Search results for "Lattice Boltzmann"
showing 10 items of 43 documents
Lattice Boltzmann versus Molecular Dynamics simulations of nanoscale hydrodynamic flows
2006
A fluid flow in a simple dense liquid, passing an obstacle in a two-dimensional thin film geometry, is simulated by Molecular Dynamics (MD) computer simulation and compared to results of Lattice Boltzmann (LB) simulations. By the appropriate mapping of length and time units from LB to MD, the velocity field as obtained from MD is quantitatively reproduced by LB. The implications of this finding for prospective LB-MD multiscale applications are discussed.
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…
X-ray computed tomography and numerical analysis of water-saturated porous materials
2012
A method for imaging a water-saturated porous material is developed in order to simulate a fluid flow through it using the Lattice Boltzmann method. The value of its flow permeability is compared to the value for the same sample when it is dry. An explanation for the difference in the experimental values of permeability for air and water is sought. A reference is given by experimental values from flow measurements that are interpreted according to Darcy's law of permeability.
Fluid flow simulations meet high-speed video : Computer vision comparison of droplet dynamics
2018
Hypothesis While multiphase flows, particularly droplet dynamics, are ordinary in nature as well as in industrial processes, their mathematical and computational modelling continue to pose challenging research tasks - patent approaches for tackling them are yet to be found. The lack of analytical flow field solutions for non-trivial droplet dynamics hinders validation of computer simulations and, hence, their application in research problems. High-speed videos and computer vision algorithms can provide a viable approach to validate simulations directly against experiments. Experiments Droplets of water (or glycerol-water mixtures) impacting on both hydrophobic and superhydrophobic surfaces …