A coupled THINC/QQ and LS framework for simulating incompressible free-surface flows with surface tension

Abstract

In this paper, we propose a simple and accurate numerical framework for simulating incompressible free-surface flows with surface tension on fixed Eulerian grids. For capturing moving interfaces, we developed a novel interface capturing scheme by coupling the THINC/QQ (THINC method with quadratic surface representation and Gaussian quadrature) and LS (Level Set) method. The new scheme, so-called THINC/QQLS (coupled THINC/QQ and LS), possesses certain advantages, for instance, improving the accuracy of interface reconstruction, ensuring rigorous volume/mass conservation, and providing accurate LS field for computing surface tension force. In order to accurately calculate the interface curvature, we propose a simple and accurate curvature model. We verified the proposed THINC/QQLS scheme as well as the curvature model with classical benchmark tests and realistic free-surface flow simulations. Numerical results reveal that the proposed numerical framework can accurately capture free surfaces and provide an accurate approach for computing surface tension force and suppressing the parasitic currents.