A simple interface sharpening technique with a hyperbolic tangent function applied to compressible two-fluid modeling

Abstract

A simple interface sharpening technique based on hyperbolic tangent interpolation, which was proposed in the previous study [F. Xiao, Y. Honma, K. Kono, A simple algebraic interface capturing scheme using hyperbolic tangent function, Int. J. Numer. Methods Fluids 48 (2005) 1023–1040], is applied to the compressible two-fluid modeling. The implementation of this scheme is very simple: the interpolation of the volume fraction in the monotonicity-upwind-scheme-for-conservation-law (MUSCL) solver is just replaced by the hyperbolic tangent interpolation, while the MUSCL interpolations for other variables are maintained. This technique is limited for the region near the interface to prevent the spurious oscillations of a minor phase. The one-dimensional and two-dimensional problems are solved, and the results are compared with those of the original MUSCL solver. The results show that the interface is significantly sharpened with this technique, and its sharpness is well controlled by one parameter. In addition, the robustness of the scheme does not change with sharpening the interface in the range we investigated.