Evaluation of the finite element lattice Boltzmann method for binary fluid flows

Abstract

In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underly- forcing terms in the advection term, the current scheme applies collision and forcing terms locally for a simpler finite element formulation. A series of thorough benchmark studies reveal that this does not compromise stability and that the scheme is able to accurately simulate flows at large density and viscosity contrasts.

Finite-element lattice Boltzmann simulations of contact line dynamics

“…We assess the performance of the scheme by first considering a droplet with radius R in a stationary flow. The average parasitic kinetic energy in the interfacial region R ± ξ of the droplet is reported in Table I for the mixed scheme described in Section II C alongside values obtained using the nodal discretization presented in our earlier work [30]. The mixed discretization scheme is observed to succesfully decrease the parasitic currents by two orders of magnitude compared to the nodal discretization.…”

“…whereψ eq α = ψ eq α , τ = λ/δt, and the moments ofψ recover the same macroscopic fields as the moments of ψ. The force term can be treated in an implicit manner and integrated locally in the collision step [30]. It is observed, however, that integrating the force term in the streaming step as done in [29] greatly enhances stability when simulating surface wettability, and allows to minimize spurious currents through careful selection of the spatial discretization scheme (as discussed in greater detail below).…”

“…A different class of LBM exists generally known as offlattice Boltzmann methods, where the spatial and temporal discretizations are decoupled for enhanced geometric flexibility. This class consists of finite volume [22][23][24] and finite element schemes [25][26][27][28][29][30]. However, previ- * rastin@nbi.ku.dk † misztal@nbi.ku.dk ous work on multiphase finite element LBM (FE-LBM) has only regarded the intermolecular force term [29,30] and liquid-solid interactions have not been accounted for.…”

“…This class consists of finite volume [22][23][24] and finite element schemes [25][26][27][28][29][30]. However, previ- * rastin@nbi.ku.dk † misztal@nbi.ku.dk ous work on multiphase finite element LBM (FE-LBM) has only regarded the intermolecular force term [29,30] and liquid-solid interactions have not been accounted for. In this paper we present an extension of our previous characteristic-based FE-LBM scheme [30] by implementing wetting boundary conditions and moving the intermolecular force term to the streaming step.…”

“…However, previ- * rastin@nbi.ku.dk † misztal@nbi.ku.dk ous work on multiphase finite element LBM (FE-LBM) has only regarded the intermolecular force term [29,30] and liquid-solid interactions have not been accounted for. In this paper we present an extension of our previous characteristic-based FE-LBM scheme [30] by implementing wetting boundary conditions and moving the intermolecular force term to the streaming step. Our formulation is shown to further reduce spurious currents at equilibrium compared to the implementation in [30].…”