Xiaoyi He

On pressure and velocity boundary conditions for the lattice Boltzmann BGK model

Pressure ~density! and velocity boundary conditions are studied for 2-D and 3-D lattice Boltzmann BGK models ~LBGK! and a new method to specify these conditions is proposed. These conditions are constructed in consistency with the wall boundary condition, based on the idea of bounceback of the non-equilibrium distribution. When these conditions are used together with the incompressible LBGK model @J. Stat. Phys. 81 ,3 5 ~1995!# the simulation results recover the analytical solution of the plane Poiseuille flow driven by a pressure ~density! difference. The half-way wall bounceback boundary condition is also used with the pressure ~density! inlet/outlet conditions proposed in this paper and in Phys. Fluids 8, 2527 ~1996! to study 2-D Poiseuille flow and 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback boundary condition is comparable with that of other published boundary conditions and it has better stability behavior.

Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model

In this paper we analytically solve the velocity of the lattice Boltzmann BGK equation (LBGK) for several simple flows. The analysis provides a framework to theoretically analyze various boundary conditions. In particular, the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition. We find that the slip velocity is zero as long as Σαfαeα=0 at boundaries, no matter what combination of distributions is chosen. The schemes proposed by Nobleet al. and by Inamuroet al. yield the correct zeroslip velocity, while some other schemes, such as the bounce-back scheme and the equilibrium distribution scheme, would inevitably generate a nonzero slip velocity. The bounce-back scheme with the wall located halfway between a flow node and a bounce-back node is also studied for the simple flows considered and is shown to produce results of second-order accuracy. The momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries. To be specific, the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids.

Extending the range of rate constants available from BIACORE: interpreting mass transport-influenced binding data.

Surface-based binding assays are often influenced by the transport of analyte to the sensor surface. Using simulated data sets, we test a simple two-compartment model to see if its description of transport and binding is sufficient to accurately analyze BIACORE data. First we present a computer model that can generate realistic BIACORE data. This model calculates the laminar flow of analyte within the flow cell, its diffusion both perpendicular and parallel to the sensor surface, and the reversible chemical reaction between analyte and immobilized reactant. We use this computer model to generate binding data under a variety of conditions. An analysis of these data sets with the two-compartment model demonstrates that good estimates of the intrinsic reaction rate constants are recovered even when mass transport influences the binding reaction. We also discuss the conditions under which the two-compartment model can be used to determine the diffusion coefficient of the analyte. Our results illustrate that this model can significantly extend the range of association rate constants that can be accurately determined from BIACORE.

Thermodynamic Foundations of Kinetic Theory and Lattice Boltzmann Models for Multiphase Flows

This paper demonstrates that thermodynamically consistent lattice Boltzmann models for single-component multiphase flows can be derived from a kinetic equation using both Enskogs theory for dense fluids and mean-field theory for long-range molecular interaction. The lattice Boltzmann models derived this way satisfy the correct mass, momentum, and energy conservation equations. All the thermodynamic variables in these LBM models are consistent. The strengths and weaknesses of previous lattice Boltzmann multiphase models are analyzed.

On the three-dimensional Rayleigh–Taylor instability

The three-dimensional Rayleigh–Taylor instability is studied using a lattice Boltzmann scheme for multiphase flow in the nearly incompressible limit. This study focuses on the evolution of the three-dimensional structure of the interface. In addition to the bubble and spike fronts, a saddle point is found to be another important landmark on the interface. Two layers of heavy-fluid roll-ups, one at the spike tip and the other at the saddle point, were observed. The secondary instability in the horizontal planes entangles the already complicated structure of the interface. Parallel computations are utilized to accommodate the massive computational requirements of the simulations.

Lattice Boltzmann simulation of electrochemical systems

We propose a lattice Boltzmann model for studying electrochemical processes. A new lattice Boltzmann equation is introduced to simulate ion transports, including migration in an electric field, diffusion in a concentration gradient, and convection with fluid flow. The electrode reaction is incorporated via special boundary conditions for electric potential and ion flux. Benchmark studies on a variety of electrochemical problems, including the convective diffusion, the primary and secondary current distributions, and a general case, yield satisfactory results.

Interface and surface tension in incompressible lattice Boltzmann multiphase model

This paper studies the interfacial dynamics and surface tension in an incompressible lattice Boltzmann multiphase model proposed recently by He et al. [J. Comput. Phys. 152 (1999) 642]. The model tracks different phases and the interface between them using an index fluid with molecular interaction. When the molecular interaction is strong enough, the index fluid automatically segregates into two different phases. The surface tension is implemented in the model using a term as a function of the gradient of the index fluid density. The strength of the surface tension depends on the molecular interaction, and can be adjusted conveniently by a free parameter. Numerical simulations for a variety of flow conditions with surface tension are carried out to demonstrate the capability of the model.

Simulation of Combustion Field with Lattice Boltzmann Method

Turbulent combustion is ubiquitously used in practical combustion devices. However, even chemically non-reacting turbulent flows are complex phenomena, and chemical reactions make the problem even more complicated. Due to the limitation of the computational costs, conventional numerical methods are impractical in carrying out direct 3D numerical simulations at high Reynolds numbers with detailed chemistry. Recently, the lattice Boltzmann method has emerged as an efficient alternative for numerical simulation of complex flows. Compared with conventional methods, the lattice Boltzmann scheme is simple and easy for parallel computing. In this study, we present a lattice Boltzmann model for simulation of combustion, which includes reaction, diffusion, and convection. We assume the chemical reaction does not affect the flow field. Flow, temperature, and concentration fields are decoupled and solved separately. As a preliminary simulation, we study the so-called “counter-flow” laminar flame. The particular flow geometry has two opposed uniform combustible jets which form a stagnation flow. The results are compared with those obtained from solving Navier–Stokes equations.

Some progress in the lattice Boltzmann method: Reynolds number enhancement in simulations

Abstract A newly proposed lattice Boltzmann algorithm is used to simulate flows with high Reynolds number. The new algorithm is not limited by the lattice Reynolds number which constrains all previous lattice Boltzmann models. Not only is the Reynolds number enhanced in the simulation using the new algorithm, but also is the numerical stability improved significantly. Numerical simulations of the flow in a 2_D symmetrical sudden expansion were conducted to demonstrate the effectiveness of the new algorithm.

Surface tension effects on two-dimensional two-phase Kelvin–Helmholtz instabilities

Abstract The two-dimensional Kelvin–Helmholtz instability is studied using a lattice Boltzmann multi-phase model in the nearly incompressible limit. This study focuses on the effects of surface tension on the evolution of vortex pairing in a two-dimensional mixing layer. Several types of interface pinch-off are observed and the corresponding mechanisms are discussed. The contribution of surface tension to the flow kinetic energy is mainly negative. Part of this kinetic energy can be transformed to potential energy stored in the surface tension. The contribution of surface tension to the flow enstrophy is positive and small vortices are generated near interfaces. Broken interfaces and small vortices near interfaces dominate the late stage of flow fields with strong surface tension.