Numerical Simulation of Rayleigh-Taylor Instability With Two-Fluid Model and Interface Sharpening

The free surface flows are successfully modeled with one of the existing free surface models, such as: level set method, volume of fluid method, front tracking method, two-fluid model (two momentum equations) with modified interphase force and some others. The main disadvantage of the two-fluid model used for simulations of free surface flows is numerical diffusion of the interface, which can be significantly reduced as presented in this paper. The interface is sharpened with the conservative level set method, where after the advection step of volume fraction the numerical diffusion of the interface is reduced in such a way that the thickness of the interface is kept constant during the simulation. The reduction of the interface diffusion can also be called interface sharpening. In the present paper the two-fluid model with interface sharpening is validated with Rayleigh-Taylor instability. Under assumptions of isothermal and incompressible flow of two immiscible fluids, we simulated a system with the fluid of higher density located above the fluid of smaller density in two dimensions. Due to the gravity in the system, the fluid with a higher density moves below the fluid with a smaller density. The initial condition is not a flat interface between the fluids, but a cosine wave with small amplitude, which develops into a mushroom-like structure. Mushroom-like structure in simulation of Rayleigh-Taylor instability later develops into small droplets as result of numerical dispersion of interface (interface sharpening) or to narrow trails with interface diffusion (no interface sharpening). The results of the two-fluid model with interface sharpening are compared to two-fluid model without interface sharpening and single-fluid-model with/without interface sharpening. The analytic solution of amplitude growth can be found for small amplitudes and was also compared to simulation.