Numerical study of incompressible interfacial flows by an one-step level set method

Abstract

We develop a two-phase flow model for solving the nonlinear level set (LS) equation and Navier-Stokes equations in two dimension. In the proposed one-step LS method, the sharp interface is captured by implicitly representing the zero LS contour. The nonlinear LS equation is solved by upwinding Combined Compact Difference (CCD) scheme for the convection terms and center difference scheme for the other terms in space for predicting propagation of interface. Within the framework of Navier-Stokes solver, the semi-implicit Gear algorithm on a semi-staggered fixed grid is used for velocity-pressure coupling. The interface normal and curvature are calculated in terms of a hyperbolic tangent profile across the interface. To verify the proposed LS method, we consider reversed single vortex and Zalesak’s cases which are amenable to exact solutions. The proposed two-phase model is also investigated by solving the dam-break, Rayleigh-Taylor instability and bubble rising problems.

Disclosure statement

We declare no conflicts of interest to this work.

Additional information

Funding

RuiDong An and ChingHao Yu acknowledge support by National Natural Science Foundation of China under the grant No. 51979178, Department of Science and Technology of Sichuan Province under the grant No. 2019YJ0118, Fundamental Research Funds for the Central Universities under the grant No. YJ201837 and Innovation Spark Project under the grant No. SCUH0049 for this research. Yan-Ting Lin would like to thank the Ministry of Science and Technology for funding the project under project No. MOST 108-3116-F-042A-006.