# Non-singular boundary integral methods for fluid mechanics applications

## TL;DR

This paper introduces a boundary integral method that analytically removes singularities, enabling more accurate and efficient solutions for various fluid mechanics problems like potential flow, Helmholtz, Stokes, and elasticity equations.

## Contribution

It develops a non-singular boundary integral formulation applicable to multiple PDEs in fluid and continuum mechanics, improving computational robustness.

## Key findings

- Successfully removes singularities analytically from integral equations.
- Applicable to Laplace, Helmholtz, Stokes, and elasticity problems.
- Demonstrates broad applicability in practical fluid mechanics scenarios.

## Abstract

A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad applicability of the approach is illustrated with a number of problems of practical interest to fluid and continuum mechanics including the solution of the Laplace equation for potential flow, the Helmholtz equation as well as the equations for Stokes flow and linear elasticity.