Microflow Simulations via the Lattice Boltzmann Method

The exact solution to the hierarchy of nonlinear lattice Boltzmann kinetic equations, for the stationary planar Couette flow for any Knudsen number was presented by S. Ansumali et al. [Phys. Rev. Lett., 98 (2007), 124502]. In this paper, simulation results at a non-vanishing value of the Knudsen number are compared with the closed-form solutions for the higher-order moments. The order of convergence to the exact solution is also studied. The lattice Boltzmann simulations are in excellent agreement with the exact solutio

Entropic Lattice Boltzmann Simulation of the Flow Past Square Cylinder

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier-Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from $Re\sim O(10)$ to $Re\leq 1000$ were predicted by a single simulation algorithm.Comment: 12 pages, 5 figures, to appear in Int. J. Mod. Phys.

Inertial Frame Independent Forcing for Discrete Velocity Boltzmann Equation: Implications for Filtered Turbulence Simulation

We present a systematic derivation of a model based on the central moment lattice Boltzmann equation that rigorously maintains Galilean invariance of forces to simulate inertial frame independent flow fields. In this regard, the central moments, i.e. moments shifted by the local fluid velocity, of the discrete source terms of the lattice Boltzmann equation are obtained by matching those of the continuous full Boltzmann equation of various orders. This results in an exact hierarchical identity between the central moments of the source terms of a given order and the components of the central moments of the distribution functions and sources of lower orders. The corresponding source terms in velocity space are then obtained from an exact inverse transformation due to a suitable choice of orthogonal basis for moments. Furthermore, such a central moment based kinetic model is further extended by incorporating reduced compressibility effects to represent incompressible flow. Moreover, the description and simulation of fluid turbulence for full or any subset of scales or their averaged behavior should remain independent of any inertial frame of reference. Thus, based on the above formulation, a new approach in lattice Boltzmann framework to incorporate turbulence models for simulation of Galilean invariant statistical averaged or filtered turbulent fluid motion is discussed.Comment: 37 pages, 1 figur

Stabilized Lattice Boltzmann-Enskog method for compressible flows and its application to one and two-component fluids in nanochannels

A numerically stable method to solve the discretized Boltzmann-Enskog equation describing the behavior of non ideal fluids under inhomogeneous conditions is presented. The algorithm employed uses a Lagrangian finite-difference scheme for the treatment of the convective term and a forcing term to account for the molecular repulsion together with a Bhatnagar-Gross-Krook relaxation term. In order to eliminate the spurious currents induced by the numerical discretization procedure, we use a trapezoidal rule for the time integration together with a version of the two-distribution method of He et al. (J. Comp. Phys 152, 642 (1999)). Numerical tests show that, in the case of one component fluid in the presence of a spherical potential well, the proposed method reduces the numerical error by several orders of magnitude. We conduct another test by considering the flow of a two component fluid in a channel with a bottleneck and provide information about the density and velocity field in this structured geometry.Comment: to appear in Physical Review

Energy Conserving Lattice Boltzmann Models for Incompressible Flow Simulations

In this paper, we highlight the benefits resulting from imposing energy-conserving equilibria in entropic lattice Boltzmann models for isothermal flows. The advantages are documented through a series of numerical simulations, such as Taylor-Green vortices, cavity flow and flow past a spher