Sharp interface limit of Phase Field Model

概要

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Phase field model is widely used as the model of computer simulations on crystal growth. [1] Though its model construction is bit rough and it includes un-observable quantities, it shows good behavior which agrees with experiments. One of the key parameter which can not be observed is the thickness of boundary layer. Without this parameter this model can show neither the motion of boundary nor the existence of surface free energy. In this paper we will show how we can construct the reduced theory by taking the zero limit of boundary layer thickness, and then how the reduced theory represents the physical effects. This kind of work i.e., sharp interface limit of phase field model is already done by several authors [3], but all of them is written by using Cartesian coordinates which makes treatment much complicated, and such theory is given only in two dimensional case (surface is line). We use general curved coordinates and make the reduced theory in three dimension. Use of Riemannian geometry permits us to treat the general curved surface.
北海道工業大学の論文
2007-03-26