Tetrahedral adaptive mesh refinement for two-phase flows using conservative level-set method

Abstract

In this article, we describe a parallel adaptive mesh refinement strategy for two-phase flows using tetrahedral meshes. The proposed methodology consists of combining a conservative level-set method with tetrahedral adaptive meshes within a finite volume framework. Our adaptive algorithm applies a cell-based refinement technique and adapts the mesh according to physics-based refinement criteria defined by the two-phase application. The new adapted tetrahedral mesh is obtained from mesh manipulations of an input mesh: operations of refinement and coarsening until a maximum level of refinement is achieved. For the refinement method of tetrahedral elements, geometrical characteristics are taking into consideration to preserve the shape quality of the subdivided elements. The present method is used for the simulation of two-phase flows, with surface tension, to show the capability and accuracy of 3D adapted tetrahedral grids to bring new numerical research in this context. Finally, the applicability of this approach is shown in the study of the gravity-driven motion of a single bubble/droplet in a quiescent viscous liquid on regular and complex domains.