Abstract
To improve the stability of the lattice Boltzmann method (LBM) at high Reynolds number the cascaded LBM has recently been introduced. As in the multiple relaxation time (MRT) method the cascaded LBM introduces additional relaxation times into the collision operator, but does so in a co-moving reference frame. This has been shown to significantly increase stability at low viscosity in the single phase case. Here the cascaded LBM is further developed to include multiphase flow. For this the force term is calculated by the interaction potential method, and introduced into the collision operator via the exact difference method (EDM). Comparisons are made with the lattice Bhatnagar–Gross–Krook (LBGK) method, and an MRT implementation. Both the cascaded and MRT methods are shown to significantly reduce spurious velocities over the LBGK method. For the particular case of the Shan–Chen interparticle force term calculation with the EDM, the cascaded LBM is successfully combined with a multiphase method, and shown to perform as well as the more established MRT method. The cascaded LBM is found to be a considerably improved approach to the simulation of multiphase flow over the LBGK, significantly increasing the stability range of both density ratio and Reynolds number. Additionally the importance of including third order velocity terms in the equilibria of both the cascaded and MRT methods is discussed.
Highlights
The lattice Boltzmann method (LBM) is a rapidly developing approach to computational fluid dynamics (CFD)
It has been shown that an implementation of the cascaded lattice Boltzmann method can significantly reduce the spurious velocities found around curved interfaces in a multiphase system, which uses the Shan–Chen interparticle model to calculate the forcing term
Comparisons were made with an multiple relaxation time (MRT) implementation, in both cases the exact difference method was used, so differences between models due to the collision operator alone could be observed
Summary
The lattice Boltzmann method (LBM) is a rapidly developing approach to computational fluid dynamics (CFD). A number of improvements to the interaction potential model have been proposed, and can be divided into two categories; those that modify the force calculation, such as increasing the order of isotropy [13] or modifying the equation of state [14], and those that improve the incorporation of the force into the equilibrium distribution functions, such as the exact difference method (EDM) [15], and the method by Guo et al [16]. Geier et al [28] proposed the cascaded LBM, in which the collision operator relaxes moments in a co-moving reference frame, and showed improvements over results obtained using the MRT collision operator. This cascaded LBM is applied to the multiphase case, with results compared to an MRT implementation.
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