Evaluation of the Finite Element Lattice Boltzmann Method for Binary Fluid Flows

TL;DR

This paper evaluates an off-lattice finite element lattice Boltzmann method that efficiently simulates binary fluid flows with large property contrasts, maintaining stability and accuracy with larger time steps.

Contribution

It introduces a characteristic-based streaming integration combined with a free-energy multiphase model, enabling larger time steps and simplified local collision and forcing terms.

Findings

Stable simulations at high density and viscosity contrasts.

Time steps over an order of magnitude larger than relaxation time.

Accurate results confirmed through comprehensive benchmarks.

Abstract

In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex boundaries. The current work combines characteristic-based integration of the streaming step with the free-energy based multiphase model by Lee et. al. [Journal of Computational Physics, 206 (1), 2005 ]. This allows for simulation time steps more than an order of magnitude larger than the relaxation time. Unlike previous work by Wardle et. al. [Computers and Mathematics with Applications, 65 (2), 2013 ] that integrated intermolecular 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.