  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 K\"orner 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.

Numerical Analysis;Fluid Dynamics