Over the last decade the Lattice Boltzmann Method (LBM) has gained significant interest as a numerical solver for multiphase flows. However most of the LBvariants proposed to date are still faced with discreteness art...Over the last decade the Lattice Boltzmann Method (LBM) has gained significant interest 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 spurious currents 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 values of 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.展开更多
文摘Over the last decade the Lattice Boltzmann Method (LBM) has gained significant interest 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 spurious currents 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 values of 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.
