Narrow Results

A new boundary condition is developed to enhance numerical stability for moving walls in lattice-Boltzmann simulations. It includes a population "adjustment" procedure at boundaries which allows stable simulations closer to the theoretical limit of τ = 0.5. Couette and lid-driven cavity flow simulations show improved velocity profiles, lower stable relaxation timestep τ and higher Reynolds number Re limits. The new method needs fewer timesteps to achieve steady-state.

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 nanoflow is still well described by hydrodynamic equations.

We propose a numerical model of blood flow and blood clotting whose purpose is to describe thrombus formation in cerebral aneurysms. We identify possible mechanisms that can cause occurence of spontaneous thrombosis in unruptured giant intracranial aneurysms. Our main claim is that, under normal conditions, there is a low shear rate threshold below which thrombosis starts and growths. This assumption is supported by several evidences from literature. The proposed mechanisms are incorporated into a Lattice Boltzmann (LB) model for blood flow and platelets adhesion and aggregation. Numerical simulations show that the low shear rate threshold assumption together with aneurysm geometry account well for the observations.

This paper carries out numerical simulation for pressure driven microscale gas flows in transition flow regime. The relaxation time of LBM model was modified with the application of near wall effective mean free path combined with a combination of Bounce-back and Specular Reflection (BSR) boundary condition. The results in this paper are more close to those of DSCM and IP-DSCM compared with the results obtained by other LBM models. The calculation results show that in transition regime, with the increase of Knudsen number, the dimensionless slip velocity at the wall significantly increases, but the maximum linear deviation of nonlinear pressure distribution gradually decreases.

The accuracy of the lattice-Boltzmann method (LBM) is moderated by several factors, including Mach number, spatial resolution, boundary conditions, and the lattice mean free path. Results obtained with 3D lattices suggest that the accuracy of certain two-dimensional (2D) flows, such as Poiseuille and Couette flow, persist even when the mean free path between collisions is large, but that of the 3D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3D low-Reynolds-number flow. The influence of boundary representations on LBM accuracy is captured by the proposed index, when the accuracy of the prescribed boundary conditions is consistent with that of LBM.

In this article we use a lattice-Boltzmann simulation to examine the effects of shear flow on an equilibrium droplet in a phase separated binary mixture. We find that large drops break up as the shear is increased but small drops dissolve. We also show how the tip-streaming, observed for deformed drops, leads to a state of dynamic equilibrium.

The classical lattice-Boltzmann scheme is extended in an attempt to represent visco-elastic fluids in two dimensions. At each lattice site, two new quantities are added. A suitable coupling of these quantities with the viscous stress tensor leads to a nonzero shear modulus and visco-elastic effects. A Chapman–Enskog expansion gives us the equilibrium populations and conditions for isotropy of the model. A finite wave vector analysis is needed to study the relaxation of sound waves and to determine the dependence of the transport coefficients upon the frequency.

A lattice-Boltzmann scheme for natural convection in porous media is developed and applied to the heat transfer problem of a 1000 kg potato packaging. The scheme has features new to the field of LB schemes. It is mapped on a orthorhombic lattice instead of the traditional cubic lattice. Furthermore the boundary conditions are formulated with a single paradigm based upon the particle fluxes. Our scheme is well able to reproduce (1) the analytical solutions of simple model problems and (2) the results from cooling down experiments with potato packagings.

The application of lattice-Boltzmann methods to electroviscous transport problems is discussed, generalising the moment propagation method for convective-diffusion problems. As a simple application, electro-osmotic flow in a parallel-sided slit is analysed, and the results compared favourably with available analytic solutions for this geometry.

We present a comparison between the finite-element and the lattice-Boltzmann method for simulating fluid flow in a SMRX static mixer reactor. The SMRX static mixer is a piece of equipment with excellent mixing performance and it is used in highly efficient chemical reactors for viscous systems like polymers. The complex geometry of this mixer makes such 3D simulations nontrivial. An excellent agreement between the results of the two simulation methods and experimental data was found.

Results for time-dependent, viscous, incompressible flows were investigated using the lattice-Boltzmann (BGK) automata. The decay of a synthetic turbulent flow field and the time evolution of an initial vortex were simulated for validation purposes. The focal point was the investigation of the instationary flow around a square obstacle in a two-dimensional channel for a range of Reynolds numbers between 80 and 300 and a blockage ratio of 0.125. The Strouhal number was measured for this case and found to be in the range of data given in the literature.

After a short discussion of recent discretization techniques for the lattice-Boltzmann equations we motivate and discuss some alternative approaches using implicit, nonuniform FD discretization and mesh refinement techniques. After presenting results of a stability analysis we use an implicit approach to simulate a boundary layer test problem. The numerical results compare well to the reference solution when using strongly refined meshes. Some basic ideas for a nonuniform mesh refinement (with non-cartesian mesh topology) are introduced using the standard discretization procedure of alternating collision and propagation.

