An explicit finite volume element method for solving characteristic level set equation on triangular grids

Abstract

Level set methods are widely used for predicting evolutions of complex free surface topologies, such as the crystal and crack growth, bubbles and droplets deformation, spilling and breaking waves, and two-phase flow phenomena. This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme. An explicit finite volume element method is developed to discretize the equation on triangular grids. Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time. The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension. The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.