Boundary conditions for free interfaces with the lattice Boltzmann method

In this paper we analyze the boundary treatment of the Lattice Boltzmann method for simulating 3D flows with free surfaces. The widely used free surface boundary condition of Körner is shown to be first order accurate. The article presents new free surface boundary schemes that are suitable for the lattice Boltzmann method and that have second order spatial accuracy. The new method takes the free boundary position and orientation with respect to the computational lattice into account. Numerical experiments confirm the theoretical findings and illustrate the the difference between the old and the new method.