arXiv subjects

F. Toschi

Publications and source records attributed to F. Toschi.

At least 55 records · Page 3Linked to original sources

arXiv2006

Generalized Lattice Boltzmann Method with multi-range pseudo-potential

The physical behaviour of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudo-potential method is developed, which permits to tune the equation of state and surface tension independently of each other. The spurious velocity contributions of this extended model are shown to vanish in the limit of high grid refinement and/or high order isotropy. Higher order schemes to implement self-consistent forcings are rigorously computed for 2d and 3d models. The extended scenario developed in this work clarifies the theoretical foundations of the Shan-Chen methodology for the lattice Boltzmann method and enhances its applicability and flexibility to the simulation of multiphase flows to density ratios up to O(100).

nlin.CG↗

arXiv2006

Shear-Improved Smagorinsky Model for Large-Eddy Simulation of Wall-Bounded Turbulent Flows

A shear-improved Smagorinsky model is introduced based on recent results concerning shear effects in wall-bounded turbulence by Toschi et al. (2000). The Smagorinsky eddy-viscosity is modified subtracting the magnitude of the mean shear from the magnitude of the instantaneous resolved strain-rate tensor. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at two different Reynolds numbers. First comparisons with the dynamic Smagorinsky model and direct numerical simulations, including mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition of being physically sound, has a low computational cost and possesses a high potentiality of generalization to more complex non-homogeneous turbulent flows.

nlin.CD↗

arXiv2006

A mesoscopic approach for multi-phase flows in nano-corrugated channels

An approach based on a lattice version of the Boltzmann kinetic equation for describing multi-phase flows in nano- and micro-corrugated devices is proposed. We specialize it to describe the wetting/dewetting transition of fluids in presence of nanoscopic grooves etched on the boundaries. This approach permits to retain the essential supra-molecular details of fluid-solid interactions without surrendering -actually boosting- the computational efficiency of continuum methods. The mesoscopic method is first validated quantitatively against Molecular Dynamics (MD) results of Cottin-Bizonne et al. [Nature Mater. 2, 237 (2003)] and then applied to more complex situations which are hardly accessible to MD simulations. The resulting analysis confirms that surface roughness and capillary effects may conspire to promote a counter-intuitive but significant reduction of the flow drag with substantial enhancement in the mass flow rates and slip-lengths in the micrometric range for highly hydrophobic surfaces.

nlin.CG↗

arXiv2006

Exponentially growing solutions in homogeneous Rayleigh-Benard convection

It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially growing, separable solutions of the full non-linear system of equations. These solutions are clearly manifest in numerical simulations above a computable critical value of the Rayleigh number. In our numerical simulations they are subject to secondary numerical noise and resolution dependent instabilities that limit their growth to produce statistically steady turbulent transport.

nlin.CD↗

arXiv2006

Mesoscopic modeling of a two-phase flow in the presence of boundaries: the Contact Angle

We present a mesoscopic model, based on the Boltzmann Equation, for the interaction between a solid wall and a non-ideal fluid. We present an analytic derivation of the contact angle in terms of the surface tension between the liquid-gas, the liquid-solid and the gas-solid phases. We study the dependency of the contact angle on the two free parameters of the model, which determine the interaction between the fluid and the boundaries, i.e. the equivalent of the wall density and of the wall-fluid potential in Molecular Dynamics studies. We compare the analytical results obtained in the hydrodynamical limit for the density profile and for the surface tension expression with the numerical simulations. We compare also our two-phase approach with some exact results for a pure hydrodynamical incompressible fluid based on Navier-Stokes equations with boundary conditions made up of alternating slip and no-slip strips. Finally, we show how to overcome some theoretical limitations connected with a discretized Boltzmann scheme and we discuss the equivalence between the surface tension defined in terms of the mechanical equilibrium and in terms of the Maxwell construction.

nlin.CD↗

arXiv2006

Dynamics and statistics of heavy particles in turbulent flows

We present the results of Direct Numerical Simulations (DNS) of turbulent flows seeded with millions of passive inertial particles. The maximum Taylor's Reynolds number is around 200. We consider particles much heavier than the carrier flow in the limit when the Stokes drag force dominates their dynamical evolution. We discuss both the transient and the stationary regimes. In the transient regime, we study the growt of inhomogeneities in the particle spatial distribution driven by the preferential concentration out of intense vortex filaments. In the stationary regime, we study the acceleration fluctuations as a function of the Stokes number in the range [0.16:3.3]. We also compare our results with those of pure fluid tracers (St=0) and we find a critical behavior of inertia for small Stokes values. Starting from the pure monodisperse statistics we also characterize polydisperse suspensions with a given mean Stokes.

