A conservative finite volume method for incompressible two-phase flows on unstructured meshes

• Published in: Numerical heat transfer. Part B, Fundamentals Fundamentals, 2024-04, Vol.85 (4), p.426-453
• Main Authors: Parameswaran, S., Mandal, J. C.
• Format: Article
• Language: English
• Subjects: Artificial compressibility method; Compressibility; conservative level set method; contact capturing schemes; Finite element method; Finite volume method; Fluid flow; Incompressible flow; multiphase flow; Robustness (mathematics); Surface tension; Topology; Two phase flow; unstructured mesh
• ISSN: 1040-7790; 1521-0626
• DOI: 10.1080/10407790.2023.2236791

A robust finite volume framework for solving incompressible two-phase flow problems based on an explicit dual-time stepping based artificial compressibility formulation has been developed by Parameswaran and Mandal (2019) for structured meshes. This artificial compressibility framework is extended to unstructured meshes in the present paper. In order to further enhance the applicability to real life engineering problems, the surface tension effect is also modeled here. To deal with arbitrary unstructured mesh topology, least square and Green-Gauss integral based methods are used. The efficacy of the proposed method is demonstrated using a set of scalar advection based test problems and a set of standard incompressible two-phase flow test problems involving gravitational, viscous and surface tension forces. The numerical results show improvement in accuracy compared to the results of the structured mesh formulation.