An improved CE/SE scheme for incompressible multiphase flows and its applications

Abstract

A new space-time conservation element-solution element (CE/SE) scheme, which is based on the hexahedron mesh, is proposed by constructing a new structure of solution elements (SEs) and conservation elements (CEs) and extended to two-dimensional incompressible multiphase flows. This scheme is applied to several incompressible flow problems, such as lid-driven cavity flow, dam break flow, motions of falling droplets, flow instability and water-kerosene interaction. The numerical results and their comparison with lecture results and experimental data are presented. The comparisons demonstrate that the computational scheme developed currently is clear in physical concept, easy to be implemented and highly accurate and efficient for the above-mentioned problems. The highlight is that the pretreatment method is proposed, transforming the elliptic-parabolic equations to the hyperbolic equations, which can be directly simulated by the improved CE/SE scheme. Thus, the improved CE/SE scheme can be applied to incompressible multiphase flows widely.