Fourier series (based) multiscale method for computational analysis in science and engineering: IV. Fourier series multiscale solution for the convection-diffusion-reaction equation

TL;DR

This paper develops and applies a Fourier series multiscale method to solve convection-diffusion-reaction equations, demonstrating its effectiveness and convergence through numerical examples in science and engineering.

Contribution

It introduces a novel Fourier series multiscale solution approach for convection-diffusion-reaction equations, enhancing computational efficiency and accuracy.

Findings

Convergence of the Fourier series multiscale solutions is confirmed numerically.

Optimized schemes improve the application of the multiscale method.

The method effectively captures multiscale characteristics of the equations.

Abstract

Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fourth paper, the application of the Fourier series multiscale method to the one- and two-dimensional convection-diffusion-reaction equations is implemented, where the Fourier series multiscale solutions are derived, the convergence characteristics of the Fourier series multiscale solutions are investigated by numerical examples, the schemes for application of the Fourier series multiscale method are optimized, and the multiscale characteristics of the convection-diffusion-reaction equations are demonstrated. The preliminary study on applications verifies the effectiveness of the present Fourier series multiscale method and provides a reliable reference which can be used for persistent improvement in computational performance of other multiscale methods.