An interface capturing method with a continuous function: The THINC method on unstructured triangular and tetrahedral meshes

A novel interface-capturing method is proposed to compute moving interfaces on unstructured grids with triangular (2D) and tetrahedral (3D) elements. Different from the conventional VOF (volume of fluid) method which involves geometric reconstructions of the interface, the present method is based on the algebraic reconstruction approach originally developed in the THINC (tangent of hyperbola interface capturing) scheme by Xiao et al. (2005) [17]. A continuous multidimensional hyperbolic tangent function is employed for retrieving the jump-like distribution of the indicator function, which avoids the explicit geometric representation of the interface and thus substantially reduces the algorithmic complexity in unstructured grids. Numerical diffusion and smearing are effectively eliminated, and the compact thickness of the jump transition layer in the volume fraction is retained throughout the computation even for largely deformed interface. The solution quality of the present scheme is comparable to the VOF method with PLIC (piecewise linear interface calculation) algorithm.