Benefits of using a Wendland Kernel for free-surface flows

The aim of this paper Is lo discuss the influence of the selection of the interpolation kernel in the accuracy of the modeling of the internal viscous dissipation in Tree surface Hows, Simulations corresponding to a standing wave* for which an analytic solution available, are presented. Wendland and renormalized Gaussian kernels are considered. The differences in the flow pattern* and Internal dissipation mechanisms are documented for a range of Reynolds numbers. It is shown that the simulations with Wendland kernels replicate the dissipation mechanisms more accurately than those with a renormalized Gaussian kernel. Although some explanations are hinted we have Tailed to clarify which the core structural reasons for Mich differences are

Reynolds number and Shallow Depth Sloshing

The dependence on the Reynolds number of shallow depth sloshing flows inside rectangular tanks subjected to forced harmonic motion is studied in this paper with weakly compressible SPH. We are interested in assessing the in fluenceof viscous effects on the dynamics of shallow depth sloshing flows by using an SPH solver and by comparing with a Navier-Stokes level-set solver results. The goal of trying to model these viscous flows is compromised by the resolution requested due to their Reynolds number, if boundary layer effects are to be modeled. The convenience and feasibility of the implementation of free-slip and no-slip boundary conditions is also discusse

On the non-slip boundary condition enforcement in SPH methods.

The implementation of boundary conditions is one of the points where the SPH methodology still has some work to do. The aim of the present work is to provide an in-depth analysis of the most representative mirroring techniques used in SPH to enforce boundary conditions (BC) along solid profiles. We specifically refer to dummy particles, ghost particles, and Takeda et al. [1] boundary integrals. A Pouseuille flow has been used as a example to gradually evaluate the accuracy of the different implementations. Our goal is to test the behavior of the second-order differential operator with the proposed boundary extensions when the smoothing length h and other dicretization parameters as dx/h tend simultaneously to zero. First, using a smoothed continuous approximation of the unidirectional Pouseuille problem, the evolution of the velocity profile has been studied focusing on the values of the velocity and the viscous shear at the boundaries, where the exact solution should be approximated as h decreases. Second, to evaluate the impact of the discretization of the problem, an Eulerian SPH discrete version of the former problem has been implemented and similar results have been monitored. Finally, for the sake of completeness, a 2D Lagrangian SPH implementation of the problem has been also studied to compare the consequences of the particle movemen

Time domain analysis of ship motion and wave loads by boundary integral equations

In this presentation, we like to discuss some aspects of a more general computational algorithm for the prediction of ship motion and loads induced by the interaction with wave systems. In particular, unlikely the more conventional models in frequency domain, we attack the problem by a time domain formulation. The purpose is twofold. First, within the framework of a linear analysis, the ship response function to a general wave excitation can be numerically determined by a transient test (i.e. the interaction with a wave pulse compact in time). In this way, a substantial saving of computational time with respect to the existing algorithm is achieved. Second, a time domain modeling is intrinsically prone to deal with the fully nonlinear problem or, at least, to recover some nonlinear effects

Vorticity dynamics past an inclined elliptical cylinder at different re numbers: from periodic to chaotic solutions

Vortex methods offer an alternative way for the numerical simulation of problems regarding incompressible flows. In the present paper, a Vortex Particle Method (VPM) is combined with a Boundary Element Method for the study of viscous incompressible planar flow around solid bodies. The method is based on the viscous splitting approach of Chorin [3] for the Navier-Stokes equations in vorticity-velocity formulation and consists of an advection step followed by a diffusion step. The evaluation of the advection velocity exploits the Helmholtz- Hodge Decomposition (HHD), while the no–slip condition is enforced by an indirect boundary integral equation. In order to deal with the problem of disordered spacial distribution of particles, caused by the advection along the Lagrangian trajectories [1], in the present method the particles are redistributed on a Regular Point distribution (RPD) during the diffusive step. The RPDs close to the solid bodies are generated through a packing algorithm developed by [4], thanks to which the use of a mesh generator is avoided. The developed Vortex Particle Method has been called Diffused Vortex Hydrodynamics (DVH) and it is implemented within a completely meshless framework, hence, neither advection nor diffusion requires topological connection of the computational nodes. The DVH has been extensively validated in the past years (see e.g. [8]) and is used in the present article to study the vorticity evolution past an inclined elliptical cylinder while increasing the Reynolds number from 200 up to 10,000 in a 2D framework. The flow evolution is characterized by a periodic behaviour for the lower Reynolds numbers which is gradually lost to give its the place to a chaotic behaviour

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 ?-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 ? -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 ?-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

Study of ship wave breaking patterns using 3D parallel SPH simulations

An analysis of the 3D wave pattern generated by a ship in stationary forward motion has been performed with a specific focus on the bow breaking wave. For this purpose a novel 3D parallel SPH solver has been designed and preliminarily tested using a specifically conceived geometry. Since the numerical effort to simulate 3D flows is considerable, an ad hoc hybrid MPI-OpenMP programming model has been developed to achieve simulations of hundred million of particles running on a computer cluster. The outcomes have been compared with experimental measurements and numerical results from RANS calculations

Headway in large-eddy-simulation within the SPH models

In the present paper we show some preliminary resuslts of a novel LES-SPH scheme that extends andgeneralizes the approach described in [2]. Differently from that work, the proposed scheme is based on the definition of a Quasi-Langragian Large-Eddy-Simulation model where a small velocity deviation is added to the actual fluid velocity. When the LES equations are rearranged in the SPH framework, the velocity deviation is modelled through the Particle Shifting Technique (PST), similary to the δplus-SPH scheme derived in [3]. The use of the PST allows for regular particle distributions, reducing the numerical errors in the evaluation of the spatial differential operators. As a preliminary study of the proposed model, we consider the evolution of freely decaying turbulence in 2D. In a particular we show that the present scheme predicts the correct tendencies for the direct and inverse energy cascades

Theoretical Analysis of the No-Slip Boundary Condition Enforcement in SPH Methods

The aim of the present work is to provide an in-depth analysis of the most representative mirroring techniques used in SPH to enforce boundary conditions (BC) along solid profiles. We specifically refer to dummy particles, ghost particles, and Takeda et al. [Prog. Theor. Phys. 92 (1994), 939] boundary integrals. The analysis has been carried out by studying the convergence of the first- and second-order differential operators as the smoothing length (that is, the characteristic length on which relies the SPH interpolation) decreases. These differential operators are of fundamental importance for the computation of the viscous drag and the viscous/diffusive terms in the momentum and energy equations. It has been proved that close to the boundaries some of the mirroring techniques leads to intrinsic inaccuracies in the convergence of the differential operators. A consistent formulation has been derived starting from Takeda et al. boundary integrals (see the above reference). This original formulation allows implementing no-slip boundary conditions consistently in many practical applications as viscous flows and diffusion problems