An Interface-Capturing Approach with Bounded Continuous Renormalization for Free Surface Flows

Abstract

An interface capturing approach based on a level set function for simulating transient twofluid viscous incompressible flows is presented. Each fluid is indicated with a positive or negative value of the level set function, corresponding to a liquid phase and a gaseous one, respectively, in the particular case of free surface flows, where the interface is represented by the zero level set. The methodology is numerically solved in three stages: the first one is a two-fluid Navier–Stokes solver, followed by an advective step for transporting the level set function. The third stage consist in the level set function correction through a bounded renormalization with continuous penalization which keeps certain properties over the transition between fluids. The proposed procedure, and particularly the renormalization stage, are evaluated in different typical cases: advection-renormalization examples and fluid-advectionrenormalization problems.