Second-order model for free surface convection and interface reconstruction

Abstract

To improve the numerical analysis of free surface convection and interface reconstruction, both first- and second-order algorithms are developed based on the volume-of-fluid method. The methodology applied to the second-order model is to define the second-order linear curve having both face slopes as near horizontal as possible while satisfying the cell's defined volume fraction. The second-order method is compared with the FLAIR method and the first-order method through simulation of the convection for various sizes of circular liquid shapes and solitary waves. For small curvature of the free surface, e.g. circles with large diameter, linear methods such as the FLAIR method and the first-order method show relatively good predictions. However, for large-curvature configurations, e.g. circles with relatively small diameter or solitary waves, the linear approach shows large distortion of the free surface. In contrast, the second-order model always shows powerful prediction capabilities of free surface convection. © 1998 John Wiley & Sons, Ltd.