A lattice Boltzmann model for natural convection in cavities

We study a multiple relaxation time lattice Boltzmann model for natural convection with moment–based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second–order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 106. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy

Discrete solution of the electrokinetic equations

We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete solution of the convection-diffusion equation for the different charged and neutral species that compose the fluid. The method is based on identifying the elementary fluxes between nodes, which ensures the absence of spurious fluxes in equilibrium. We show how the model is suitable to study electro-osmotic flows. As an illustration, we show that, by introducing appropriate dynamic rules in the presence of solid interfaces, we can compute the sedimentation velocity (and hence the sedimentation potential) of a charged sphere. Our approach does not assume linearization of the Poisson-Boltzmann equation and allows us for a wide variation of the Peclet number.Comment: 24 pages, 7 figure

Lattice Boltzmann simulations of 3D crystal growth: Numerical schemes for a phase-field model with anti-trapping current

A lattice-Boltzmann (LB) scheme, based on the Bhatnagar-Gross-Krook (BGK) collision rules is developed for a phase-field model of alloy solidification in order to simulate the growth of dendrites. The solidification of a binary alloy is considered, taking into account diffusive transport of heat and solute, as well as the anisotropy of the solid-liquid interfacial free energy. The anisotropic terms in the phase-field evolution equation, the phenomenological anti-trapping current (introduced in the solute evolution equation to avoid spurious solute trapping), and the variation of the solute diffusion coefficient between phases, make it necessary to modify the equilibrium distribution functions of the LB scheme with respect to the one used in the standard method for the solution of advection-diffusion equations. The effects of grid anisotropy are removed by using the lattices D3Q15 and D3Q19 instead of D3Q7. The method is validated by direct comparison of the simulation results with a numerical code that uses the finite-difference method. Simulations are also carried out for two different anisotropy functions in order to demonstrate the capability of the method to generate various crystal shapes