Accurate hybrid AUSMD type flux algorithm with generalized discontinuity sharpening reconstruction for two-fluid modeling

Abstract

This paper presents a single-pressure-field two-fluid model with finite-volume discretization to solve the equations of motion of compressible multiphase flows. To capture the discontinuities caused by shock waves and fluid interfaces, we propose a generalized discontinuity sharpening technique that combines the conventional monotonic upstream scheme for conservation law (MUSCL) and tangent of hyperbola interface capturing (THINC) schemes. In addition, a slope ratio-weighted parameter, ζ, is used to control the proportion of values reconstructed by MUSCL and THINC, and we show that the present method can retain sharp interfaces when the value of the parameter β in the THINC scheme is set ranging from 1.6 to 3.0. Fluxes across various interfaces are evaluated using a hybrid AUSMD-type flux algorithm, where the mass flux and pressure induced on the cell faces are calculated using an approximate Riemann solver. The accuracy and robustness of the proposed method are validated by solving a series of one- and two-dimensional single-phase flows. Furthermore, complex wave patterns arising from two-dimensional shock bubble/water-column interactions are examined, which indicate that compared with the existing schemes applied to two-fluid modeling, the proposed scheme significantly sharpens the interfaces and captures more details of the flow features. Finally, simulations of a three-dimensional example of the liquid jet crossflow are conducted. The proposed scheme shows more details of the fluid interface, including the interfacial instabilities on the windward side of the liquid jet and droplet formation due to the breakup phenomenon in the downstream of the crossflow, than the existing schemes.