nlin.CD↗

arXiv2005

Acceleration statistics of heavy particles in turbulence

We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution $512^3$ ($R_λ\approx 185$). Following the trajectories of up to 120 million particles with Stokes numbers, $St$, in the range from 0.16 to 3.5 we are able to characterize in full detail the statistics of particle acceleration. We show that: ({\it i}) The root-mean-squared acceleration $a_{\rm rms}$ sharply falls off from the fluid tracer value already at quite small Stokes numbers; ({\it ii}) At a given $St$ the normalised acceleration $a_{\rm rms}/(ε^3/ν)^{1/4}$ increases with $R_λ$ consistently with the trend observed for fluid tracers; ({\it iii}) The tails of the probability density function of the normalised acceleration $a/a_{\rm rms}$ decrease with $St$. Two concurrent mechanisms lead to the above results: preferential concentration of particles, very effective at small $St$, and filtering induced by the particle response time, that takes over at larger $St$.

nlin.CD↗

arXiv2005

Mesoscopic two-phase model for describing apparent slip in micro-channel flows

The phenomenon of apparent slip in micro-channel flows is analyzed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactins. The weakly-inhomogeneous limit of this model is solved analytically. The present mesoscopic approach permits to access much larger scales than molecular dynamics, and comparable with those attained by continuum methods. However, at variance with the continuum approach, the existence of a gas layer near the wall does not need to be postulated a priori, but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is therefore argued that a mesoscopic Lattice Boltzmann approach with non-ideal fluid-fluid and fluid-wall interactions might achieve an optimal compromise between physical realism and computational efficiency for the study of channel micro-flows.

physics.flu-dyn↗

arXiv2005

Multi-particle dispersion in fully developed turbulence

The statistical geometry of dispersing Lagrangian clusters of four particles (tetrahedra) is studied by means of high-resolution direct numerical simulations of three-dimensional homogeneous isotropic turbulence. We give the first evidence of a self-similar regime of shape dynamics characterized by almost two-dimensional, strongly elongated geometries. The analysis of four-point velocity-difference statistics and orientation shows that inertial-range eddies typically generate a straining field with a strong extensional component aligned with the elongation direction and weak extensional/compressional components in the orthogonal plane.

nlin.CD↗

arXiv2005

Mesoscopic modeling of heterogeneous boundary conditions for microchannel flows

We present a mesoscopic model of the fluid-wall interactions for flows in microchannel geometries. We define a suitable implementation of the boundary conditions for a discrete version of the Boltzmann equations describing a wall-bounded single phase fluid. We distinguish different slippage properties on the surface by introducing a slip function, defining the local degree of slip for mesoscopic molecules at the boundaries. The slip function plays the role of a renormalizing factor which incorporates, with some degree of arbitrariness, the microscopic effects on the mesoscopic description. We discuss the mesoscopic slip properties in terms of slip length, slip velocity, pressure drop reduction (drag reduction), and mass flow rate in microchannels as a function of the degree of slippage and of its spatial distribution and localization, the latter parameter mimicking the degree of roughness of the ultra-hydrophobic material in real experiments. We also discuss the increment of the slip length in the transition regime, i.e. at O(1) Knudsen numbers. Finally, we compare our results with Molecular Dynamics investigations of the dependency of the slip length on the mean channel pressure and local slip properties (Cottin-Bizonne et al. 2004) and with the experimental dependency of the pressure drop reduction on the percentage of hydrophobic material deposited on the surface -- Ou et al. (2004).

nlin.CD↗

arXiv2005

Lagrangian statistics of particle pairs in homogeneous isotropic turbulence

We present a detailed investigation of the particle pair separation process in homogeneous isotropic turbulence. We use data from direct numerical simulations up to Taylor's Reynolds number 280 following the evolution of about two million passive tracers advected by the flow over a time span of about three decades. We present data for both the separation distance and the relative velocity statistics. Statistics are measured along the particle pair trajectories both as a function of time and as a function of their separation, i.e. at fixed scales. We compare and contrast both sets of statistics in order to gain an insight into the mechanisms governing the separation process. We find very high levels of intermittency in the early stages, that is, for travel times up to order ten Kolmogorov time scales. The fixed scale statistics allow us to quantify anomalous corrections to Richardson diffusion in the inertial range of scales for those pairs that separate rapidly. It also allows a quantitative analysis of intermittency corrections for the relative velocity statistics.

