An Eulerian interface sharpening algorithm for compressible two-phase flow: The algebraic THINC approach

We describe a novel interface-sharpening approach for efficient numerical resolution of a compressible homogeneous two-phase flow governed by a quasi-conservative five-equation model of Allaire et al. (2001) [1]. The algorithm uses a semi-discrete wave propagation method to find approximate solution of this model numerically. In the algorithm, in regions near the interfaces where two different fluid components are present within a cell, the THINC (Tangent of Hyperbola for INterface Capturing) scheme is used as a basis for the reconstruction of a sub-grid discontinuity of volume fractions at each cell edge, and it is complemented by a homogeneous-equilibrium-consistent technique that is derived to ensure a consistent modeling of the other interpolated physical variables in the model. In regions away from the interfaces where the flow is single phase, standard reconstruction scheme such as MUSCL or WENO can be used for obtaining high-order interpolated states. These reconstructions are then used as the initial data for Riemann problems, and the resulting fluctuations form the basis for the spatial discretization. Time integration of the algorithm is done by employing a strong stability-preserving Runge–Kutta method. Numerical results are shown for sample problems with the Mie–Grüneisen equation of state for characterizing the materials of interests in both one and two space dimensions that demonstrate the feasibility of the proposed method for interface-sharpening of compressible two-phase flow. To demonstrate the competitiveness of our approach, we have also included results obtained using the anti-diffusion interface sharpening method.