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

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. This work has been financially supported by the Ministerio de Economía y Competitividad, Secretaría de Estado de Investigación, Desarrollo e Innovación, Spain (ENE2017-88697-R), and by Termo Fluids S.L. Oscar Antepara acknowledges financial support in form of a doctoral scholarship DI-14-06886 of the Ministerio de Economía y Competitividad and 2015DI-68 of the Secretaria d’ Universitats i Recerca del Departament d’Economia i Coneixement de la Generalitat de Catalunya, Spain. Néstor Balcázar acknowledges financial support of the Programa Torres Quevedo, Ministerio de Economía y Competitividad, Secretaría de Estado de Investigación, Desarrollo e Innovación (PTQ-14-07186), Spain. Three-dimensional simulations were carried out using computer time provided by PRACE 14th Call (Project 2016153612) and RES project(FI-2018-1-0025) through the MareNostrum IV supercomputer based in Barcelona, Spain. We acknowledge Santander Supercomputacion support group at the University of Cantabria who provided access to the supercomputer Altamira Supercomputer at the Institute of Physics of Cantabria (IFCA-CSIC), member of the Spanish Supercomputing Network, for performing simulations/analyses (RES project FI-2018-3-0037).