nlin.CD↗

arXiv2005

Acceleration and vortex filaments in turbulence

We report recent results from a high resolution numerical study of fluid particles transported by a fully developed turbulent flow. Single particle trajectories were followed for a time range spanning more than three decades, from less than a tenth of the Kolmogorov time-scale up to one large-eddy turnover time. We present some results concerning acceleration statistics and the statistics of trapping by vortex filaments.

nlin.CD↗

arXiv2004

Effects of collisions against thermal impurities in the dynamics of a trapped fermion gas

We present a theoretical study of the dynamical behavior of a gas made of ultracold fermionic atoms, which during their motions can collide with a much smaller number of thermal bosonic impurities. The atoms are confined inside harmonic traps and the interactions between the two species are treated as due to s-wave scattering with a negative scattering length modeling the 40K-87Rb fermion-boson system. We set the fermions into motion by giving a small shift to their trap center and examine two alternative types of initial conditions, referring to (i) a close-to-equilibrium situation in which the two species are at the same temperature (well below the Fermi temperature and well above the Bose-Einstein condensation temperature); and (ii) a far-from-equilibrium case in which the impurities are given a Boltzmann distribution of momenta while the fermions are at very low temperatures. The dynamics of the gas is evaluated by the numerical solution of the Vlasov-Landau equations for the one-body distribution functions, supported by some analytical results on the collisional properties of a fermion gas. We find that the trapped gaseous mixture is close to the collisionless regime for values of the parameters corresponding to current experiments, but can be driven towards a collisional regime even without increasing the strength of the interactions, either by going over to heavier impurity masses or by matching the width of the momentum distribution of the impurities to the Fermi momentum of the fermion gas.

cond-mat.other↗

arXiv2004

A lattice Boltzmann study of non-hydrodynamic effects in shell models of turbulence

A lattice Boltzmann scheme simulating the dynamics of shell models of turbulence is developed. The influence of high order kinetic modes (ghosts) on the dissipative properties of turbulence dynamics is studied. It is analytically found that when ghost fields relax on the same time scale as the hydrodynamic ones, their major effect is a net enhancement of the fluid viscosity. The bare fluid viscosity is recovered by letting ghost fields evolve on a much longer time scale. Analytical results are borne out by high-resolution numerical simulations. These simulations indicate that the hydrodynamic manifold is very robust towards large fluctuations of non hydrodynamic fields.

nlin.CD↗

arXiv2004

Multifractal statistics of Lagrangian velocity and acceleration in turbulence

The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. We present results for Lagrangian velocity structure functions, the acceleration probability density function and the acceleration variance conditioned on the instantaneous velocity. These are compared with predictions of the multifractal formalism and its merits and limitations are discussed.

nlin.CD↗

arXiv2004

Lagrangian statistics in fully developed turbulence

The statistical properties of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. Single trajectory statistics is investigated in a time range spanning more than three decades, from less than a tenth of the Kolmogorov timescale up to one large-eddy turnover time. Acceleration and velocity statistics show a neat quantitative agreement with recent experimental results. Trapping effects in vortex filaments give rise to enhanced small-scale intermittency on Lagrangian observables.

nlin.CD↗

arXiv2004

Anomalous scaling and universality in hydrodynamic systems with power-law forcing

The problem of the interplay between normal and anomalous scaling in turbulent systems stirred by a random forcing with a power law spectrum is addressed. We consider both linear and nonlinear systems. As for the linear case, we study passive scalars advected by a 2d velocity field in the inverse cascade regime. For the nonlinear case, we review a recent investigation of 3d Navier-Stokes turbulence, and we present new quantitative results for shell models of turbulence. We show that to get firm statements is necessary to reach considerably high resolutions due to the presence of unavoidable subleading terms affecting all correlation functions. All findings support universality of anomalous scaling for the small scale fluctuations.

nlin.CD↗

arXiv2003

Transition to hydrodynamics in colliding fermion clouds

We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov-Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as temperature decreases.

cond-mat↗