Curvature estimation from a volume of fluid indicator function for the simulation of surface tension and wetting with a free surface lattice Boltzmann method

TL;DR

This paper improves the free surface lattice Boltzmann method by developing a new curvature estimation technique from the VOF indicator function, enhancing the simulation of surface tension and wetting effects.

Contribution

It introduces a novel least squares curvature reconstruction method for better interface curvature estimation in FSLBM, addressing errors in surface tension modeling.

Findings

Numerical results show reduced errors in velocity fields with the new curvature method.

FSLBM effectively simulates wetting effects at solid boundaries.

Limitations due to the simplified advection scheme are identified and discussed.

Abstract

The free surface lattice Boltzmann method (FSLBM) is a combination of the hydrodynamic lattice Boltzmann method (LBM) with a volume of fluid (VOF) interface apturing technique for the simulation of incompressible free surface flows. Capillary effects are modeled by extracting the curvature of the interface from the VOF indicator function and imposing a pressure jump at the free boundary. However, obtaining accurate curvature estimates from a VOF description can introduce significant errors. This article reports numerical results for three different surface tension models in standard test cases, and compares the according errors in the velocity field (spurious currents). Furthermore, the FSLBM is shown to be suited to simulate wetting effects at solid boundaries. To this end, a new method is developed to represent wetting boundary conditions in a least squares curvature econstruction technique. The main limitations of the current FSLBM are analyzed and are found to be caused by its simplified advection scheme. Possible improvements are suggested.