Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Belytschko T., Lu Y.Y., Gu L.: Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 37, 229–256 (1994)
Chen J.S., Wu C.T., Yoon Y.: A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering, 50,:435–466 (2001)
Cueto E., Cegoñino J., Calvo B., Doblaré M.: On the imposition of essential boundary conditions in Natural neighbor Galerkin Methods. Communications in Numerical Methods in Engineering, 19, 361–376 (2002)
Duarte C.A., Oden J.T.: An H-p adaptative method using clouds. Computer Methods in Applied Mechanics and Engineering 139, 237–262 (1996)
Hiyoshi H., Sugura K.: Improving continuity of Voronoi-based interpolation over Delaunay spheres. Computational Geometry, 22, 167–183 (2002)
Ji H., Chopp D., Dolbow J.E.: A hybrid finite element/level set method for modeling phase transformations. International journal for numerical methods 54, 1209–1233 (2002)
Ladevèze P.: Non Linear Computational Structural Mechanics. Springer:, New York (1998)
Lewis, R., Ravindran, K.: Finite element simulation of metal casting. International journal for numerical methods in engineering, 47, 93–102 (2000)
Liu W.K., Jun S., Zhang Y.F.: Reproducing Kernel Particle Methods. Int. J. Numer. Methods Fluids 21, 1081–1106 (1995)
Lucy L.B.: A numerical approach to the testing of fusion process. The astronomic journal 88, 1013–1024 (1977)
Lynch D., O’Neill K.: Continuously deforming finite elements for the solution of parabolic problems, with and without phase change. International Journal for Numerical Methods in Engineering, 17, 81–96 (1981)
Melenk, J.M., Babusžka, I.: The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 139, 289–314 (1996)
Merle R., Dolbow J.E.: Natural neighbor Galerkin methods. Solving thermal and phase change with the extended finite element method, 28(5), 339–350 (2002)
Nayroles B., Touzot G., Villon P.: Generalizing the finite element method: diffuse approximation and diffuse elements. Computational mechanics 10, 307–318 (1992)
Udaykumar, H., Mittal, R, Shyy W.: Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids. Journal of computational physics, 153, 535–574 (1999)
Sambridge M., Braun J., McQueen M.: Geophisical parameterization and interpolation of irregular data using natural neighbors. Geophys. i. J. Int, 122
Schönhardt E.: Uber die zerlegung von dreieckspolyedern in tetraeder. Math. Annalen, 98, (1928) 837–857 (1995)
Seidel R.: Constrained Delaunay triangulations and Voronoi diagrams with obstacles In: “1978–1988 Ten Years IIG” 178–191. (1988)
Shewchuck J.R.: Tetrahedral mesh generation by delaunay refinement. In: Proceedings of the fourteenth annual symposium on computational geometry, Minneapolis, Minnesota, june 1998; pp. 86–95, association for computing machinery (1988)
Shewchuck J.R.: Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations. In: Proceedings of the sixteenth annual symposium on computational geometry, Hong-Kong, june 2000; pp. 350–359, association for computing machinery (2000)
Sibson R.: A vector Identity for the Dirichlet tesselations. Math. Proc. Camb. Phil. Soc., 87, 151–155 (1980)
Sukumar N., Chop D., Moës N., Belytschko T.: Modeling holes and inclusions by level sets in the extended finte element method. Computer methods in appled mechanics and engineering 190, 6183–6200 (2001)
Sukumar N., Moran B., Belytschko T.: The natural elements method in solid mechanics. International Journal for Numerical Methods in Engineering, 43, 839–887 (1998)
Sukumar N., Moran B., Semenov Y., Belikov V.V.: Natural neighbor Galerkin methods. International Journal for Numerical Methods in Engineering, 50, 207–219 (2001)
Sussman M., Smereka P., Osher S.: A level set approach for computing solutions to incompressible two-phase flows. Journal of computational physics 114, 146–159 (1994)
Vuik C.:Some historical notes about the Stefan problem. In: CWI-tract 90 (CWI, Amsterdam) (1993)
Yvonnet J., Ryckelynck D., Lorong P., Chinesta P.: Interpolation naturelle sur les domaines non convexes par l’utilisation du diagramme de Voronoi contraint-MŐthode des ŐlŐments C-Naturels. Revue EuropŐenne des éléments Finis 12(4), 487–509 (2003)
Yvonnet J., Ryckelynck D., Lorong P., Chinesta P.: A new extension of the natural element method for non convex and dscontinuous problems, the constrained natural element method (C-NEM). International Journal for Numerical Methods in Engineering, accepted.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yvonnet, J., Ryckelynck, D., Lorong, P., Chinesta, F. (2005). Treating Moving Interfaces in Thermal Models with the C-NEM. In: Griebel, M., Schweitzer, M.A. (eds) Meshfree Methods for Partial Differential Equations II. Lecture Notes in Computational Science and Engineering, vol 43. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-27099-X_14
Download citation
DOI: https://doi.org/10.1007/3-540-27099-X_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23026-7
Online ISBN: 978-3-540-27099-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)