Maio 2014 vol. 1 num. 1 - 10th World Congress on Computational Mechanics
Full Article - Open Access.
TEMPERATURE GRADIENT DISCONTINUITY AWARE NUMERICAL SCHEME FOR SOLIDIFICATION PROBLEMS
A new enriched finite element formulation for solving isothermal phase change problems is presented. The proposed method is a fixed domain one, where the discontinuity in the temperature gradient is represented by means of enriching the finite element space through a function whose definition admits a discontinuity in its derivative. Generally, in this kind of formulations, the location where to enrich (as the location of the solidification front), is determined through a level set auxiliary formulation. In this work a different approach is explored, this position is determined implicitly through a constraint that imposes that the temperature attained at the phase change boundary is the melting temperature. Some numerical examples to show the application of the method are presented and finally the conclusions are exposed
Palavras-chave: Enriched Finite Element Method, Solidification Problems, Stefan Problem, Phase Change Problems, XFEM,
-  V. Alexiades and A. D. Solomon. Mathematical Modeling of Melting and Freezing Processes. Hemisphere Publishing Corporation, Taylor and Francis Group, 1993.
-  R. F. Ausas, G. C. Buscaglia, and S. R. Idelsohn. A new enrichment space for the treatment of discontinuous pressures in multi-fluid flows. International Journal for Numerical Methods in Fluids, 2011. ISSN 1097-0363.
-  F. Basombr´io. El problema de dos fases en materiales heterog´eneos. aplicaciones. Revista internacional de m´etodos num´ericos, 13(3):351–366, 1997.
-  M. Bernauer and R. Herzog. Implementation of an X-FEM solver for the classical twophase Stefan problem. Journal of Scientific Computing, pages 1–23, 2011. ISSN 0885- 747
-  J. Chessa, P. Smolinski, and T. Belytschko. The extended finite element method (XFEM) for solidification problems. International Journal for Numerical Methods in Engineering, 53(8):1959, 2002.
-  A. H. Coppola-Owen and R. Codina. Improving eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions. International Journal for Numerical Methods in Fluids, 49(12):1287–1304, 2005. ISSN 1097-0363.
-  L. A. Crivelli and S. R. Idelsohn. A temperature-based finite element solution for phasechange problems. International Journal for Numerical Methods in Engineering, 23(1): 99–119, 1986. ISSN 1097-020
-  V. Fachinotti, A. Cardona, A. Cosimo, B. Baufeld, and O. Van der Biest. Evolution of temperature during shaped metal deposition: Finite element predictions vs. observations. Mecánica Computacional, 19:4915–4926, 2010.
-  V. D. Fachinotti, A. Cardona, and A. E. Huespe. A fast convergent and accurate temperature model for phase-change heat conduction. International Journal for Numerical Methods in Engineering, 44(12):1863–1884, 199 ISSN 1097-0207.
-  T.-P. Fries and T. Belytschko. The extended/generalized finite element method: An overview of the method and its applications. International Journal for Numerical Methods in Engineering, 20
-  T.-P. Fries and A. Zilian. On time integration in the XFEM. International Journal for Numerical Methods in Engineering, 79(1):69, 2009.
-  S. Idelsohn, M. Storti, and L. Crivelli. Numerical methods in phase-change problems. Archives of Computational Methods in Engineering, 1:49–74, 1994.
-  H. Ji, D. Chopp, and J. E. Dolbow. A hybrid extended finite element/level set method for modeling phase transformations. International Journal for Numerical Methods in Engineering, 54(8):1209–1233, 2002. ISSN 1097-0207.
-  C. T. Kelley. Iterative Methods for Optimization. Society for Industrial and Applied Mathematics, Philadelphia, 1999.
-  P. Ladev´eze and J. G. Simmonds. Nonlinear computational structural mechanics: new approaches and non-incremental methods of calculation. Springer, 1999.
-  D. R. Lynch and K. O’Neill. Continuously deforming finite elements for the solution of parabolic problems, with and without phase change. International Journal for Numerical Methods in Engineering, 17(1):81–96, 1981. ISSN 1097-0207.
-  R. Merle and J. Dolbow. Solving thermal and phase change problems with the extended finite element method. Computational Mechanics, 28(5):339, 2002.
-  A. K. Nallathambi, E. Specht, and A. Bertram. Computational aspects of temperaturebased finite element technique for the phase-change heat conduction problem. Computational Materials Science, 47(2):332, 2009.
-  N. Nigro, A. Huespe, and V. Fachinotti. Phasewise numerical integration of finite element method applied to solidification processes. International Journal of Heat and Mass Transfer, 43(7):1053–1066, 2000.
-  M. Salcudean and Z. Abdullah. On the numerical modelling of heat transfer during solidification processes. International Journal for Numerical Methods in Engineering, 25(2):445–473, 1988. ISSN 1097-0207.
-  J. A. Sethian. Level Set Methods and Fast Marching Methods. Cambridge University Press., 1996.
-  A. Simone. Partition of unity-based discontinuous finite elements: GFEM, PUFEM, XFEM. Revue europ´eenne de g´enie civil, 11(7-8):1045, 2007.
-  M. Storti, L. A. Crivelli, and S. R. Idelsohn. Making curved interfaces straight in phasechange problems. International Journal for Numerical Methods in Engineering, 24(2): 375–392, 1987. ISSN 1097-0207.
-  D. A. Tarzia. Advanced Topics in Mass Transfer, chapter 20, pages 439–484. InTech, 2011.
-  P. Wriggers. Nonlinear Finite Element Methods. Springer, Berlin, 2008.
Cosimo, Alejandro; Fachinotti, V´ıctor; Cardona, Alberto; "TEMPERATURE GRADIENT DISCONTINUITY AWARE NUMERICAL SCHEME FOR SOLIDIFICATION PROBLEMS", p. 1326-1342 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1].
São Paulo: Blucher,
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18375
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