Analysis and comparison of boundary condition variants in the free‐surface lattice Boltzmann method

Abstract

The accuracy of the free‐surface lattice Boltzmann method (FSLBM) depends significantly on the boundary condition employed at the free interface. Ideally, the chosen boundary condition balances the forces exerted by the liquid and gas pressure. Different variants of the same boundary condition are possible, depending on the number and choice of the particle distribution functions (PDFs) to which it is applied. This study analyzes and compares four variants, in which (i) the boundary condition is applied to all PDFs oriented in the opposite direction of the free interface's normal vector, including or (ii) excluding the central PDF. While these variants overwrite existing information, the boundary condition can also be applied (iii) to only missing PDFs without dropping available data or (iv) to only missing PDFs but at least three PDFs as suggested in the literature. It is shown that neither variant generally balances the forces exerted by the liquid and gas pressure at the free surface. The four variants' accuracy was compared in five different numerical experiments covering various applications. These include a standing gravity wave, a rectangular and cylindrical dam break, a rising Taylor bubble, and a droplet impacting a thin pool of liquid. Overall, variant (iii) was substantially more accurate than the other variants in the numerical experiments performed in this study.

Numerical Simulation of Water and Mud Inrush Processes in Mountain Tunnels Using Coupled Lattice Boltzmann/Discrete Element Methods

“…A collision model for phase-resolved direct numerical simulation of sediment transport, coupling fluid-particle via the immersed moving boundary method [24,25], was presented [26]. Four variants of boundary conditions were analyzed and compared in terms of their accuracy in the free-surface lattice Boltzmann method [27]. A numerical framework, rooted in a multiple relaxation time lattice Boltzmann model and innovative discrete techniques, has been proposed for the simulation of compressible flows, offering enhanced accuracy and versatility [28].…”