155 research outputs found
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 to 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
Optimizing Learned Bloom Filters: How Much Should Be Learned?
The learned Bloom filter (LBF) combines a machine learning model (learner) with a traditional Bloom filter to improve the false positive rate (FPR) that can be achieved for a given memory budget. The LBF has recently been generalized by making use of the full spectrum of the learner's prediction score. However, in all those designs, the machine learning model is fixed. In this letter, for the first time, the design of LBFs is proposed and evaluated by considering the machine learning model as one of the variables in the process. In detail, for a given memory budget, several LBFs are constructed using different machine learning models and the one with the lowest FPR is selected. We demonstrate that our approach can achieve much better performance than existing LBF designs providing reductions of the FPR of up to 90% in some settings.This work was supported by the EU H2020 Project PIMCITY under Grant H2020-871370. This manuscript was recommended for publication by A. Kumar
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