A hybrid method for moving interface problems with application to the Hele-Shaw flow
A hybrid method for moving interface problems with application to the Hele-Shaw flow
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DOI：
10.1006/jcph.1997.5689
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发表时间：
1997-07-01
影响因子：
4.1
通讯作者：
Zhao, HK
中科院分区：
文献类型：
--
作者：
Hou, TY;Li, ZL;Zhao, HK
本文提出了一种将沉浸式界面方法和水平集方法相结合的混合方法。浸没界面法的快速形式被用来求解微分方程组，其解及其导数可能由于界面上系数或/和奇异源的不连续而在界面上不连续。然后使用新开发的快速水平集公式来更新移动界面，该公式只涉及在包含界面的一些小管子内进行计算。该方法结合了两种方法的优点，给出了界面问题的二阶欧拉离散。详细讨论了实施过程中的几个关键步骤。然后将这种新方法应用于Hele-Shaw流，这是一种涉及两种粘度非常不同的流体的不稳定流动。(C)1997年学术出版社。
In this paper, a hybrid approach which combines the immersed interface method with the level set approach is presented. The fast version of the immersed interface method is used to solve the differential equations whose solutions and their derivatives may be discontinuous across the interfaces due to the discontinuity of the coefficients or/and singular sources along the interfaces. The moving interfaces then are updated using the newly developed fast level set formulation which involves computation only inside some small tubes containing the interfaces. This method combines the advantage of the two approaches and gives a second-order Eulerian discretization for interface problems. Several key steps in the implementation are addressed in detail. This new approach is then applied to Hele-Shaw flow, an unstable flow involving two fluids with very different viscosity. (C) 1997 Academic Press.