A comparison between the surface compression method and an interface reconstruction method for the VOF approach

In direct numerical simulations of multiphase flows, based on the Volume of Fluid (VOF) approach, the advection of the volume fraction field is a crucial point. The choice of the discretisation scheme for the transport of the volume fraction is decisive for an accurate description of surface dynamics. In this paper we assess two numerical methods: a high order discretisation scheme, namely the surface compression scheme, and an interface reconstruction scheme based on a piecewise linear interface calculation (PLIC). We compare accuracy, convergence rate and computational cost of these methods with results from literature. The comparative study includes reference 2D and 3D advection test cases. Moreover, the advection algorithm is tested coupled to an incompressible Navier-Stokes solver and used to simulate a rising bubble in a liquid for different Eötvös and Reynolds numbers. We establish via the advection tests and through the study of rising bubbles that the PLIC method converges to second order while the compression method fails to converge systematically. The computational overhead of both methods is negligible compared to an incompressible flow solver to which it might be coupled.