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Quasi-equilibrium lattice Boltzmann method

EUROPEAN PHYSICAL JOURNAL B 2007年第2期56卷 135-139页

作者： Ansumali, S. Arcidiacono, S. Chikatamarla, S. S. Prasianakis, N. I. Gorban, A. N. Karlin, I. V. Nanyang Technol Univ CBE Singapore 639798 Singapore Paul Scherrer Inst Combust Res Unit CH-5232 Villigen Switzerland ETH Aerothermochem & Combust Syst Lab CH-8092 Zurich Switzerland Univ Leicester Dept Math Leicester LE1 7RH Leics England

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly compressible flow with a given Prandtl number are derived and validated.

关键词： computational methods in fluid dynamics Kinetic theory

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Numerical simulations of the aspherical collapse of laser and acoustically generated bubbles

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ULTRASONICS SONOCHEMISTRY 2007年第4期14卷 456-469页

作者： Tsiglifis, Kostas Pelekasis, Nikos A. Univ Thessaly Dept Mech & Ind Engn Volos 38334 Greece

The details of nonlinear axisymmetric oscillations and collapse of bubbles subject to large internal or external pressure disturbances, are studied via a boundary integral method. Weak viscous effects on the liquid side are accounted for by integrating the equations of motion across the boundary layer that is formed adjacent to the interface. Simulations of single-cavitation bubble luminescence (SCBL) and single-bubble sonoluminescence (SBSL) are performed under conditions similar to reported experimental observations, aiming at capturing the details of bubble collapse. It is shown that any small initial deviation from sphericity, modeled through a small initial elongation along the axis of symmetry, may result in the formation and impact of two counter-propagating jets during collapse of the bubble, provided the amplitude of the initial disturbance is large enough and the viscosity of the surrounding fluid is small enough. Comparison between simulations and experimental observations show that this is the case for bubbles induced via a nano-second laser pulse (SCBL) during a luminescence event. In a similar fashion, simulations show that loss of sphericity accompanied with jet formation and impact during collapse is also possible with acoustically trapped bubbles in a standing pressure wave (SBSL), due to the many afterbounces of the bubble during its collapse phase. In both cases jet impact occurs as a result Of P-2 growth in the form of an afterbounce instability. When the sound amplitude is decreased or liquid viscosity is increased the intensity of the afterbounce is decreased and jet impact is suppressed. When the sound amplitude is increased jet formation is superceded by Rayleigh-Taylor instability. In the same context stable luminescence is quenched in experimental observations. In both SCBL and SBSL simulations the severity of jet impact during collapse is quite large, and its local nature quite distinct. This attests to the fact that it is an energy focusi

关键词： nonlinear acoustics sonoluminescence computational methods in fluid dynamics jets bubble dynamics weak viscous effects collapse laser bubbles

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Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures

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EPL 2007年第4期80卷

作者： Tuezel, E. Pan, G. Ihle, T. Kroll, D. M. N Dakota State Univ Dept Phys Fargo ND 58105 USA

A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model immiscible binary mixtures. Excluded-volume interactions between the two components are modeled by stochastic multiparticle collisions which depend on the local velocities and densities. Momentum and energy are conserved locally, and entropically driven phase separation occurs for high collision rates. An explicit expression for the equation of state is derived, and the concentration dependence of the bulk free energy is shown to be the same as that of the Widom-Rowlinson model. Analytic results for the phase diagram are in excellent agreement with simulation data. Results for the interfacial tension obtained from the analysis of the capillary wave spectrum of a two-dimensional droplet agree with measurements based on the Laplace's equation. The introduction of '' amphiphilic '' dimers makes it possible to model the phase behavior and dynamics of ternary surfactant mixtures. Copyright (c) EPLA, 2007.

关键词： Molecular dynamics and particle methods computational methods in fluid dynamics Fluctuation phenomena, random processes, noise, and Brownian motion

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Knudsen layer theory for high-order lattice Boltzmann models

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EPL 2007年第2期80卷

作者： Szalmas, L. Univ Roma La Sapienza Dipartimento Fis I-00158 Rome Italy

A Knudsen layer theory is presented within the framework of a high-order lattice Boltzmann model obtained from the fourth-order Gauss-Hermite quadrature. The Kramers problem is analyzed in detail. We employ a multi-relaxation collision operator which is shown to permit a variable layer width. Computer simulations are performed which give excellent agreement with the theoretical derivations. Good qualitative agreement is achieved with the accurate numerical solution of the Boltzmann equation for hard sphere molecules. Our theoretical result clearly indicates that the lattice Boltzmann models with high symmetric velocity sets naturally develop to physically relevant Knudsen layers due to the discrete ordinate origin of the method. Copyright (C) EPLA, 2007.

关键词： computational methods in fluid dynamics Rarefied gas dynamics Kinetic theory

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Transport coefficients of dissipative particle dynamics with finite time step

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EPL 2007年第3期79卷

作者： Noguchi, H. Gompper, G. Forschungszentrum Julich Inst Festkorperforsch D-52425 Julich Germany

The viscosity and self-diffusion constant of a mesoscale hydrodynamic method, dissipative particle dynamics (DPD), are investigated. The viscosity of DPD with finite time step, including the Lowe-Anderson thermostat, is derived analytically for the ideal-gas equation of state and phenomenologically for systems with soft repulsive potentials. The results agree well with numerical data. A velocity-scaling version of the profile-unbiased thermostat is shown to be useful to obtain faster diffusion than for the DPD thermostat.

