Howard, Elizabeth (2003) A front tracking method for modelling thermal growth. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-03042003-115138
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)|
|Defense Date:||25 July 2002|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||06 Mar 2003|
|Last Modified:||26 Dec 2012 02:33|
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