A coupled volume-of-fluid and level set method based on general curvilinear grids with accurate surface tension calculation

In this paper, a coupled volume-of-fluid (VOF) and level set (LS) method on general curvilinear grids, combining the advantages of VOF method and LS method is developed for interfacial flow simulations. In this method, an iterative geometric operation is introduced to calculate the level set function on physical domain and computational domain. In particular, a direct construction of the distance function is successfully implemented on the physical domain and thus the numerical error induced by contravariant transformation from the computational domain could be avoided. The level set based continuum surface tension (CSF) model on curvilinear grids is derived to model surface tension accurately, and then the model as well as the proposed coupled volume tracking method is incorporated into an incompressible Navier–Stokes solver. Finally, four benchmark problems including time-reversed single vortex flow, static droplet, dam break and single bubble rising problems are tested on irregular domains to validate the accuracy and robustness of the proposed method to deal with complex domains. The results show good agreement with previous experimental data or numerical results, good characteristics of mass conservation are also observed, indicating that the present method can accurately simulate incompressible two-phase flows.