Coupled THINC and level set method: A conservative interface capturing scheme with high-order surface representations

Highlights: • Volume of fluid method with high-order representation for moving interface. • Rigorous conservation of mass/volume of the transported VOF field. • Sub-grid resolution for fine interfacial structures that are smaller than mesh size. • Easy-to-code and straightforward algorithm for 3D unstructured-grid. • Verified superior solution quality in comparison with classical VOF methods. In this paper, we propose a simple and accurate numerical method for capturing moving interfaces on fixed Eulerian grids by coupling the Tangent of Hyperbola Interface Capturing (THINC) method and Level Set (LS) method. The innovative and practically-significant aspects of the proposed method, so-called THINC/LS method, lie in (1) representing the interface with polynomial of high-order (arbitrary order in principle) rather than the plane representation commonly used in the Piecewise Linear Interface Calculation (PLIC) Volume of fluid (VOF) methods, (2) conserving rigorously the mass of the transported VOF field, (3) being able to resolving fine interface structures under mesh resolution, and (4) providing a straightforward and easy-to-code algorithm for 3D implementation. We verified the proposed scheme with the widely used benchmark tests. Numerical results show that this new method can obtain high-order accuracy for interface reconstruction and can produce more accurate results in capturing moving interfaces compared to the classical VOF methods.