Evaluation of the Finite Element Lattice Boltzmann Method for Binary   Fluid Flows
  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. 
Rastin Matin, Marek Krzysztof Misztal, Anier Hernandez-Garcia and   Joachim Mathiesen
physics.flu-dyn