Method of fundamental solutions for the problem of doubly-periodic potential flow

TL;DR

This paper introduces a novel method using periodic fundamental solutions with theta functions to effectively solve doubly-periodic potential flow problems in two dimensions.

Contribution

It presents a new approach that approximates doubly-periodic potential flow using a linear combination of periodic fundamental solutions with theta functions.

Findings

Method effectively approximates doubly-periodic potential flow

Numerical examples demonstrate high accuracy and efficiency

Approach overcomes limitations of conventional methods

Abstract

In this paper, we propose a method of fundamental solutions for the problem of two-dimensional potential flow in a doubly-periodic domain. The solution involves a doubly-periodic function, to which it is difficult to give an approximation by the conventional method of fundamental solutions. We propose to approximate it by a linear combination of the periodic fundamental solutions, that is, complex logarithmic potential with sources in a doubly-periodic array constructed using the theta functions. Numerical examples show the effectiveness of our method.