An efficient level set remedy approach for simulations of two-phase flow based on sigmoid function

The current work presents an improved, concise and inexpensive remedy approach for level set methods to deal with the mass non-conservation issue especially in large-scale simulations, where computational cost is always a constraint limiting broad applications. In this work, a sigmoid function originated from the work of Olsson and Kreiss (2005) is further utilized to describe the local relationship between the signed distance function of level set method and the liquid volume fraction. An improved criterion on determining the correction within relevant cells is introduced. And the upwind scheme for curvature calculation is implemented to handle small and/or thin structures. Several benchmark validations and gas-liquid flow problems are carried out to assess the approach. The main advantage of this approach is that the additional CPU cost for multiphase solver caused by remedy procedure, when relative to that without remedy, can be greatly reduced from about 100% to less than 10%, making it suitable for large-scale simulations. This approach also gains a higher accuracy in predicting the interface location while inherits the good performance of the previous method on ensuring mass conservation. Analyses prove that the level set remedy approach is suitable and reliable in simulating two-phase flows.