An efficient numerical method for studying interfacial motion in two-dimensional creeping flows
An efficient numerical method for studying interfacial motion in two-dimensional creeping flows
复制标题
研究二维蠕动流界面运动的有效数值方法
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
M. Kropinski
中科院分区：
文献类型：
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作者：
M. Kropinski
我们提出了计算二维闭合界面在慢粘性流动中运动的新方法。界面速度是通过求解一个积分方程解得到的，该积分方程解的解析形式基于双调和方程的复变量理论。求解积分方程组的数值方法在频谱上是精确的，并采用了一种基于多极子的快速迭代求解过程，该过程只需要O(N)次运算，其中N是界面离散化中的节点数。界面是用光谱描述的，我们使用演化方程来保持标记点的弧长相等。通过小尺度分解来提取界面演化中的主导项，我们证明了这个主导项导致了CFL型稳定性约束。当在等弧长的标架中时，这一项是线性的，并且我们证明了在傅立叶空间中显式的隐式时间积分格式是可以表示的。我们通过几个数值算例验证了这一分析。
We present new methods for computing the motion of two-dimensional closed interfaces in a slow viscous flow. The interfacial velocity is found through the solution to an integral equation whose analytic formulation is based on complex-variable theory for the biharmonic equation. The numerical methods for solving the integral equations are spectrally accurate and employ a fast multipole-based iterative solution procedure, which requires only O(N) operations where N is the number of nodes in the discretization of the interface. The interface is described spectrally, and we use evolution equations that preserve equal spacing in arclength of the marker points. A small-scale decomposition is performed to extract the dominant term in the evolution of the interface, and we show that this dominant term leads to a CFL-type stability constraint. When in an equal arclength frame, this term is linear and we show that implicit time-integration schemes that are explicit in Fourier space can be formulated. We verify this analysis through several numerical examples.