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

Benjamin Lalanne (1) , Lucia Rueda Villegas (1) , Sébastien Tanguy (1) , Frédéric Risso (1)

1 IMFT - Institut de mécanique des fluides de Toulouse

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, of Kang and al. [10] and Sussman and al. [23], propose very different approaches to deal with viscous terms. However, few information on their respective efficiency is currently available. In this paper, we present theoretical and numerical results to show that these two approaches are equivalent from a continuous point of view and we compare their accuracies in relevant test-cases. As these two approaches are not perfectly suited to every situation, since methods presented in [10] cannot be used if phase change occurs whereas methods proposed in [23] can hardly be used with an implicit temporal discretization of the viscous terms, we also propose a new method for both situations. In addition, the efficiency of Delta Function method [22] is also assessed and compared to the three previous ones allowing a detailed overview on the accuracy of each method. The test-cases involve configurations where viscosity is a relevant phenomenon and where theoretical results or experimental data can provide references solutions: simulations of spherical rising bubbles, shape-oscillating bubbles and deformed rising bubbles at low Reynolds numbers.

Mots clés: Level Set; Ghost Fluid Method; Two-phase flows; Viscosity jump condition

Domaines: Physique Numérique [physics.comp-ph]

Benjamin Lalanne, Lucia Rueda Villegas, Sébastien Tanguy, Frédéric Risso. On the computation of viscous terms for incompressible two-phase flows with Level Set/Ghost Fluid Method. Journal of Computational Physics, 2015, vol. 301, pp.289-307. ⟨10.1016/j.jcp.2015.08.036⟩. ⟨hal-01308135⟩