Improved lattice Boltzmann modeling of binary flow based on the conservative Allen Cahn equation.
The primary and key task of binary fluid flow modeling is to track the interface with good accuracy, which is usually challenging due to the sharp interface limit and numerical dispersion. This article concentrates on further development of the conservative Allen Cahn equation (ACE) [Geier et al. Phys. Rev. E 91, 063309 (2015)10.1103/PhysRevE.91.063309] under the framework of the lattice Boltzmann method (LBM) with incorporation of the incompressible hydrodynamic equations [Liang et al. Phys. Rev. E 89, 053320 (2014)10.1103/PhysRevE.89.053320] Utilizing a modified equilibrium distribution function and an additional source term, this model is capable of correctly recovering the conservative ACE through the Chapman Enskog analysis. We also simulate four phase tracking benchmark cases, including one three dimensional case; all show good accuracy as well as low numerical dispersion. By coupling the incompressible hydrodynamic equations, we also simulate layered Poiseuille flow and the Rayleigh Taylor instability, illustrating satisfying performance in dealing with complex flow problems, e.g. high viscosity ratio, high density ratio, and high Reynolds number situations. The present work provides a reliable and efficient solution for binary flow modeling.
Physical review. E