A new interface capturing method based on double interface functions

We describe a novel double-interface-function (DIF) reconstruction method for efficient numerical resolution of a compressible two-phase flow. Based on the new method, double sine interface capturing scheme (DSINC) is obtained. Five-equation model is solved to analyze the effect of different interface functions such as DIF and Single Interface function (SIF) on the interfaces captured numerically. Near the interfaces, the algorithm uses the DIF or SIF as a basis for the reconstruction of a sub-grid discontinuity of volume fractions. In regions away from the interfaces, WENO is used to reconstruct the convective term, and time integration of the algorithm is done by employing the TVD Runge-Kutta method. Comparing with tangent of hyperbola for interface capturing (THINC) using SIF method, the left and right states reconstructed by DSINC is simpler and we need not solve a transcendental equation. Numerical results are shown with the Mie-üneisen equation of state (EOS) for sample problems such as discontinuous advection, two-phase triple problem and shock-bubble interaction problem with THINC and DSINC. It can be found that DSINC is able to get as efficient resolution interface as THINC and shows to be more stable in the simulation.