Abstract
The free-energy lattice Boltzmann (LB) model is one of the major multiphase models in the LB community. The present study is focused on a class of free-energy LB models in which the divergence of thermodynamic pressure tensor or its equivalent form expressed by the chemical potential is incorporated into the LB equation via a forcing term. Although this class of free-energy LB models may be thermodynamically consistent at the continuum level, it suffers from thermodynamic inconsistency at the discrete lattice level owing to numerical errors [Guo et al., Phys. Rev. E 83, 036707 (2010)10.1103/PhysRevE.83.036707]. The numerical error term mainly includes two parts: one comes from the discrete gradient operator and the other can be identified in a high-order Chapman-Enskog analysis. In this paper, we propose an improved scheme to eliminate the thermodynamic inconsistency of the aforementioned class of free-energy LB models. The improved scheme is constructed by modifying the equation of state of the standard LB equation, through which the discretization of ∇(ρc_{s}^{2}) is no longer involved in the force calculation and then the numerical errors can be significantly reduced. Numerical simulations are subsequently performed to validate the proposed scheme. The numerical results show that the improved scheme is capable of eliminating the thermodynamic inconsistency and can significantly reduce the spurious currents in comparison with the standard forcing-based free-energy LB model.
Highlights
The lattice Boltzmann (LB) method [1,2,3,4,5], which is a mesoscopic numerical approach originating from the lattice gas automaton method [6], has been proven to be suitable for studying multiphase and multicomponent systems [7,8] where the interfacial dynamics and phase transition are present
From the table we can see that in all the cases the maximum spurious currents yielded by the improved scheme are on the order of 10−14 ∼ 10−15, which are smaller by 10 orders of magnitude than those caused by the standard forcing-based free-energy LB model
We have investigated the problem of thermodynamic inconsistency of a class of free-energy LB models in which the divergence of thermodynamic pressure tensor or its equivalent form expressed by the chemical potential is incorporated into the LB equation via a forcing term
Summary
The lattice Boltzmann (LB) method [1,2,3,4,5], which is a mesoscopic numerical approach originating from the lattice gas automaton method [6], has been proven to be suitable for studying multiphase and multicomponent systems [7,8] where the interfacial dynamics and phase transition are present. An important advantage of diffuse-interface models lies in that the motion of the liquidgas interface does not need to be tracked explicitly [8] Among these multiphase LB models, the free-energy model proposed by Swift et al [12,13] was devised based on thermodynamic theory. They proposed to modify the secondorder moment of the equilibrium density distribution function so as to include a nonideal thermodynamic pressure tensor.
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