Boundary Conditions for Free Interfaces with the Lattice Boltzmann Method
For researchers using LBM to simulate free surface flows, this work improves accuracy from first to second order, addressing a known bottleneck in boundary treatment.
The paper shows that the widely used free surface boundary condition for LBM is first-order accurate and proposes a new second-order accurate scheme that accounts for surface position and orientation, validated through numerical experiments.
In this paper we analyze the boundary treatment of the lattice Boltzmann method (LBM) for simulating 3D flows with free surfaces. The widely used free surface boundary condition of Körner et al. (2005) is shown to be first order accurate. The article presents a new free surface boundary scheme that is suitable for second order accurate simulations based on the LBM. The new method takes into account the free surface position and its orientation with respect to the computational lattice. Numerical experiments confirm the theoretical findings and illustrate the different behavior of the original method and the new method.