A method of fundamental solutions for doubly-periodic potential flow problems using the Weierstrass elliptic function

Hidenori Ogata

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arXiv · 2006.15992

A method of fundamental solutions for doubly-periodic potential flow problems using the Weierstrass elliptic function

Hidenori Ogata

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Abstract

In this paper, we propose a method of fundamental solutions for the problems of two-dimensional potential flow past a doubly-periodic array of obstacles. The solutions of these problems involve doubly-periodic functions, and it is difficult to apply the conventional method of fundamental solutions to approximate them. The method that we propose gives approximate solutions which is expressed by a linear combination of periodic fundamental solutions constructed using the Weierstrass elliptic functions, and it satisfies the periodicity that we expect. Numerical examples show the effectiveness of our method.

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Hidenori Ogata. 2020-06-26. A method of fundamental solutions for doubly-periodic potential flow problems using the Weierstrass elliptic function. https://arxiv.org/abs/2006.15992

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