A projection method for motion of triple junctions by level sets
A projection method for motion of triple junctions by level sets
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DOI：
10.4171/ifb/61
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发表时间：
2002
影响因子：
1
通讯作者：
Kurt A. Smith
中科院分区：
文献类型：
--
作者：
Kurt A. Smith
我们开发了一种投影方法来处理水平集公式中多个连接点（例如接触线）的运动。多个连接点与许多领域相关，包括流体动力学、泡沫和半导体制造。在水平集方法中，界面被定义为平滑函数的零水平集。对于 N 相系统，所有界面的位置可以由 N − 1 个函数指定（因此，两相系统只需要一个水平集函数）。对于 N > 2，我们描述 N 个水平集函数到 N -1 维流形的对称投影。相空间的减少消除了水平集函数的不可接受的值（例如在给定点有多个为正的情况）。这可以防止在界面演化过程中在多个连接处形成真空或重叠。此外，该方法可以应用于任意数量的相位和空间维度。我们提出的二维和三维结果表明该方法给出了正确的平衡接触角并在多相流体中产生准确的动力学。
We develop a projection method to treat the motion of multiple junctions (such as contact lines) in the level set formulation. Multiple junctions are relevant to many fields including fluid dynamics, foams, and semiconductor manufacture. In the level set method an interface is defined as the zero level set of a smooth function. For an N -phase system the location of all interfaces can be specified by N − 1 functions (hence only one level set function is needed for a two-phase system). For N > 2 we describe a symmetric projection of the N level set functions onto an N −1 dimensional manifold. This reduction in phase space eliminates unacceptable values of the level set functions (such as cases where more than one is positive at a given point.) This prevents the formation of vacuums or overlaps at multiple junctions during interface evolution. Further, this method can be applied to any number of phases and spatial dimensions. We present twoand three-dimensional results showing that the method gives correct equilibrium contact angles and produces accurate dynamics in multi-phase fluids.