Development of a compressive surface capturing formulation for modelling free-surface flow by using the volume-of-fluid approach

Abstract

With the aim of accurately modelling free-surface flow of two immiscible fluids, this study presents the development of a new volume-of-fluid free-surface capturing formulation. By building on existing volume-of-fluid approaches, the new formulation combines a blended higher resolution scheme with the addition of an artificial compressive term to the volume-of-fluid equation. This reduces the numerical smearing of the interface associated with explicit higher resolution schemes while limiting the contribution of the artificial compressive term to ensure the integrity of the interface shape is maintained. Furthermore, the computational efficiency of the the higher resolution scheme is improved through the reformulation of the normalised variable approach and the implementation of a new higher resolution blending function. The volume-of-fluid equation is discretised via an unstructured vertex-centred finite volume method and solved via a Jacobian-type dual time-stepping approach.