A simple numerical method for Hele-Shaw type problems by the method of fundamental solutions
A simple numerical method for Hele-Shaw type problems by the method of fundamental solutions
复制标题
基本解法求解Hele-Shaw类问题的简单数值方法
DOI：
10.1007/s13160-022-00530-1
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发表时间：
2022
影响因子：
0.9
通讯作者：
Yazaki Shigetoshi
中科院分区：
文献类型：
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作者：
Sakakibara Koya;Shimoji Yusaku;Yazaki Shigetoshi
具有随时间变化的间隙的Hele-Shaw流动产生了指进模式，而Hele-Shaw单元中的磁性流体产生了有趣的模式。利用基本解法给出了一种求解Hele-Shaw型问题的简单数值方法。基本解方法是求解位势问题的一种无网格数值方法，尽管它简单，但它提供了一个高精度的近似解。此外，该数值方法与渐近均匀分布方法相结合，满足保体积性质。在基本解方法中，我们用天野之弥的方法来安排奇点。我们给出了几个数值结果来证明我们的数值格式的有效性。
Hele-Shaw flows with time-dependent gaps create fingering patterns, and magnetic fluids in Hele–Shaw cells create intriguing patterns. We propose a simple numerical method for Hele–Shaw type problems by the method of fundamental solutions. The method of fundamental solutions is one of the mesh-free numerical solvers for potential problems, which provides a highly accurate approximate solution despite its simplicity. Moreover, the numerical method satisfies the volume-preserving property combining with the asymptotic uniform distribution method. We use Amano’s method to arrange the singular points in the method of fundamental solutions. We show several numerical results to exemplify the effectiveness of our numerical scheme.