A Level Set Approach for Dynamics of Flow in Accelerating Rectangular Container

Abstract

The level set approach is a numerical technique to capture the interface for a system of two immiscible fluids separated by a sharp interface. Since the interface is captured by an implicit function using this approach, this is a Eulerian formulation of the evolution of interface. The different fluids must be identified by using a marker function, called the level set function that takes different values in the various fluids. The present work uses a level set approach for modeling the dynamics of flow and the shape of the liquid free surface in a partly filled rectangular tank which is subjected to an impulsive motion from rest. The governing equations are written about a non-inertial frame attached to the container in motion. Extremely high viscosity and density ratios of the two immiscible fluids make the problem more challenging. The surface tension forces are ignored in this study. The signed distance property of the level set function is retained by using the reinitialization algorithm. In the present study, we have compared the computed shapes of equilibrium free surface with theoretically predicted shapes at equilibrium.