NUMERICAL ANALYSIS OF 2D REACTION-DIFFUSION EQUATION: TECHNIQUES AND APPLICATION

Abstract

This study focuses on the reaction-diffusion process inside a two dimensional (2D) simple microfluidic channel. The material initially concentrated at the middle of the channel and was affected by diffusion and a first-order decay reaction. This work aims to investigate the numerical methods to solve 2D reaction-diffusion systems. We employ the Finite Difference Method (FDM) and Finite Volume Method (FVM) to solve the governing equations. The simulations are implemented in Python language, in order to compare the accuracy of the methods in relation with the analytical solution. The results revealed that FDM and FVM are in good agreement and suitable with the analytical solution and indicated that FVM is more practical due to efficiency and maintains lower max error and L2 norm values in the case of coarse grids, while the efficiency of the FDM is evident when the mesh is finer.

The study concludes that FVM is a better choice for simulating reaction-diffusion problems where we have complex geometry or coarse mesh, while FDM is better for fine mesh or regular geometry.