关键词： Viscosity of liquids, diffusive momentum transport computational techniques, simulations computational methods in fluid dynamics

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Particle-based mesoscale hydrodynamic techniques

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EPL 2007年第1期78卷

作者： Noguchi, H. Kikuchi, N. Gompper, G. Forschungszentrum Julich Inst Festkorperforsch D-52425 Julich Germany Univ Halle Wittenberg Fachbereich Phys D-06099 Halle Germany

Dissipative particle dynamics (DPD) and multi-particle collision (MPC) dynamics are powerful tools to study mesoscale hydrodynamic phenomena accompanied by thermal fluctuations. To understand the relations of these types of mesoscale simulation techniques in more detail, we propose two new methods, which are intermediate between DPD and MPC-DPD with multibody thermostat (DPD-MT), and MPC-Langevin dynamics (MPC- LD). The key features are applying a Langevin thermostat to the relative velocities of pairs of particles or multi-particle collisions, and whether or not to employ collision cells. The viscosity of MPC-LD is derived analytically, in very good agreement with the results of numerical simulations. Copyright (c) EPLA, 2007.

关键词： computational techniques, simulations computational methods in fluid dynamics Viscosity of liquids, diffusive momentum transport

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A LES-Langevin model for turbulence

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EUROPEAN PHYSICAL JOURNAL B 2006年第4期49卷 471-481页

作者： Laval, J. -P. Dubrulle, B. CNRS UMR 8107 Lab Mecan Lille F-59655 Villeneuve Dascq France CEA Saclay DSM DRECAM SPECGrp Instabilities & Turbulence F-91191 Gif Sur Yvette France CNRS URA 2464 F-91191 Gif Sur Yvette France

We propose a new model of turbulence for use in large-eddy simulations (LES). The turbulent force, represented here by the turbulent Lamb vector, is divided in two contributions. The contribution including only subfilter fields is deterministically modeled through a classical eddy-viscosity. The other contribution including both filtered and subfilter scales is dynamically computed as solution of a generalized (stochastic) Langevin equation. This equation is derived using Rapid Distortion Theory (RDT) applied to the subfilter scales. The general friction operator therefore includes both advection and stretching by the resolved scale. The stochastic noise is derived as the sum of a contribution from the energy cascade and a contribution from the pressure. The LES model is thus made of an equation for the resolved scales, including the turbulent force, and a generalized Langevin equation integrated on a twice-finer grid. We compare the full model with several approximations. In the first one, the friction operator of the Langevin equation is simply replaced by an empirical constant, of the order of the resolved scale correlation time. In the second approximation, the integration is replaced by a condition of instantaneous adjustment to the stochastic force. In this approximation, our model becomes equivalent to the velocity-estimation model of Domaradzki et al. [1-3]. In the isotropic, homogeneous situations we study, both approximations provide satisfactory results, at a reduced computational cost. The model is finally validated by comparison to DNS and is tested against classical LES models for isotropic homogeneous turbulence, based on eddy viscosity. We show that even in this situation, where no walls are present, our inclusion of backscatter through the Langevin equation results in a better description of the flow.

关键词： Turbulence simulation and modeling Turbulent flows computational methods in fluid dynamics

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A note on the lattice Boltzmann method beyond the Chapman-Enskog limits

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EUROPHYSICS LETTERS 2006年第3期73卷 370-376页

作者： Sbragaglia, M Succi, S Univ Roma Tor Vergata Dipartimento Fis I-00133 Rome Italy Ist Nazl Fis Nucl I-00133 Rome Italy CNR IAC I-00161 Rome Italy

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the lattice Boltzmann method, can provide semi-quantitative results also in the non-hydrodynamic, finite-Knudsen regime, up to Kn similar to O(1). This challenges the pessimistic stance, according to which the lattice Boltzmann method should only be used for strictly hydrodynamic purposes. It may also help the interpretation of recent simulations of microflows, which show satisfactory agreement with continuum kinetic theory in the moderate-Knudsen regime.

关键词： computational methods in fluid dynamics Rarefied gas dynamics

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

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EUROPHYSICS LETTERS 2006年第4期74卷 651-657页

作者： Benzi, R Biferale, L Sbragaglia, M Succi, S Toschi, F Univ Roma Tor Vergata Dipartimento Fis I-00133 Rome Italy Univ Roma Tor Vergata Ist Nazl Fis Nucl I-00133 Rome Italy CNR IAC I-00161 Rome Italy Ist Nazl Fis Nucl I-44100 Ferrara Italy

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 interactions. 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.

关键词： Drops and bubbles Wall slip and apparent slip computational methods in fluid dynamics

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Consistent particle-based algorithm with a non-ideal equation of state

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EUROPHYSICS LETTERS 2006年第5期73卷 664-670页

作者： Ihle, T Tüzel, E Kroll, DM N Dakota State Univ Dept Phys Fargo ND 58102 USA Univ Minnesota Sch Phys & Astron Minneapolis MN 55455 USA Univ Minnesota Inst Supercomp Walter Lib 599 Minneapolis MN 55455 USA

A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded-volume interactions are modeled by means of biased stochastic multiparticle collisions which depend on the local velocities and densities. Momentum and energy are conserved locally. The equation of state is derived and compared to independent measurements of the pressure. Results for the kinematic shear viscosity and self-diffusion constants are presented. For fixed density, a caging and order/disorder transition is observed with increasing collision frequency.

关键词： Molecular dynamics and particle methods computational methods in fluid dynamics Fluctuation phenomena, random processes, noise, and Brownian motion

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