2,868 research outputs found
A Lifting Relation from Macroscopic Variables to Mesoscopic Variables in Lattice Boltzmann Method: Derivation, Numerical Assessments and Coupling Computations Validation
In this paper, analytic relations between the macroscopic variables and the
mesoscopic variables are derived for lattice Boltzmann methods (LBM). The
analytic relations are achieved by two different methods for the exchange from
velocity fields of finite-type methods to the single particle distribution
functions of LBM. The numerical errors of reconstructing the single particle
distribution functions and the non-equilibrium distribution function by
macroscopic fields are investigated. Results show that their accuracy is better
than the existing ones. The proposed reconstruction operator has been used to
implement the coupling computations of LBM and macro-numerical methods of FVM.
The lid-driven cavity flow is chosen to carry out the coupling computations
based on the numerical strategies of domain decomposition methods (DDM). The
numerical results show that the proposed lifting relations are accurate and
robust
Electrokinetic Lattice Boltzmann solver coupled to Molecular Dynamics: application to polymer translocation
We develop a theoretical and computational approach to deal with systems that
involve a disparate range of spatio-temporal scales, such as those comprised of
colloidal particles or polymers moving in a fluidic molecular environment. Our
approach is based on a multiscale modeling that combines the slow dynamics of
the large particles with the fast dynamics of the solvent into a unique
framework. The former is numerically solved via Molecular Dynamics and the
latter via a multi-component Lattice Boltzmann. The two techniques are coupled
together to allow for a seamless exchange of information between the
descriptions. Being based on a kinetic multi-component description of the fluid
species, the scheme is flexible in modeling charge flow within complex
geometries and ranging from large to vanishing salt concentration. The details
of the scheme are presented and the method is applied to the problem of
translocation of a charged polymer through a nanopores. In the end, we discuss
the advantages and complexities of the approach
Initialization of lattice Boltzmann models with the help of the numerical Chapman-Enskog expansion
We extend the applicability of the numerical Chapman-Enskog expansion as a
lifting operator for lattice Boltzmann models to map density and momentum to
distribution functions. In earlier work [Vanderhoydonc et al. Multiscale Model.
Simul. 10(3): 766-791, 2012] such an expansion was constructed in the context
of lifting only the zeroth order velocity moment, namely the density. A lifting
operator is necessary to convert information from the macroscopic to the
mesoscopic scale. This operator is used for the initialization of lattice
Boltzmann models. Given only density and momentum, the goal is to initialize
the distribution functions of lattice Boltzmann models. For this
initialization, the numerical Chapman-Enskog expansion is used in this paper.Comment: arXiv admin note: text overlap with arXiv:1108.491
Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow
In this paper, three-dimensional (3D) multi-relaxation time (MRT)
lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to
the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT
models the rates of relaxation processes owing to collisions of particle
populations may be independently adjusted. As a result, the MRT models offer a
significant improvement in numerical stability of the LB method for simulating
fluids with lower viscosities. We show through the Chapman-Enskog multiscale
analysis that the continuum limit behavior of 3D MRT LB models corresponds to
that of the macroscopic dynamical equations for multiphase flow. We extend the
3D MRT LB models developed to represent multiphase flow with reduced
compressibility effects. The multiphase models are evaluated by verifying the
Laplace-Young relation for static drops and the frequency of oscillations of
drops. The results show satisfactory agreement with available data and
significant gains in numerical stability.Comment: Accepted for publication in the Journal of Computational Physic
Incorporating Forcing Terms in Cascaded Lattice-Boltzmann Approach by Method of Central Moments
Cascaded lattice-Boltzmann method (Cascaded-LBM) employs a new class of
collision operators aiming to improve numerical stability. It achieves this and
distinguishes from other collision operators, such as in the standard single or
multiple relaxation time approaches, by performing relaxation process due to
collisions in terms of moments shifted by the local hydrodynamic fluid
velocity, i.e. central moments, in an ascending order-by-order at different
relaxation rates. In this paper, we propose and derive source terms in the
Cascaded-LBM to represent the effect of external or internal forces on the
dynamics of fluid motion. This is essentially achieved by matching the
continuous form of the central moments of the source or forcing terms with its
discrete version. Different forms of continuous central moments of sources,
including one that is obtained from a local Maxwellian, are considered in this
regard. As a result, the forcing terms obtained in this new formulation are
Galilean invariant by construction. The method of central moments along with
the associated orthogonal properties of the moment basis completely determines
the expressions for the source terms as a function of the force and macroscopic
velocity fields. In contrast to the existing forcing schemes, it is found that
they involve higher order terms in velocity space. It is shown that the
proposed approach implies "generalization" of both local equilibrium and source
terms in the usual lattice frame of reference, which depend on the ratio of the
relaxation times of moments of different orders. An analysis by means of the
Chapman-Enskog multiscale expansion shows that the Cascaded-LBM with forcing
terms is consistent with the Navier-Stokes equations. Computational experiments
with canonical problems involving different types of forces demonstrate its
accuracy.Comment: 55 pages, 4 figure
Steady State Convergence Acceleration of the Generalized Lattice Boltzmann Equation with Forcing Term through Preconditioning
Several applications exist in which lattice Boltzmann methods (LBM) are used
to compute stationary states of fluid motions, particularly those driven or
modulated by external forces. Standard LBM, being explicit time-marching in
nature, requires a long time to attain steady state convergence, particularly
at low Mach numbers due to the disparity in characteristic speeds of
propagation of different quantities. In this paper, we present a preconditioned
generalized lattice Boltzmann equation (GLBE) with forcing term to accelerate
steady state convergence to flows driven by external forces. The use of
multiple relaxation times in the GLBE allows enhancement of the numerical
stability. Particular focus is given in preconditioning external forces, which
can be spatially and temporally dependent. In particular, correct forms of
moment-projections of source/forcing terms are derived such that they recover
preconditioned Navier-Stokes equations with non-uniform external forces. As an
illustration, we solve an extended system with a preconditioned lattice kinetic
equation for magnetic induction field at low magnetic Prandtl numbers, which
imposes Lorentz forces on the flow of conducting fluids. Computational studies,
particularly in three-dimensions, for canonical problems show that the number
of time steps needed to reach steady state is reduced by orders of magnitude
with preconditioning. In addition, the preconditioning approach resulted in
significantly improved stability characteristics when compared with the
corresponding single relaxation time formulation.Comment: 47 pages, 21 figures, for publication in Journal of Computational
Physic
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