A novel steepness-adjustable harmonic volume-of-fluid method for interface capturing

Abstract

The algebraic volume-of-fluid (VOF) method based on the construction strategy of switching technique has received extensive attention recently. However, all the previous algebraic VOF methods were constructed by combining different methods of compressible differencing scheme (CDS) and the high resolution scheme (HRS), which would switch back and forth in most cases. Thus the final algebraic VOF method usually becomes to be complicated, and the numerical instabilities would be increased. In this paper, a novel algebraic VOF method, without the operations of switching back and forth, is constructed within a unified framework of the steepness-adjustable harmonic (SAH) scheme (He et al. (2022) [33]). A thorough validation of the present method is conducted, examining the pure advection of the interface indicator function. The results indicate that the present method can resolve the interface capturing with substantially low numerical diffusion and low numerical oscillations.