A coupled level-set and tangent of hyperbola interface capturing (THINC) scheme with a single-step time integration for incompressible flows

Abstract

In this paper, we present a concise and efficient interface capturing scheme on polyhedral unstructured mesh with its numerical implementation for incompressible fluid simulation with surface tension. The so-called coupled Level-Set and Tangent of Hyperbola INterface Capturing scheme with a Consistent Single-step time integration (THINC/CSLS) updates both the volume-of-fluid (VOF) and level-set function simultaneously from a THINC reconstruction function. The proposed scheme has the potential to integrate the positive aspects of mass conservation from the VOF method and the accurate geometric representation from the level-set method. Other innovative and noteworthy aspects of the present scheme are listed as (1) an adaptive THINC reconstruction strategy is applied to ensure the boundness of the VOF function for various Courant–Friedrichs–Lewy (CFL) numbers and the high quality of the level-set function for surface tension; (2) a single-step update procedure for both VOF and level-set function is implemented for better algorithmic consistency and efficiency; (3) a well-adapted numerical model is developed for incompressible simulation with free surface for both structured and unstructured grids. A comprehensive numerical procedure is introduced and validated by various well-received benchmark tests. Convincing evidence suggests that the present scheme is both accurate and efficient compared with other most advanced methods.