A NUMERICAL-METHOD FOR TRACKING CURVE NETWORKS MOVING WITH CURVATURE MOTION
A NUMERICAL-METHOD FOR TRACKING CURVE NETWORKS MOVING WITH CURVATURE MOTION
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DOI：
10.1006/jcph.1995.1149
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发表时间：
1995-08-01
影响因子：
4.1
通讯作者：
WETTON, BTR
中科院分区：
文献类型：
--
作者：
BRONSARD, L;WETTON, BTR
提出了一种有限差分法来跟踪曲线，其法向速度由其曲率给出，并在不同类型的路口相遇。原型的例子是，满足在规定的角度相界面，虽然共晶结和交互through非局部效应也被认为是。该方法是基于一个直接离散的基本抛物型问题和边界条件，线性稳定性分析，我们的计划以及计算研究，确认二阶收敛到光滑的解决方案。在曲线网络中的奇异性之后，解决方案不再光滑，我们证明了“几乎”二阶收敛。奇异性类型的数值研究的情况下，满足在规定的角度在三通。最后，不同的离散化和隐式时间推进的方法，并进行了比较。(C)出版社：Academic Press
A finite difference method is proposed to track curves whose normal velocity is given by their curvature and which meet at different types of junctions. The prototypical example is that of phase interfaces that meet at prescribed angles, although eutectic junctions and interactions th rough nonlocal effects are also considered. The method is based on a direct discretization of the underlying parabolic problem and boundary conditions, A linear stability analysis is presented for our scheme as well as computational studies that confirm the second order convergence to smooth solutions. After a singularity in the curve network where the solution is no longer smooth, we demonstrate ''almost'' second-order convergence. A numerical study of singularity types is done for the case of networks that meet at prescribed angles at triple junctions. Finally, different discretizations and methods for implicit time stepping are presented and compared. (C) 1995 Academic Press, Inc.