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A New Algorithm for Solving the Energy Conservation Equation Based on ADI Method

  • Xiaofeng Niu
  • Zhongping Que
  • Weili Cheng
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 235)

Abstract

The explicit finite difference (EFD) method is used for calculating the casting temperature field during solidification. Because the time step is limited, the computational efficiency of the EFD method is lower. In order to improve the computational efficiency, a fourth-order in space and second-order in time model based on the equivalent specific heat method and the alternating direction implicit (ADI) method is established. The degree of similarity between the simulation results and experimental results is analyzed quantitatively by the hamming distance (HD). The results show that the simulation results of this high order mathematical model are close to the experimental results.

Keywords

High order ADI method Finite difference method Temperature field Solidification process Hamming distance Degree of similarity 

References

  1. 1.
    Tsai DC, Hwang WS (2010) Numerical simulation of solidification morphologies of Cu-0.6Cr casting alloy using modified cellular automaton model. Trans Nonferrous Met Soc China 20:1072–1077CrossRefGoogle Scholar
  2. 2.
    Chen Y, Zhao YH, Hou H (2006) Numerical simulation for thermal flow filling process casting. Trans Nonferrous Met Soc China 16:214–218Google Scholar
  3. 3.
    Niu XF, Liang W, Zhao YH, Hou H (2011) New algorithm for solving 3D incompressible viscous equations based on projection method. Trans Nonferrous Met Soc China 21:1826–1832CrossRefGoogle Scholar
  4. 4.
    Niu XF, Liang W, Zhao YH, Hou H (2012) A new implicit finite difference algorithm of thermal melt flow in filling process based on projection method. J Comput Theor Nanosci 9:1826–1832Google Scholar
  5. 5.
    Chiu YF, Tsai YL, Hwang WS (2003) Mathematical modeling for the solidification heat-transfer phenomena during the reflow process of lead–tin alloy solder joint in electronics packaging. Appl Math Model 27:565–579MATHCrossRefGoogle Scholar
  6. 6.
    Zhang XP, Xiong SM, Xu QY (2006) Numerical method to improve the computational efficiency of solidification simulation for the investment casting process. Mater Process Technol 173:70–74CrossRefGoogle Scholar
  7. 7.
    Mampaey F (1989) A numerical technique to increase the stability of the ADI method in solidification simulation. J Comput Appl Math 28:297–308MATHCrossRefGoogle Scholar
  8. 8.
    Karaa S, Zhang J (2004) High order ADI Method for solving unsteady convection-diffusion problems. J Comput Phys 198:1–9MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringTaiyuan University of TechnologyTaiyuanChina

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