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

Abstract

SummaryIn 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.

Unstructured Level-Set Method For Saturated Liquid-Vapor Phase Change

“…Validations, verifications and extensions of the unstructured CLS method without phase change [10,15] have been reported in our previous works, for instance: buoyancy-driven rising bubbles [10,11,9,5,4], thermocapillary-driven motion of droplets [14,6], bubbly flows [13,9,15,16], falling droplets [8], binary droplet collision with bouncing outcome [13], bouncing collision of a droplet against a fluid-fluid interface [13], Taylor bubbles [26,27,4], gas-liquid jets [45], deformation of droplets under shear stresses [2,12], non-Newtonian two-phase flow [3], and mass transfer in bubbly flows [15,16,7]. Furthermore, a comparison of the unstructured CLS method [10] and coupled VoF-LS method [12] is reported in [8].…”

A finite volume coupled level set and volume of fluid method with a mass conservation step for simulating two-phase flows

“…Various studies have proposed different methodologies for improving mass conservation of the LS method 21,22,23,18,24,25,26,27,28,29,30,31,32 . The particle level set (PLS) in 18 is a semi-lagrangian level set method based on the advection of particles at both sides of the interface.…”

A massively parallel accurate conservative level set algorithm for simulating turbulent atomization on adaptive unstructured grids

“…In this work, the Accurate Conservative Level Set (ACLS) method is used to capture the interface on 2D and 3D unstructured grids: this method accurately predicts the interface dynamics while conserving liquid mass [23,24,25]. ACLS on unstructured grids has been proposed before in [12,13] on static meshes, and by Antepara et al [26] for adaptive tetrahedral grids. In this latter, non-conforming AMR with an octree data structure is used.…”