Stefano Sibilla

Fluid mechanics and the SPH method: theory and applications

Smoothed particle hydrodynamics (SPH) is one of the most popular mesh-free methods in computational fluid mechanics, especially when the required solution involves heterogeneous media or rapidly moving free surfaces. Several review articles and books have been written in recent years to describe the fundamentals of the method and its application to the simulation of different flows. Now, Damien Violeau exploits his vast experience as researcher at Électricité de France (EDF) and as former chairman of the SPH European Research Interest Community (SPHERIC) to propose SPH from a rather different perspective. As the author states in the introduction, while working on SPH, he realized the close links of the method to theoretical mechanics and he developed the idea of a book showing how such a Lagrangian method stems directly from the fundamentals of hydraulics. This book comes therefore from the desire to analyse in detail the way in which the correct SPH algorithms can be obtained and explained directly from the principles of Lagrangian and Hamiltonian mechanics, as well as of statistical mechanics. The title of the book already clarifies the goal of the author: not simply “Smoothed Particle Hydrodynamics” but “Fluid mechanics and the SPH method”, i.e. the main scope is to lay down all of the physical and mathematical bricks which build up the SPH method (particle and continuum mechanics, incompressible and weakly compressible fluid dynamics, turbulence) in a rigorous and coherent frame before bringing them together to explain the most recent developments regarding interpolation techniques, accuracy, stability analysis, time integration schemes, boundary treatment and turbulence models. It must be underlined that this consequential layout is not a mere matter of love for a rigorous mathematical formalism (which should nevertheless be required in a text on computational fluid dynamics): all the properties of the most efficient numerical algorithms used in SPH are always derived from the previously outlined principles of fundamental mechanics. Just to make a specific example, when the author investigates the energy-conserving properties of the different time integration schemes for the SPH discretized equations, he founds his analysis on the ability of each scheme to preserve the Hamiltonian structure of the equations of mechanics within the discretized time context, which eventually leads to his justified preference for the symplectic time integrator. Following its scope, the book is therefore organized into two main parts, dealing with the physics of weakly compressible fluids and with the SPH method in hydraulics, respectively. Each part is divided into four chapters. In the first part, the first chapter describes the bases of the mechanics of particle systems:PART I: PHYSICS OF WEAKLY COMPRESSIBLE FLUIDS 1. Lagrangian and Hamiltonian mechanics 2. Statistical Mechanics 3. Continuous media and viscous fluids 4. Turbulent flows PART II: THE SPH METHOD IN HYDRAULICS 5. Principles of the SPH method 6. Advanced hydraulics with SPH 7. SPH method validation 8. SPH applied to hydraulic works Appendix A: Tensorial formalism Appendix B: Fourier transform

SPH Simulation of Sediment Flushing Induced by a Rapid Water Flow

This paper shows an advanced application of the smoothed particle hydrodynamics (SPH) method to the numerical modeling of noncohesive sediment flushing aiming at the setup of a reliable engineering tool for the prediction of the coupled water-sediment dynamics at the bottom of an artificial reservoir. Both liquid and granular materials are modeled as weakly compressible viscous fluids, whose motion results from the numerical solution of the continuity and momentum equations discretized according to standard SPH formulation. The effect of two alternative erosion criteria on the description of the failure mechanism of bottom sediments is analyzed. These criteria are based, respectively, on Mohr-Coulomb yielding criterion and Shields theory. A sensitivity analysis is performed in order to assess, for both criteria, the influence of the model parameters on the simulation of the erosion process; the method is eventually validated by comparing numerical results with the experimental data obtained in a two-dimen...

SPH Modeling of Solid Boundaries Through a Semi-Analytic Approach

Abstract: This paper presents a general semi-analytic approach for modeling solid boundaries in the SPH method: boundaries are here considered as a material continuum with a suitable distribution of velocity and pressure; their contributions to each term of the SPH mass and momentum equations can be expressed in terms of a suitable integral extended to the part of the sphere of influence of the particle delimited by the boundary surface. Analytical details with reference to a slightly compressible viscous Newtonian fluid in three dimensions are given. The validity of the method is checked by comparing the obtained numerical results with available experimental data in a benchmark flow case.

Polymer stress statistics in the near-wall turbulent flow of a drag-reducing solution

The direct numerical simulation of the turbulent flow of a dilute polymer solution in a plane channel at low-Reynolds number has been performed in order to investigate the reduction in friction drag. The polymer solution has been represented as a continuum fluid whose constitutive equations have been derived on the basis of a modified FENE-P dumbbell model. The mean polymer dynamics in the turbulent flow have been studied through statistical moments of the configuration tensor. The analysis of the results obtained suggests that polymers can be effective in terms of drag reduction only if their relaxation time is comparable to the characteristic time of their convection in the normal-to-the-wall direction within near-wall turbulent structures. The energy budget of the normal components of the Reynolds stress tensor suggests that elongated polymers inhibit turbulence regeneration by opposing pressure redistribution from streamwise to cross-flow velocity fluctuations.

3D SPH modelling of hydraulic jump in a very large channel

The formation of different undular hydraulic jumps in a very large channel is investigated and reproduced using a weakly-compressible XSPH scheme which includes a mixing-length turbulence model. An analysis of the ability and of the limits of the SPH method to reproduce undular hydraulic jumps is preliminarily performed on reference two-dimensional cases. The numerical description of the three-dimensional jump in a very large channel, where the hydraulic-jump front is trapezoidal and the lateral shock waves induce a large recirculation region along the side walls, is compared with experiments in a laboratory flume on two undular jumps at upstream Froude number equal to 3.9 and 8.3. Acoustic Doppler velocity measurements were compared with SPH instantaneous and time-averaged flow fields in order to evaluate whether the numerical method could help in having a clearer understanding of both hydraulic-jump development and lateral shockwave formation. The predicted free-surface elevations and velocity profiles show a satisfactory agreement with measurements and most of the peculiar features of the flow, such as the trapezoidal shape of the wave front and the flow separations at the toe of the oblique shock wave along the side walls, are qualitatively and quantitatively reproduced.

