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Global error analysis of two-dimensional panel methods for dirichlet formulation

机译：Dirichlet公式的二维面板方法的整体误差分析

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摘要

A rigorous analytical study of the global error of panel methods is presented. The analysis is performed for a wide variety of body shapes and different panel geometries to fully understand their effect on the convergence of the method. In particular, we study the global error associated with panel methods applied to thin or thick bodies with purely convex parts or with both convex and concave parts, and with smooth or non-smooth boundaries. Most previous studies focused on the analysis of local error, considering only the influence of the nearest panels and excluding the rest. The difference is shown to be appreciable in many configurations. Generally, there is a lack of consensus concerning the order of magnitude of the error for panel methods even in the simplest case with flat panels and a constant distribution of doublets along them. This paper clarifies apparently different or inconsistent results obtained by other authors.
机译：对面板方法的整体误差进行了严格的分析研究。对各种各样的身体形状和不同的面板几何形状进行了分析，以充分了解它们对方法收敛的影响。尤其是，我们研究了与面板方法相关的全局误差，该方法适用于具有纯凸部分或凸和凹部分同时具有光滑或不光滑边界的薄或厚实体。以前的大多数研究都集中在对局部误差的分析上，只考虑了最近的小组的影响，而没有考虑其他因素。在许多配置中，这种差异显示为可观的。通常，对于面板方法的误差量级，即使在最简单的平板情况下，双峰沿其恒定分布的情况，也缺乏共识。本文阐明了其他作者获得的明显不同或不一致的结果。

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