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A front tracking method for modelling thermal growth

Citation

Howard, Elizabeth Anne (2003) A front tracking method for modelling thermal growth. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-03042003-115138

Abstract

Several important thermal growth problems involve a solid growing into an undercooled liquid. The heat that is released at the interface diffuses into both the solid and the liquid phases. This is a free boundary problem where the position of the interface is an unknown which must be found as part of the solution. The problem can conveniently be represented as an integral equation for the unknown interface. However, a history integral must be evaluated at each time step which requires information about the boundary position at all previous times. The time and memory required to perform this calculation quickly becomes unreasonable. We develop an alternative way to deal with the problems that the history integral presents. By taking advantage of properties of the diffusion equation, we can use a method with a constant operation count and amount of memory required for each time step. We show that a numerical algorithm can be implemented for a two-dimensional, symmetric problem with equal physical parameters in both phases. The results agree well with the exact solution for the expanding circle case and microscopic solvability theory. We also extend the method to the nonsymmetric case. Additionally, a stability analysis is done of a simple, parabolic moving front to perturbations on the surface. As the eigenvalues of our problem increase, the interface becomes more increasingly oscillatory.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Front Tracking; Thermal Growth
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Meiron, Daniel I.
Thesis Committee:
  • Meiron, Daniel I. (chair)
  • Leonard, Anthony
  • Cohen, Donald S.
  • Cross, Michael Clifford
  • Hou, Thomas Y.
Defense Date:25 July 2002
Record Number:CaltechETD:etd-03042003-115138
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-03042003-115138
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:860
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:06 Mar 2003
Last Modified:28 Jul 2014 23:23

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