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A numerical method for coupled surface and grain boundary motion

Published online by Cambridge University Press:  01 June 2008

ZHENGUO PAN  and
BRIAN WETTON
ZHENGUO PAN
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C. CanadaV6T 1Z email: panzg@math.ubc.ca
BRIAN WETTON
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C. CanadaV6T 1Z2 email: wetton@math.ubc.ca
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Abstract

We study the coupled surface and grain boundary motion in a bi-crystal in the context of the ‘quarter loop’ geometry. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. Three curves meet at points where junction conditions are given. A formulation that describes the coupled normal motion of the curves and preserves arc length parametrisation up to scaling is proposed. The formulation is shown to be well-posed in a simple, linear setting. Equations and junction conditions are approximated by finite difference methods. Numerical convergence to exact travelling wave solutions is shown. The method is applied to other problems of physical interest.

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Papers
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European Journal of Applied Mathematics , Volume 19 , Issue 3 , June 2008 , pp. 311 - 327
Copyright
Copyright © Cambridge University Press 2008

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