Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition
Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition
复制标题
扩展微观可解性的范围：Kruskal-Segur 方法与 Zauderer 分解的组合
DOI：
10.1209/0295-5075/81/54004
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
K. Kassner
中科院分区：
文献类型：
--
作者：
T. Fischaleck;K. Kassner
成功应用的Kruskal-Segur方法界面图案的形成仍然是有限的，由于一个整体制定的问题的必要性。这排除了非线性体方程，使对流难以处理。结合该方法与Zauderer的渐近分解方案，我们能够大大扩展其适用范围，并解决选择问题的基础上自由边界配方的偏微分方程。为了证明该技术，我们给出了第一个解析解的问题的速度选择枝晶生长在一个强制的势流。
Successful applications of the Kruskal-Segur approach to interfacial pattern formation have remained limited due to the necessity of an integral formulation of the problem. This excludes nonlinear bulk equations, rendering convection intractable. Combining the method with Zauderer's asymptotic decomposition scheme, we are able to strongly extend its scope of applicability and solve selection problems based on free boundary formulations in terms of partial differential equations alone. To demonstrate the technique, we give the first analytic solution of the problem of velocity selection for dendritic growth in a forced potential flow.