Search results for "Lattice Boltzmann methods"
showing 10 items of 37 documents
Derivation of transient relativistic fluid dynamics from the Boltzmann equation
2012
In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inve…
Mesoscopic Simulation Methods for Studying Flow and Transport in Electric Fields in Micro- and Nanochannels
2012
In the past decades, several mesoscale simulation techniques have emerged as tools to study hydrodynamic flow phenomena on scales in the range of nanoto micrometers. Examples are Dissipative Particle Dynamics (DPD), Multiparticle Collision Dynamics (MPCD), or Lattice Boltzmann (LB) methods. These methods allow one to access time and length scales which are not yet within reach of atomistic Molecular Dynamics (MD) simulations, often at relatively moderate computational expense. They can be coupled with particle-based (e.g., molecular dynamics) simulation methods for thermally fluctuating nanoscale objects, such as colloids or large molecules. This makes them particularly attractive for the a…
Relative importance of second-order terms in relativistic dissipative fluid dynamics
2013
In Denicol et al., Phys. Rev. D 85, 114047 (2012), the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in Knudsen number, in inverse Reynolds number, or their product. Terms of second order in Knudsen number give rise to non-hyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massless Boltzmann gas. Terms of …
Investigation of an entropic stabilizer for the lattice-Boltzmann method
2015
The lattice-Boltzmann (LB) method is commonly used for the simulation of fluid flows at the hydrodynamic level of description. Due to its kinetic theory origins, the standard LB schemes carry more degrees of freedom than strictly needed, e.g., for the approximation of solutions to the Navier-stokes equation. In particular, there is freedom in the details of the so-called collision operator. This aspect was recently utilized when an entropic stabilizer, based on the principle of maximizing local entropy, was proposed for the LB method [I. V. Karlin, F. Bosch, and S. S. Chikatamarla, ¨ Phys. Rev. E 90, 031302(R) (2014)]. The proposed stabilizer can be considered as an add-on or extension to b…
LATTICE–BOLTZMANN SIMULATION OF DENSE NANOFLOWS: A COMPARISON WITH MOLECULAR DYNAMICS AND NAVIER–STOKES SOLUTIONS
2007
In a recent work, a dense fluid flow across a nanoscopic thin plate was simulated by means of Molecular Dynamics (MD) and Lattice Boltzmann (LB) methods. It was found that in order to recover quantitative agreement with MD results, the LB simulation must be pushed down to sub–nanoscopic scales, i.e. fractions of the range of molecular interactions. In this work, we point out that in this sub–nanoscopic regime, the LB method works outside the hydrodynamic limit at the level of a single cell spacing. A quantitative comparison with the Navier–Stokes (NS) solution shows however that LB and NS results are quite similar, thereby indicating that, apart for a small region past the plate, this nano…
On the existence of kinetic equations
1974
The existence of the Boltzmann equation and its generalizations is studied by analysing the order of magnitude of their terms. As a consequence we conclude that the reduced distribution functions are not analytic in the density.
Electrokinetic Phenomena Revisited: A Lattice—Boltzmann Approach
2003
The Lattice-Boltzmann method (LBM) is an efficient tool to solve the Navier-Stokes equations. Based on this method we have developed a scheme to investigate electrokinetic phenomena in charged colloidal suspensions. The equations of motion that are solved are the so-called electrokinetic equations, i.e. a set of partial differential equations that couple the gradient of the electrostatic potential to the hydrodynamic flow by means of a mean field theory. These equations have been extensively used to study electroviscous phenomena for the limit of a weakly charged sphere in an unbounded electrolyte. We demonstrate that our method can be applied beyond these limit. As an example we discuss th…
High-order regularization in lattice-Boltzmann equations
2017
A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order nonequilibrium moments are filtered, i.e., only the corresponding advective parts are retained afte…
Self-Assembly of Polymeric Particles in Poiseuille Flow: A Hybrid Lattice Boltzmann/External Potential Dynamics Simulation Study
2017
We present a hybrid simulation method which allows one to study the dynamical evolution of self-assembling (co)polymer solutions in the presence of hydrodynamic interactions. The method combines an established dynamic density functional theory for polymers that accounts for the nonlocal character of chain dynamics at the level of the Rouse model, the external potential dynamics (EPD) model, with an established Navier–Stokes solver, the Lattice Boltzmann (LB) method. We apply the method to study the self-assembly of nanoparticles and vesicles in two-dimensional copolymer solutions in a typical microchannel Poiseuille flow profile. The simulations start from fully mixed systems which are sudd…
On the derivation of a linear Boltzmann equation from a periodic lattice gas
2004
We consider the problem of deriving the linear Boltzmann equation from the Lorentz process with hard spheres obstacles. In a suitable limit (the Boltzmann-Grad limit), it has been proved that the linear Boltzmann equation can be obtained when the position of obstacles are Poisson distributed, while the validation fails, also for the "correct" ratio between obstacle size and lattice parameter, when they are distributed on a purely periodic lattice, because of the existence of very long free trajectories. Here we validate the linear Boltzmann equation, in the limit when the scatterer's radius epsilon vanishes, for a family of Lorentz processes such that the obstacles have a random distributio…