Mass Preserving Finite Element Implementations of Level Set Methods

Code:
MOX 60
Title:
Mass Preserving Finite Element Implementations of Level Set Methods
Date:
Friday 20th May 2005
Author(s):
Di Pietro, Daniele A., Lo Forte, Stefania; Parolini, Nicola
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Abstract:
In the last two decades, the level set method has been extensively used for the numerical solution of interface problems in different domains. The basic idea is to embed the interface as the level set of a regular function. In this paper we focus on the numerical solution of hypervolic interface advection equations which appears in free-surface fluid dynamics problems, where naive finite element implementations are unsatisfactory. As a matter of fact, practitioners in fluid dynamics often complain that the mass of each fluid component is not conserved, a phenomenon which is therefore often referred to a mass loss. In this paper we propose and compare two finite element implementations that cure this ill-behaviour without the need to resort to spurius strategies (such as, e.g., particle level set). The first relies on a discontinuous Galerkin discretization, which is known to give very good performance when facing hyperbolic problems the second is a stabilized continuous FEM implementation based on the stabilization method presented in [1], which is free from many of the problems that classical methods exhibit when applied to unsteady problems.