The lattice-Boltzmann (LB) method is applied to complex, moving geometries in which computational cells are partially filled with fluid. The LB algorithm is modified to include a term that depends on the percentage of the cell saturated with fluid. The method is useful for modeling suspended obstacles that do not conform to the grid. Another application is to simulations of flow through reconstructed media that are not easily segmented into solid and liquid regions. A detailed comparison is made with FIDAP simulation results for the flow about a periodic line of cylinders in a channel at a non-zero Reynolds number. Two cases are examined. In the first simulation, the cylinders are given a constant velocity along the axis of the channel, and the steady solution is acquired. The transient behavior of the system is then studied by giving the cylinders an oscillatory velocity. For both steady and oscillatory flows, the method provides excellent agreement with FIDAP simulation results, even at locations close to the surface of a cylinder. In contrast to step-like solutions produced using the "bounce-back" condition, the proposed condition gives close agreement with the smooth FIDAP predictions. Computed drag forces with the proposed condition exhibit apparent quadratic convergence with grid refinement rather than the linear convergence exhibited by other LB boundary conditions.

Cellular automata (CA) and lattice-Boltzmann (LB) models are two possible approaches to simulate fluid-like systems. CA models keep track of the many-body correlations and provide a description of the fluctuations. However, they lead to a noisy dynamics and impose strong restrictions on the possible viscosity values. On the other hand, LB models are numerically more efficient and offer much more flexibility to adjust the fluid parameters, but they neglect fluctuations. Here we discuss a multiparticle lattice model which reconciles both approaches. Our method is tested on Poiseuille flows and on the problem of ballistic annihilation in two dimensions for which the fluctuations are known to play an important role.

We use lattice-Boltzmann simulations to examine late stage spinodal decomposition in binary fluids, showing that the scaling hypothesis for phase ordering does not hold in all cases. We also examine the effects of an applied shear on the coarsening of the spinodal pattern.

A model with a volumetric stress tensor added to the Navier–Stokes Equation is used to study two-phase fluid flows. The implementation of such an interface model into the lattice-Boltzmann equation is derived from the continuous Boltzmann BGK equation with an external force term, by using the discrete coordinate method. Numerical simulations are carried out for phase separation and "dam breaking" phenomena.

An extension to the basic lattice-BGK algorithm is presented for modeling a simulation region as a porous medium. The method recovers flow through a resistance field with arbitrary values of the resistance tensor components. Corrections to a previous algorithm are identified. Simple validation tests are performed which verify the accuracy of the method, and demonstrate that inertial effects give a deviation from Darcy's law for nominal simulation velocities.

Pore-scale simulations of fluid flow and mass transport offer a direct means to reproduce and verify laboratory measurements in porous media. We have compared lattice-Boltzmann (LB) flow simulations with the results of NMR spectroscopy from several published flow experiments. Although there is qualitative agreement, the differences highlight numerical and experimental issues, including the rate of spatial convergence, and the effect of signal attenuation near solid surfaces. For the range of Reynolds numbers relevant to groundwater investigations, the normalized distribution of fluid velocities in random sphere packings collapse onto a single curve, when scaled with the mean velocity. Random-walk particle simulations in the LB flow fields have also been performed to study the dispersion of an ideal tracer. These simulations show an encouraging degree of quantitative agreement with published NMR measurements of hydrodynamic and molecular dispersion, and the simulated dispersivities scale in accordance with published experimental and theoretical results for the Peclet number rangek 1 ≤Pe≤1500. Experience with the random-walk method indicates that the mean properties of conservative transport, such as the first and second moments of the particle displacement distribution, can be estimated with a number of particles comparable to the spatial discretization of the velocity field. However, the accurate approximation of local concentrations, at a resolution comparable to that of the velocity field, requires significantly more particles. This requirement presents a significant computational burden and hence a numerical challenge to the simulation of non-conservative transport processes.

In the presence of buoyancy, multiple diffusion coefficients, and porous media, the dispersion of solutes can be remarkably complex. The lattice-Boltzmann (LB) method is ideal for modeling dispersion in flow through complex geometries; yet, LB models of solute fingers or slugs can suffer from peculiar numerical conditions (e.g., denormal generation) that degrade computational performance by factors of 6 or more. Simple code optimizations recover performance and yield simulation rates up to ~3 million site updates per second on inexpensive, single-CPU systems. Two examples illustrate limits of the methods: (1) Dispersion of solute in a thin duct is often approximated with dispersion between infinite parallel plates. However, Doshi, Daiya and Gill (DDG) showed that for a smooth-walled duct, this approximation is in error by a factor of ~8. But in the presence of wall roughness (found in all real fractures), the DDG phenomenon can be diminished. (2) Double-diffusive convection drives "salt-fingering", a process for mixing of fresh-cold and warm-salty waters in many coastal regions. Fingering experiments are typically performed in Hele-Shaw cells, and can be modeled with the 2D (pseudo-3D) LB method with velocity-proportional drag forces. However, the 2D models cannot capture Taylor–Aris dispersion from the cell walls. We compare 2D and true 3D fingering models against observations from laboratory experiments.

A lattice formulation of nonrelativistic quantum mechanics is presented, based on a formal analogy with discrete kinetic theory. The method is applied to the Gross–Pitaevski equation, a specific form of self-interacting nonlinear Schrödinger equation relevant to the study of Bose–Einstein condensation.