Roberto Benzi

The Lattice Boltzmann equation: Theory and applications

The basic elements of the theory of the lattice Boltzmann equation, a special lattice gas kinetic model for hydrodynamics, are reviewed. Applications are also presented together with some generalizations which allow one to extend the range of applicability of the method to a number of fluid dynamics related problems.

Lattice Gas Dynamics with Enhanced Collisions

An efficient strategy is developed for building suitable collision operators, to be used in a simplified version of the lattice gas Boltzmann equation. The resulting numerical scheme is shown to be linearly stable. The method is applied to the computation of the flow in a channel containing a periodic array of obstacles.

Generalized lattice Boltzmann method with multirange pseudopotential.

The physical behavior of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudopotential 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).

On the scaling of three-dimensional homogeneous and isotropic turbulence

Abstract In this paper we investigate the scaling properties of three-dimensional isotropic and homogeneous turbulence. We analyze a new form of scaling (extended self-similarity) recently introduced in the literature. We found that anomalous scaling of the velocity structure functions is clearly detectable even at a moderate and low Reynolds number and it extends over a much wider range of scales with respect to the inertial range.

Lattice Boltzmann equation for quantum mechanics

Abstract It is shown that the lattice Boltzman equation for hydrodynamics can be extended in such a way as to describe non-relativistic quantum mechanics.

The lattice Boltzmann equation: a new tool for computational fluid-dynamics

Abstract We present a series of applications which demonstrate that the lattice Boltzmann equation is an adequate computational tool to address problems spanning a wide spectrum of fluid regimes, ranging from laminar to fully turbulent flows in two and three dimensions.

Generalized scaling in fully developed turbulence

In this paper we report numerical and experimental results on the scaling properties of the velocity turbulent fields in several flows. The limits of a new form of scaling, named Extended Self-Similarity (ESS), are discussed. We show that, when a mean shear is absent, the self-scaling exponents are universal and they do not depend on the specific flow (3D homogeneous turbulence, thermal convection, MHD). In contrast, ESS is not observed when a strong shear is present. We propose a generalized version of self-scaling which extends down to the smallest resolvable scales even in cases where ESS is not present. This new scaling is checked in several laboratory and numerical experiments. A possible theoretical interpretation is also proposed. A synthetic turbulent signal having most of the properties of a real one has been generated.

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 nonideal 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 obtained by E. Lauga and H. Stone [J. Fluid. Mech. 489, 55 (2003)] and J. Philip [Z. Angew. Math. Phys. 23, 960 (1972)] 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 the discretized Boltzmann scheme proposed by X. Shan and H. Chen [Phys. Rev. E 49, 2941 (1994)] and we discuss the equivalence between the surface tension defined in terms of the mechanical equilibrium and in terms of the Maxwell construction.

Extended Self-Similarity in the Dissipation Range of Fully Developed Turbulence

In this letter we report further experimental evidence of extended self-similarity in the structure functions of the velocity field of fully developed turbulence. We study the behaviour of high-order structure functions close to the Kolmogorov scale η where extended self-similarity is observed.

Universal intermittent properties of particle trajectories in highly turbulent flows

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.