Numerical solution of two phase solidification problem using dynamic substructuring based on adaptive error estimation

Numerical solution of solidification of metals with a sharp front, in particular solidification of lead, is investigated. Considering the fact that the associated CPU time and memory requirement may be costly for large domains, alternatives are searched. It is observed that using a substructuring technique with a local mesh refinement is promising. Following, by the use of an adaptive error estimation algorithm to find the location of solidification front and mushy zone, dynamic substructuring technique is developed to decrease the computational cost and to increase the accuracy of results. Superconvergent patch recovery technique is used to obtain the heat fluxes to evaluate the error energy norm of elements at each analysis step. Solidification front, mushy zone and elements having errors above a threshold value are captured with the error estimator. Then, elements having errors above the threshold value are refined by creating a substructure which is independent from the original global mesh. Equations of the global coarse mesh are augmented with the equations of the substructure. Employing the equations of the original coarse mesh help reduce the computational cost. Numerical solutions are presented and it is shown that the proposed approach has advantages over the alternative methods and, by the virtue of the adaptive error estimation algorithm, significantly decreases the CPU time of numerical solutions while it increases the accuracy of solutions and locates precisely the solidification front and mushy zone. Keywords: Solidification; Finite Element Methods; Substructuring; Stefan Problem; Error Estimation DOI: 10.17350/HJSE19030000017 Full Text:

[1]  K. Tamma,et al.  Hierarchical p-version finite elements and adaptive a posteriori computational formulations for two-dimensional thermal analysis , 1989 .

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

[3]  Ruo Li,et al.  A multi-mesh adaptive finite element approximation to phase field models , 2009 .

[4]  Somnath Ghosh,et al.  AN ARBITRARY LAGRANGIAN-EULERIAN FINITE ELEMENT MODEL FOR HEAT TRANSFER ANALYSIS OF SOLIDIFICATION PROCESSES , 1993 .

[5]  A. A. Wheeler,et al.  Thermodynamically-consistent phase-field models for solidification , 1992 .

[6]  R. Szilard.  Theories and Applications of Plate Analysis , 2004 .

[7]  Yiming Rong,et al.  Numerical simulation on solidification and thermal stress of continuous casting billet in mold based on meshless methods , 2007 .

[8]  S. Ro.  RECENT PROGRESS IN HEAT TRANSFER DURING MELTING AND SOLIDIFICATION PROCESSES , 1992 .

[9]  N. Goldenfeld,et al.  Adaptive Mesh Refinement Computation of Solidification Microstructures Using Dynamic Data Structures , 1998, cond-mat/9808216.

[10]  O. C. Zienkiewicz,et al.  A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .

[11]  Veera Sundararaghavan,et al.  Multi-scale homogenization of moving interface problems with flux jumps: application to solidification , 2009 .

[12]  John M. Sullivan,et al.  Heat conservation in deforming element phase change simulation , 1985 .

[13]  Y. Im,et al.  Finite element analysis of solidification of aluminum with natural convection , 1995 .

[14]  Juan C. Heinrich,et al.  Modeling dendritic growth of a binary alloy , 2003 .

[15]  P. Liley,et al.  Thermal Conductivity of the Elements , 1972 .

[16]  Baskar Ganapathysubramanian,et al.  Modelling dendritic solidification with melt convection using the extended finite element method , 2006, J. Comput. Phys..

[17]  Nicholas Zabaras,et al.  Front tracking thermomechanical model for hypoelastic-viscoplastic behavior in a solidifying body , 1990 .

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

[19]  S. Atluri,et al.  Temperature Field Due to a Moving Heat Source: A Moving Mesh Finite Element Analysis , 1985 .

[20]  T. Belytschko,et al.  The extended finite element method (XFEM) for solidification problems , 2002 .

[21]  D. Juric,et al.  A Front-Tracking Method for Dendritic Solidification , 1996 .

[22]  K. Haghighi,et al.  Adaptive Finite Element Analysis of Transient Thermal Problems , 1994 .

[23]  S. I. Abu-eishah,et al.  A NEW CORRELATION FOR THE SPECIFIC HEAT OF METALS, METAL OXIDES AND METAL FLUORIDES AS A FUNCTION OF TEMPERATURE , 2004 .

[24]  C. Gandin,et al.  A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes , 1994 .

[25]  Ruo Li,et al.  Efficient computation of dendritic growth with r-adaptive finite element methods , 2008, J. Comput. Phys..

[26]  X. Richard Zhang,et al.  Finite Element Analysis of Pulsed Laser Bending: The Effect of Melting and Solidification , 2004 .

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

[28]  Boning Li,et al.  An Interface-Fitted Finite Element Level Set Method with Application to Solidification and Solvation. , 2011, Communications in computational physics.

[29]  Carlos Armando Duarte,et al.  Transient analysis of sharp thermal gradients using coarse finite element meshes , 2011 .