Efficient solver for a special class of convection-diffusion problems

TL;DR

This paper introduces an exact and efficient numerical algorithm for solving a specific class of convection-diffusion equations by transforming them into pure diffusion problems with complex potentials, enabling accurate solutions.

Contribution

The paper presents a novel transformation-based algorithm that simplifies certain convection-diffusion equations into pure diffusion problems, improving computational efficiency and accuracy.

Findings

Algorithm reduces convection-diffusion to pure diffusion problems.

Enables use of standard PDE solvers for complex equations.

Achieves high accuracy and efficiency in solutions.

Abstract

We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard to treat due to the presence of a convection term, represented by a first order derivative in the spatial co-ordinate. Our algorithm reduces the convection-diffusion equation to a pure diffusion problem within a complex-valued potential which can be solved efficiently and accurately using conventional parabolic partial differential equation solvers.