Finite element implementation of an improved conservative level set method for two-phase flow

• Instead of Heaviside function, the normal vectors are evaluated from standard level set function.
• Excellent mass conservation properties and smoother interface were shown.
• The method can capture small structures of complicated interfaces very well even on medium grids.
• It requires little effort in coding compared with other coupling methods.
• It is implemented in a FEM context which is well capable of handling complex geometries and boundary conditions.

A novel improved conservative level set method is proposed to simulate two-phase flows in the finite element framework. The standard level set method can capture the interface smoothly and gives accurate normal vectors but suffers from an excessive amount of mass gain/loss. The conservative level set method exhibits excellent mass conservation properties but the results are usually contaminated by inaccurate interface normal vectors. To address this problem, an improved conservative level set method is proposed to capture the interface smoothly with excellent mass conservation properties. The improvement of the method lies in that the surface normal is computed from a signed distance function which is also advected and re-initialized in the flow fields instead of using the Heaviside function. The proposed method is implemented by an implicit two-step Taylor–Galerkin approximation together with the fractional step algorithm within the finite element context. The approach is validated with well-known benchmark problems, including the long term advection of a circle, rotation of a slotted disk, stretching of a circular, dam-break flow and the Rayleigh–Taylor instability problem. The results from the proposed method show good agreement with existing experimental and numerical published results and are found to be highly reliable and accurate.