Treating moving interfaces in thermal models with the C-NEM

This paper deals with the description of a new numerical simulation technique based in the constrained natural element method, a novel meshless method, able to compute multiphase thermal problems with moving interfaces without requiring the frequent mesh updating characteristics of interfaces tracking finite element techniques. This strategy combines some of the ideas of the natural element method with a particular treatment of the moving boundaries and interfaces involving discontinuities of some fields.

[1]  F. Chinesta,et al.  A new extension of the natural element method for non‐convex and discontinuous problems: the constrained natural element method (C‐NEM) , 2004 .

[2]  B. Nayroles,et al.  Generalizing the finite element method: Diffuse approximation and diffuse elements , 1992 .

[3]  M. Sambridge,et al.  Geophysical parametrization and interpolation of irregular data using natural neighbours , 1995 .

[4]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[5]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[6]  T. Belytschko,et al.  MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD , 2001 .

[7]  Daniel R. Lynch,et al.  Continuously deforming finite elements for the solution of parabolic problems, with and without phase change , 1981 .

[8]  R. Sibson.  A vector identity for the Dirichlet tessellation , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  Oden,et al.  An h-p adaptive method using clouds , 1996 .

[10]  E. Schönhardt,et al.  Über die Zerlegung von Dreieckspolyedern in Tetraeder , 1928 .

[11]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[12]  David L. Chopp,et al.  A hybrid extended finite element/level set method for modeling phase transformations , 2002 .

[13]  B. Moran,et al.  Natural neighbour Galerkin methods , 2001 .

[14]  R. Lewis,et al.  Finite element simulation of metal casting , 2000 .

[15]  Elías Cueto,et al.  On the imposition of essential boundary conditions in natural neighbour Galerkin methods , 2003 .

[16]  T. Belytschko,et al.  THE NATURAL ELEMENT METHOD IN SOLID MECHANICS , 1998 .

[17]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[18]  Jonathan Richard Shewchuk,et al.  Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations , 2000, SCG '00.

[19]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[20]  John E. Dolbow,et al.  Solving thermal and phase change problems with the eXtended finite element method , 2002 .

[21]  Jiun-Shyan Chen,et al.  A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .

[22]  W. Shyy,et al.  Computation of Solid-Liquid Phase Fronts in the Sharp Interface Limit on Fixed Grids , 1999 .

[23]  Kokichi Sugihara,et al.  Improving continuity of Voronoi-based interpolation over Delaunay spheres , 2002, Comput. Geom..

[24]  Cornelis Vuik,et al.  Some historical notes about the Stefan problem , 1993 .

[25]  Jonathan Richard Shewchuk,et al.  Tetrahedral mesh generation by Delaunay refinement , 1998, SCG '98.

[26]  Philippe Lorong,et al.  Interpolation naturelle sur les domaines non convexes par l'utilisation du diagramme de Voronoï contraint , 2003 .