Andrea Colagrossi

A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH

In literature, it is well know that the Smoothed Particle Hydrodynamics method can be affected by numerical noise on the pressure field when dealing with liquids. This can be highly dangerous when an SPH code is dynamically coupled with a structural solver. In this work a simple procedure is proposed to improve the computation of the pressure distribution in the dynamics of liquids. Such a procedure is based on the use of a density diffusion term in the equation for the mass conservation. This diffusion is a pure numerical effect, similar to the well known artificial viscosity originally proposed in SPH method to smooth out the shock discontinuities. As the artificial viscosity, the density diffusion used here goes to zero increasing the number of particles recovering consistency and convergence of the final numerical scheme adopted. Different artificial density diffusion formulas have been studied, paying attention to prevent unphysical changes of the flows. To show the improvements of the new scheme proposed here, a suitable set of examples, for which reference solutions or experimental data are available, has been tested.

Free-surface flows solved by means of SPH schemes with numerical diffusive terms

A novel system of equations has been defined which contains diffusive terms in both the continuity and energy equations and, at the leading order, coincides with a standard weakly-compressible SPH scheme with artificial viscosity. A proper state equation is used to associate the internal energy variation to the pressure field and to increase the speed of sound when strong deformations/compressions of the fluid occur. The increase of the sound speed is associated to the shortening of the time integration step and, therefore, allows a larger accuracy during both breaking and impact events. Moreover, the diffusive terms allows reducing the high frequency numerical acoustic noise and smoothing the pressure field. Finally, an enhanced formulation for the second-order derivatives has been defined which is consistent and convergent all over the fluid domain and, therefore, permits to correctly model the diffusive terms up to the free surface. The model has been tested using different free surface flows clearly showing to be robust, efficient and accurate. An analysis of the CPU time cost and comparisons with the standard SPH scheme is provided.

An Hamiltonian interface SPH formulation for multi-fluid and free surface flows

In the present work a new SPH model for simulating interface and free surface flows is presented. This formulation is an extension of the one discussed in Colagrossi and Landrini (2003) and is related to the one proposed by Hu and Adams (2006) to study multi-fluid flows. The new SPH scheme allows an accurate treatment of the discontinuity of quantities at the interface (such as the density), and permits to model flows where both interfaces and a free surface are present. The governing equations are derived following a Lagrangian variational principle leading to an Hamiltonian system of particles. The proposed formulation is validated on test cases for which reference solutions are available in the literature.

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.

Fast free-surface detection and level-set function definition in SPH solvers

The present paper proposes a novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions. Since the proposed algorithms are based on SPH interpolations their implementation does not require complex geometrical procedures. Thus the free-surface detection can be easily embedded in SPH solvers, without a significant increase of the CPU time. Throughout this procedure accurate normal vectors to the free-surface are made available. Then it is possible to define a level-set function algorithm which is presented in detail. The latter allows in-depth analyses of three-dimensional free-surface simulations by using standard visualization tools, including internal features of the flow. The algorithms proposed for detecting free-surface particles and defining the level-set function are validated on simple and complex two- and three-dimensional flow simulations. The usefulness of the proposed procedures to post-process and analyze complex flows are illustrated on realistic examples.

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.

A study of violent sloshing wave impacts using an improved SPH method

The flip-through phenomenon has been observed in several conditions characterized by a steep wave approaching a vertical wall (Peregrine 2003). One of the cases where this phenomenon has been observed and studied experimentally is the sloshing in a partially filled tank. This case has been described in Lugni et al. (2006) and in Faltinsen and Timoka (2009). Those experiments detail the features of the flip-through dynamics with an ad hoc distributions of miniaturized pressure sensors and with the records of a fast video-camera. Here, the same flow conditions have been reproduced numerically with an improved SPH method (cSPH), i.e. with MLS integral interpolators (Fries and Matthies 2003). This allows to solve the Euler equations in the case of free surfaces impacting at a wall. The extremely intense local features of the phenomenon highlight the capabilities and limits of the numerical algorithms proposed.

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.