Boundary Conditions for Free Interfaces with the Lattice Boltzmann Method

TL;DR

This paper introduces a new second-order accurate boundary scheme for the lattice Boltzmann method to simulate free surface flows, improving upon the first-order accuracy of previous methods.

Contribution

A novel free surface boundary scheme for LBM that accounts for surface position and orientation, achieving second-order accuracy in 3D flow simulations.

Findings

The new scheme is second order accurate, unlike the previous first order method.

Numerical experiments confirm the improved accuracy of the new boundary treatment.

The method effectively captures free surface dynamics with higher precision.

Abstract

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.