This paper presents an analytic approach to solving the classical problem of free boundary porous media flow. The solution is found by constructing an operator, derived from a conformal map, which is then reduced to a matrix and inverted. This matrix is then used to solve a system of linear equations with all terms in the matrix calculated exactly. To confirm the solution, we made a comparison with an iterative boundary element solution, which shows good agreement. Visual representations of the flow are also provided.

中文翻译：

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使用经边界元法验证的共形图解析多孔介质流自由边界问题


本文提出了一种解决自由边界多孔介质流经典问题的解析方法。通过构造一个从共形映射导出的算子来找到解决方案，然后将其简化为矩阵并求逆。然后使用该矩阵求解线性方程组，并精确计算矩阵中的所有项。为了确认该解，我们与迭代边界元解进行了比较，结果显示出良好的一致性。还提供了流程的视觉表示。