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

TL;DR

This paper introduces a novel method using Weierstrass elliptic functions to solve doubly-periodic potential flow problems, effectively handling periodicity and demonstrating promising numerical results.

Contribution

The paper presents a new fundamental solutions method employing Weierstrass elliptic functions for doubly-periodic potential flow problems, addressing limitations of conventional approaches.

Findings

Effective approximation of doubly-periodic potential flow

Method satisfies expected periodicity

Numerical examples confirm effectiveness

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.