Hydrodynamic Characterization of a Nozzle Check Valve by Numerical Simulation

The ability to obtain correct estimates of the hydraulic characteristics of a nozzle check valve by finite-volume numerical simulation is discussed. The evaluation of the numerical results is performed by comparison of the computed pressure drops inside the valve with experimental measurements obtained on an industrial check valve. It is shown that, even with high mesh refinement, the obtained result is highly dependent on the choice of the turbulence model. The renormalization group theory (RNG) k-e model proves to be the more accurate to describe the flow inside the valve, which is characterized by repeated flow decelerations and accelerations and by boundary layer development under adverse pressure gradient. Pressure-drop and flow coefficients computed by adopting the RNG model agree well with the experimental values at different positions of the plug. The opening transient of the valve is also analyzed by an unsteady flow simulation where the motion of the plug is taken into account. The characteristic curve of the valve obtained in steady flow conditions is finally compared with the transient opening characteristic, highlighting a temporary increase in the pressure drop, which occurs because of a large unsteady separation region downstream of the plug.

SPH numerical investigation of the velocity field and vorticity generation within a hydrofoil-induced spilling breaker

In the present work, the velocity field and the vorticity generation in the spilling generated by a NACA 0024 hydrofoil were studied. SPH simulations were obtained by a pseudo-compressible XSPH scheme with pressure smoothing; both an algebraic mixing-length model and a two-equation model were used to represent turbulent stresses. Given the key role of vortical motions in the generation of the spilling breaker, the sources of vorticity were then examined in detail to confirm the interpretation of the mean flow vortical dynamics given in a paper by Dabiri and Gharib (J Fluid Mech 330: 113–139, [1997]). The high precision of the SPH model is confirmed through a comparison with experimental data. Experimental investigations were carried out by measuring the velocity field with a backscatter, two-component four-beam optic-fiber LDA system. The agreement between the numerical results and laboratory measurements in the wake region is satisfactory and allows the evaluation of the wave breaking efficiency of the device by a detailed analysis of the simulated flow field.

Forecasting the evolution in the mixing regime of a deep subalpine lake under climate change scenarios through numerical modelling (Lake Maggiore, Northern Italy/Southern Switzerland)

The impact of air temperature rise is eminent for the large deep lakes in the Italian subalpine district, climate change being caused there by both natural phenomena and anthropogenic greenhouse-gases (GHG) emissions. These oligomictic lakes are experiencing a decrease in the frequency of winter full turnover and an intensification of stability. As a result, hypolimnetic oxygen concentrations are decreasing and nutrients are accumulating in bottom water, with effects on the whole ecosystem functioning. Forecasting the future evolution of the mixing pattern is relevant to assess if a reduction in GHG releases would be able to revert such processes. The study focuses on Lake Maggiore, for which the thermal structure evolution under climate change in the 2016–2085 period was assessed through numerical simulations, performed with the General Lake Model (GLM). Different prospects of regional air temperature rise were considered, given by the Swiss Climate Change Scenarios CH2011. Multiple realisations were performed for each scenario to obtain robust statistical predictions, adopting random series of meteorological data produced with the Vector-Autoregressive Weather Generator (VG). Results show that a reversion in the increasing thermal stability would be possible only if global GHG emissions started to be reduced by ~ 2020, allowing an equilibrium mixing regime to be restored by the end of the twenty-first century. Otherwise, persistent lack of complete-mixing, severe water warming and extensive effects on water quality are to be expected for the centuries to come. These projections can be extended to the other lakes in the subalpine district.

A 3D smoothed particle hydrodynamics model for erosional dam-break floods

ABSTRACT A mesh-less smoothed particle hydrodynamics (SPH) model for bed-load transport on erosional dam-break floods is presented. This mixture model describes both the liquid phase and the solid granular material. The model is validated on the results from several experiments on erosional dam breaks. A comparison between the present model and a 2-phase SPH model for geotechnical applications (Gadget Soil; TUHH) is performed. A demonstrative 3D erosional dam break on complex topography is investigated. The present 3D mixture model is characterised by: no tuning parameter for the mixture viscosity; consistency with the Kinetic Theory of Granular Flow; ability to reproduce the evolution of the free surface and the bed-load transport layer; applicability to practical problems in civil engineering. The numerical developments of this study are represented by a new SPH scheme for bed-load transport, which is implemented in the SPH code SPHERA v.8.0 (RSE SpA), distributed as FOSS on GitHub.

SPH numerical investigation of characteristics of hydraulic jumps

In the present work, oscillating characteristics and cyclic mechanisms in hydraulic jumps are investigated and reproduced using a weakly-compressible XSPH scheme which includes both an algebraic mixing-length model and a two-equation turbulence model to represent turbulent stresses. The numerical model is applied to analyze oscillations of different hydraulic jump types based on the laboratory experiments. The comparison between SPH and experimental results shows an influence of different turbulence models on the amplitude spectrum and peak amplitude of the time-dependent surface elevation upstream and downstream of the hydraulic jump. By analyzing a single cycle of the oscillating phenomena of a hydraulic jump it is possible to indicate their correlation with the vortex structures of the roller. Furthermore, analysis of the oscillating phenomena indicates a correlation among the surface profile elevations, velocity components and pressure fluctuations. This observation leads to conclude that oscillations phenomena are particularly important for analysis of the turbulence characteristics.