On the computation of viscous terms for incompressible two-phase flows with Level Set/Ghost Fluid Method

• Published in: Journal of computational physics 2015-11, Vol.301, p.289-307
• Main Authors: Lalanne, Benjamin, Villegas, Lucia Rueda, Tanguy, Sébastien, Risso, Frédéric
• Format: Article
• Language: English
• Subjects: Accuracy; Bubbles; Computation; Computational fluid dynamics; Computational Physics; Computer simulation; Fluid flow; Ghost Fluid Method; Ghosts; Level Set; Mathematical models; Physics; Two-phase flows; Viscosity jump condition
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2015.08.036

In this paper, we present a detailed analysis of the computation of the viscous terms for the simulation of incompressible two-phase flows in the framework of Level Set/Ghost Fluid Method when viscosity is discontinuous across the interface. Two pioneering papers on the topic, Kang et al. [10] and Sussman et al. [26], proposed two different approaches to deal with viscous terms. However, a definitive assessment of their respective efficiency is currently not available. In this paper, we demonstrate from theoretical arguments and confirm from numerical simulations that these two approaches are equivalent from a continuous point of view and we compare their accuracies in relevant test-cases. We also propose a new intermediate method which uses the properties of the two previous methods. This new method enables a simple implementation for an implicit temporal discretization of the viscous terms. In addition, the efficiency of the Delta Function method [24] is also assessed and compared to the three previous ones, which allow us to propose a general overview of the accuracy of all available methods. The selected test-cases involve configurations wherein viscosity plays a major role and for which either theoretical results or experimental data are available as reference solutions: simulations of spherical rising bubbles, shape-oscillating bubbles and deformed rising bubbles at low Reynolds numbers.