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

Abstract

The free surface lattice Boltzmann method (FSLBM) is a combination of the hydrodynamic lattice Boltzmann method with a volume-of-fluid (VOF) interface capturing 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 reconstruction 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.

A paraboloid fitting technique for calculating curvature from piecewise-linear interface reconstructions on 3D unstructured meshes

“…Then, a surface is fit to these points using a least-squares approach. There exist a variety of methods for fitting a quadric surface to points [18][19][20], as well as direct paraboloid fitting to PLIC centroids as used by Scardovelli and Zaleski [13] and Bogner, Rde, and Harting [14]. However, we find curvature calculations from such approaches not to converge under grid refinement, in line with the findings of [13].…”

“…However, they both require iterative minimization algorithms, where at each iteration computational cells must be intersected with a quadratic surface. Another approach involves fitting a paraboloid surface to a neighborhood of points found from the interface reconstruction centers of mass [12][13][14]. Denner and Wachem [15] presented a method to calculate a least-squares quadratic fit to volume fraction data, from which curvature is calculated.…”

Direct simulation of liquid–gas–solid flow with a free surface lattice Boltzmann method

“…Further details and alternative curvature computation schemes can be found in ?? Bogner, Rüde, and Harting (2016).…”

A scalable and extensible checkpointing scheme for massively parallel simulations

“…wa LB erla and the integrated physics engine ( PE ) (Götz et al, 2008; Iglberger and Rüde, 2009; Preclik and Rüde, 2015) have been used to simulate processes from various disciplines including electron beam melting for additive manufacturing (Ammer et al, 2014a, 2014b), charged particles in microfluidic flows (Bartuschat and Rüde, 2015), flow in chaotic porous media (Gil et al, 2017), free surface flows (Bogner et al, 2016), sediment transport (Rettinger et al, 2017), and discrete particle flows (Rettinger and Rüde, 2018). Apart from those examples, wa LB erla ’s modularity allows to implement general stencil algorithms on structured grids.…”