Ludwig: A parallel Lattice-Boltzmann code for complex fluids

This paper describes `Ludwig', a versatile code for the simulation of Lattice-Boltzmann (LB) models in 3-D on cubic lattices. In fact `Ludwig' is not a single code, but a set of codes that share certain common routines, such as I/O and communications. If `Ludwig' is used as intended, a variety of complex fluid models with different equilibrium free energies are simple to code, so that the user may concentrate on the physics of the problem, rather than on parallel computing issues. Thus far, `Ludwig''s main application has been to symmetric binary fluid mixtures. We first explain the philosophy and structure of `Ludwig' which is argued to be a very effective way of developing large codes for academic consortia. Next we elaborate on some parallel implementation issues such as parallel I/O, and the use of MPI to achieve full portability and good efficiency on both MPP and SMP systems. Finally, we describe how to implement generic solid boundaries, and look in detail at the particular case of a symmetric binary fluid mixture near a solid wall. We present a novel scheme for the thermodynamically consistent simulation of wetting phenomena, in the presence of static and moving solid boundaries, and check its performance.Comment: Submitted to Computer Physics Communication

Simulating fluid flows in micro and nano devices : the challenge of non-equilibrium behaviour

We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro- and nano-scale, concentrating on two different but promising approaches: extended hydrodynamic models, and lattice Boltzmann methods. Following a brief exposition of the challenges that non-equilibrium poses in micro- and nano-scale gas flows, we turn first to extended hydrodynamics, outlining the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We show that the latter models, with properly-constituted boundary conditions, can capture critical non-equilibrium flow phenomena quite well. We then review the boundary conditions required if the conventional Navier-Stokes-Fourier (NSF) fluid dynamic model is applied at the micro scale, describing how 2nd-order Maxwell-type conditions can be used to compensate for some of the non-equilibrium flow behaviour near solid surfaces. While extended hydrodynamics is not yet widely-used for real flow problems because of its inherent complexity, we finish this section with an outline of recent 'phenomenological extended hydrodynamics' (PEH) techniques-essentially the NSF equations scaled to incorporate non-equilibrium behaviour close to solid surfaces-which offer promise as engineering models. Understanding non-equilibrium within lattice Boltzmann (LB) framework is not as advanced as in the hydrodynamic framework, although LB can borrow some of the techniques which are being developed in the latter-in particular, the near-wall scaling of certain fluid properties that has proven effective in PEH. We describe how, with this modification, the standard 2nd-order LB method is showing promise in predicting some rarefaction phenomena, indicating that instead of developing higher-order off-lattice LB methods with a large number of discrete velocities, a simplified high-order LB method with near-wall scaling may prove to be just as effective as a simulation tool

A Lattice Boltzmann Method for the Advection-Diffusion Equation with Neumann Boundary Conditions

In this paper, we study a lattice Boltzmann method for the advection-diffusion equation with Neumann boundary conditions on general boundaries. A novel mass conservative scheme is introduced for implementing such boundary con- ditions, and is analyzed both theoretically and numerically. Second order convergence is predicted by the theoretical analysis, and numerical investigations show that the convergence is at or close to the predicted rate. The nu- merical investigations include time-dependent problems and a steady-state diffusion problem for computation of effective diffusion coefficients

Lattice Boltzmann simulation of droplet behaviour in microfluidic devices

We developed a lattice Boltzmann model to investigate the droplet dynamics in microfluidic devices. In our model, a stress-free boundary condition was proposed to conserve the total mass of flow system and improve the numerical stability for flows with low Reynolds number The model was extensively validated by the benchmark cases including the Laplace law, the static contact angles at solid surface, and the droplet deformation and breakup under simple shear flow We applied our model to study the effects of the Pelcect number the Capillary number and wettability on droplet formation. The results showed that the Peclet number has little effect on droplet size though it slightly affects the time of droplet formation. In the creeping flow regime, the Capillary number plays a dominating role in the droplet generation process. Wettability of fluids affects the position of droplet detachment, the droplet shape and size, and its impact becomes more significant when the Capillary number decreases. We also found that the hydrophobic surface generally can produce smaller droplet

Link-wise Artificial Compressibility Method

The Artificial Compressibility Method (ACM) for the incompressible Navier-Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the Lattice Boltzmann Method (LBM). The main advantage is the possibility of exploiting well established technologies originally developed for LBM and classical computational fluid dynamics, with special emphasis on finite differences (at least in the present paper), at the cost of minor changes. For instance, wall boundaries not aligned with the background Cartesian mesh can be taken into account by tracing the intersections of each link with the wall (analogously to LBM technology). LW-ACM requires no high-order moments beyond hydrodynamics (often referred to as ghost moments) and no kinetic expansion. Like finite difference schemes, only standard Taylor expansion is needed for analyzing consistency. Preliminary efforts towards optimal implementations have shown that LW-ACM is capable of similar computational speed as optimized (BGK-) LBM. In addition, the memory demand is significantly smaller than (BGK-) LBM. Importantly, with an efficient implementation, this algorithm may be one of the few which is compute-bound and not memory-bound. Two- and three-dimensional benchmarks are investigated, and an extensive comparative study between the present approach and state of the art methods from the literature is carried out. Numerical evidences suggest that LW-ACM represents an excellent alternative in terms of simplicity, stability and accuracy.Comment: 62 pages, 20 figure

THERMAL LATTICE BOLTZMANN TWO-PHASE FLOW MODEL FOR FLUID DYNAMICS

This dissertation presents a systematic development of a new thermal lattice Boltzmann multiphase model. Unlike conventional CFD methods, the lattice Boltzmann equation (LBE) method is based on microscopic models and mesoscopic kinetic equations in which the collective behavior of the particles in a system is used to simulate the continuum mechanics of the system. Due to this kinetic nature, the LBE method has been found to be particularly useful in applications involving interfacial dynamics and complex boundaries, e.g. multiphase or multicomponent flows. First, the methodology and general concepts of the LBE method are introduced. Following this introduction, an accurate mass conserving wall boundary condition for the LBE method is proposed together with benchmark test results. Next, the widely used Shan and Chen (SC) single component two-phase flow model is presented, as well as improvements to that model. In this model, by incorporating fluid-fluid interaction, phase separation and interfacial dynamics can be properly captured. Sharp interfaces between phases can be easily obtained without any additional numerical treatment. In order to achieve flexibility for the surface tension term, an additional force term which represents the contribution of surface tension is incorporated into the fluid-fluid interaction force term. The validity of this treatment is verified by our simulation results. Different equations of state are also incorporated into this model to compare their behavior. Finally, based on the SC model, a new and generalized lattice Boltzmann model for simulating thermal two-phase flow is described. In this model, the SC model is used to simulate the fluid dynamics. The temperature field is simulated using the passive-scalar approach, i.e. through modeling the density field of an extra component, which evolves according to the advection-diffusion equation. By coupling the fluid dynamics and temperature field through a suitably defined body force term, the thermal two-phase lattice Boltzmann model is obtained. Our simulation results show that different equations of state, variable wettability, gravity and buoyancy effects, and relatively high Rayleigh numbers can be readily simulated by this new model. Lastly, the accomplishments of this study are summarized and future perspectives are provided