reynolds numbers

Abstract A weakly compressible SPH scheme has been used to describe the evolution of viscous flows around blunt bodies at Reynolds numbers ranging from 10 to 2400. The simulation of such a wide range, rarely addressed to in the SPH literature, has been possible thanks to the use of a proper ghost-fluid technique and to an accurate enforcement of the boundary conditions along the solid boundaries. In this context, a new numerical technique based on previous works by Takeda et al. (1994) [48] , Marrone et al. (2011) [28] and De Leffe et al. (2011) [16] has been proposed, along with a new method for the evaluation of the global loads on bodies. Particular care has been taken to study the influence of the weakly-compressibility assumption and of different ghost-fluid techniques on the numerical results. An in-depth validation of the model has been performed by comparing the numerical outcome with experimental data from the literature and other numerical references. The influence of the domain size has been discussed in order to avoid wall side effects and, at the same time, to limit the computational costs. The convergence of the numerical solutions has been checked on both global and local quantities by choosing appropriate Reynolds-cell number.

Propagation of gravity waves through an SPH scheme with numerical diffusive terms

Basing on the work by Antuono et al. (2010) [1], an SPH model with numerical diffusive terms (here denoted δ-SPH) is combined with an enhanced treatment of solid boundaries to simulate 2D gravity waves generated by a wave maker and propagating into a basin. Both regular and transient wave systems are considered. In the former, a large number of simulations is performed for different wave steepness and height-to-depth ratio and the results are compared with a BEM Mixed-Eulerian–Lagrangian solver (here denoted BEM-MEL solver). In the latter, the δ-SPH model has been compared with both the experimental measurements available in the literature and with the BEM-MEL solver, at least until the breaking event occurs. The results show a satisfactory agreement between the δ-SPH model, the BEM-MEL solver and the experiments. Finally, the influence of the weakly-compressibility assumption on the SPH results is inspected and a convergence analysis is provided in order to identify the minimal spatial resolution needed to get an accurate representation of gravity waves.

Numerical and Experimental Investigation of Nonlinear Shallow Water Sloshing

Abstract A numerical and experimental analysis of sloshing phenomena (i.e. violent fluid motions inside a tank) has been conducted in shallow water regimes. A narrow tank has been used to limit three-dimensional effects and allow for an extensive study of two-dimensional waves. A large range of experimental data from small to large amplitude sway motions has been considered for five different filling heights. The numerical simulations have been performed to cover the configurations where no experiments were available and provide an exhaustive description of the shallow-water sloshing motion. Specifically, the numerical simulations have been performed through a δ-SPH model since such a scheme proved to be robust and reliable in studying violent free-surface flows.

A measure of spatial disorder in particle methods

Abstract In the present work we describe a numerical algorithm which gives a measure of the disorder in particle distributions in two and three dimensions. This applies to particle methods in general, disregarding the fact they use topological connections between particles or not. The proposed measure of particle disorder is tested on specific configurations obtained through the perturbation of a regular lattice. It turns out that the disorder measure may be qualitatively related to the mean absolute value of the perturbation. Finally, some applications of the proposed algorithm are shown by using the Smoothed Particle Hydrodynamics (SPH) method.

Beyond Boussinesq-type equations: Semi-integrated models for coastal dynamics

A novel approach for the description of both wave propagation and flow circulation in the nearshore zone has been defined. This is based on an integro-differential system which, at the leading-order, coincides with classical depth-averaged models (e.g., Boussinesq-type models) and, in addition, describes flow deviations from the depth-averaged values. Thanks to this feature, the proposed system enables exact calculation of the linear dispersion relation, of the linear shoaling coefficient, and of second-order nonlinear solutions for monochromatic waves. A simplified version of the original system has also been proposed. This latter model is exact up to the first order and predicts a linear shoaling coefficient which is comparable with the most advanced, fully nonlinear Boussinesq-type models. The general approach, which can be exploited to obtain a family of models, has clear computational advantages over those which solve the flow over the vertical and improves the flow description accuracy of typical de...

Numerical modeling of the influence of the beach profile on wave run-up

AbstractAn analysis of the run-up over different beach profiles is performed to evaluate the influence of the seabed shape on shore flooding. The analysis was carried out on the basis of numerical solutions of the nonlinear shallow water equations. The chosen solver was shown to provide reliable (both quantitatively and qualitatively) run-up results by comparing numerical solutions (of both solitary and regular waves) with the only available analytical solution forced by a localized topographic change. The run-up patterns on both a natural beach profile and three simpler and schematic profiles derived from it were evaluated. Different wave conditions (both random and groups) were used for a total amount of 96 different cases of inundation. Results are expressed in terms of both maximum (Zmax) and steady-state (Zsteady) run-up. It is found that both types of run-up depend on the offshore variable H0L0, as suggested by several available studies, and that, for all tested cases, random waves induce the larges...

Multi-resolution Delta-plus-SPH with tensile instability control: Towards high Reynolds number flows

Abstract It is well known that the use of SPH models in simulating flow at high Reynolds numbers is limited because of the tensile instability inception in the fluid region characterized by high vorticity and negative pressure. In order to overcome this issue, the δ + -SPH scheme is modified by implementing a Tensile Instability Control (TIC). The latter consists of switching the momentum equation to a non-conservative formulation in the unstable flow regions. The loss of conservation properties is shown to induce small errors, provided that the particle distribution is regular. The latter condition can be ensured thanks to the implementation of a Particle Shifting Technique (PST). The novel variant of the δ + -SPH is proved to be effective in preventing the onset of tensile instability. Several challenging benchmark tests involving flows past bodies at large Reynolds numbers have been used. Within this a simulation characterized by a deforming foil that resembles a fish-like swimming body is used as a practical application of the δ + -SPH model in biological fluid mechanics.

Run-up and backwash bore formation from dam-break flow on an inclined plane

Nonlinear shallow water equations are employed to model the inviscid slumping of fluid along an inclined plane and analytical solutions for the motion are derived using the hodograph transformation to reveal the run-up and the inception of a bore on the backwash. Starting from rest, the fluid slumps along the inclined plane, attaining a maximum run-up, before receding and forming a relatively thin and fast moving backwash. This interacts with the less rapidly moving fluid within the interior to form a bore. The evolution of the bore and the velocity and height fields either side of it are also calculated to reveal that it initially grows in magnitude before diminishing and intersecting with the shoreline. This analytical solution reveals features of the solution, such as the onset of the bore and its growth and decline, previously known only through numerical computation and the method presented here may be applied quite widely to the run-up of other initial distributions of fluid.