High-order fundamental and general solutions of convection-diffusion equation and their applications with boundary particle method

TL;DR

This paper develops high-order fundamental and general solutions for convection-diffusion equations and applies them within the boundary particle method, a meshfree collocation technique, to solve inhomogeneous problems effectively.

Contribution

It introduces high-order solutions for convection-diffusion equations and integrates them into the boundary particle method, enhancing meshfree solution capabilities.

Findings

High-order solutions improve accuracy for convection-diffusion problems.

BPM effectively solves inhomogeneous convection-diffusion equations.

The method is meshfree and boundary-only, simplifying complex geometries.

Abstract

In this study, we presented the high-order fundamental solutions and general solutions of convection-diffusion equation. To demonstrate their efficacy, we applied the high-order general solutions to the boundary particle method (BPM) for the solution of some inhomogeneous convection-diffusion problems, where the BPM is a new truly boundary-only meshfree collocation method based on multiple reciprocity principle. For the sake of completeness, the BPM is also briefly described here.