Improved Lattice Boltzmann Without Parasitic Currents for Rayleigh-Taylor Instability (Communications in Computational Physics, 2010)
Over the last decade the Lattice Boltzmann Method (LBM) has gained significantinterest as a numerical solver for multiphase flows. However most of the LBvariants proposed to date are still faced with discreteness artifacts in the form of spuriouscurrents around fluid-fluid interfaces. In the recent past, Lee et al. have proposeda new LB scheme, based on a higher order differencing of the non-ideal forces, whichappears to virtually free of spurious currents for a number of representative situations.In this paper, we analyze the Lee method and show that, although strictly speaking, itlacks exact mass conservation, in actual simulations, the mass-breaking terms exhibita self-stabilizing dynamics which leads to their disappearance in the long-term evolution.This property is specifically demonstrated for the case of a moving droplet atlow-Weber number, and contrasted with the behaviour of the Shan-Chen model. Furthermore,the Lee scheme is for the first time applied to the problem of gravity-drivenRayleigh-Taylor instability. Direct comparison with literature data for different valuesof the Reynolds number, shows again satisfactory agreement. A grid-sensitivitystudy shows that, while large grids are required to converge the fine-scale details, thelarge-scale features of the flow settle-down at relatively low resolution. We concludethat the Lee method provides a viable technique for the simulation of Rayleigh-Taylorinstabilities on a significant parameter range of Reynolds and Weber numbers.