Comparison of refilling schemes in the free-surface lattice Boltzmann method

TL;DR

This paper compares five refilling schemes in the free-surface lattice Boltzmann method across diverse fluid dynamics scenarios, finding that the simplest equilibrium-based scheme offers the best stability, accuracy, and efficiency.

Contribution

It provides a comprehensive comparison of refilling schemes in FSLBM, highlighting the superiority of a simple equilibrium-based approach for stability and performance.

Findings

The equilibrium-based scheme is most stable and accurate.

Some schemes are numerically unstable in certain scenarios.

The simplest equilibrium scheme is recommended for practical use.

Abstract

Simulating mobile liquid-gas interfaces with the free-surface lattice Boltzmann method (FSLBM) requires frequent re-initialization of fluid flow information in computational cells that convert from gas to liquid. The corresponding algorithm, here referred to as the refilling scheme, is crucial for the successful application of the FSLBM in terms of accuracy and numerical stability. This study compares five refilling schemes that extract information from the surrounding liquid and interface cells by averaging, extrapolating, or assuming one of the three different equilibrium states. Six numerical experiments were performed, covering a broad spectrum of possible scenarios. These include a standing gravity wave, a rectangular and cylindrical dam break, a Taylor bubble, a drop impact into liquid, and a bubbly plane Poiseuille flow. In some simulations, the averaging, extrapolation, and one equilibrium-based scheme were numerically unstable. Overall, the results have shown that the simplest equilibrium-based scheme should be preferred in terms of numerical stability, computational cost, accuracy, and ease of implementation.