A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using level set methods

Many multiphase flows relevant to natural phenomena and technical applications are characterized by large density ratios between the phases or fluids. Numerical simulations of such flows are especially challenging if the phase interface has a complex shape and is subject to large shear. This scenario is typical for atomization of liquids under ambient conditions. In this paper we discuss some of the reasons why one-fluid level-set based methods are prone to become unstable for high-density ratio/high shear atomizing flows and present a consistent rescaled momentum transport method that addresses the identified shortcomings. We present results obtained with the new method for a number of high-density ratio test cases, including the advection of a 1 000 000:1 density ratio impulsively accelerated drop, a 1000:1 density ratio damped surface wave, and the collapse of a water column in air under ambient conditions. The new method shows significantly improved results compared to standard level set based single-fluid methods.