surface lattice Boltzmann method (FSLBM). The FSLBM is a volume-of-fluid-based approach for

simulating multiphase flow in which the dynamic of the lighter and less viscous phase, i.e., the gas

phase, is neglected. Therefore, the problem essentially reduces to a free surface problem where fluid

flow is only simulated in the liquid phase. The computational domain is split into gas and liquid

cells which are separated by a closed layer of interface cells. As flow is not simulated in gas cells,

particle distribution functions (PDFs) are only available in liquid and interface cells. Thus, the

PDFs streaming from gas to liquid are unknown and need to be reconstructed with respect to a free

surface boundary condition. In the original approach [1], not only missing PDFs are reconstructed

but also PDFs that are already known. This, however, discards available and valid information

such that one might consequentially consider reconstructing only those PDFs that are actually

missing. Some authors have mentioned that the latter approach avoids anisotropic artifacts [2],

while others have not found any significant difference in their simulation results when comparing

the two approaches [3].

We theoretically analyze and compare these two approaches and validate them with different

numerical simulation setups.

[1] C. Körner, M. Thies, T. Hofmann, N. Thürey, and U. Rüde, “Lattice Boltzmann Model for

Free Surface Flow for Modeling Foaming,” Journal of Statistical Physics, vol. 121, no. 1, 2005.

doi: 10.1007/s10955-005-8879-8.

[2] S. Bogner, R. Ammer, and U. Rüde, “Boundary conditions for free interfaces with the lattice

Boltzmann method,” Journal of Computational Physics, vol. 297, 2015. doi: 10.1016/j.jcp.

2015.04.055.

[3] Y. Thorimbert, B. Chopard, and J. Lätt, “Implementation of lattice Boltzmann free-surface

and shallow water models and their two-way coupling,” MethodsX, vol. 8, 2021. doi: 10.1016/

j.mex.2021.101338.