Numerical Simulations Of Moving Interfaces By Level Set Method In The Partition Of Unity Concept.

In this paper we present a hybrid eXtended Finite Element/Level Set Method to simulate a two dimensional moving interfaces. The discrete discontinuity (material interfaces) is treated by the extended finite element method (X-FEM), in the partition of unity concept, whereby interface discontinuities are completely independent of the mesh. In this context, the discontinuity is represented without explicitly meshing its shape and the moving interface simulations are carried out without any re-meshing. Enriched approximations to the velocities and deformation fields are developed in the context of the eXtended Finite-Element Method, and the level-set representation of the interface was used to model the evolution of the discontinuity interface in time. The X-FEM utilizes the partition of unity property, of the finite element shape functions to incorporate arbitrary enrichment functions into the approximation. An explicit Newmark algorithm and one-point integration scheme with hourglass mode control is used to update the discontinuous fields. Material interface simulations as well as some free surface simulations, follow theoretical aspects presented in. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]