IMEX Runge-Kutta time-integrators for air-pollution tracking model

Abstract

This study investigates the application of Implicit–Explicit Runge–Kutta (IMEX-RK) methods for the numerical simulation of air pollution tracking models. These models, governed by advection–diffusion–reaction (ADR) equations, play a vital role in predicting the dispersion and concentration of pollutants in the atmosphere. Conventional numerical methods often struggle to efficiently and accurately solve ADR equations, particularly in the presence of stiff components. The IMEX-RK framework overcomes these challenges by treating the stiff components implicitly while handling the non-stiff components explicitly. In this work, a class of IMEX-RK schemes is developed and analysed, including the IMEX Trapezoidal Method (IMEX2s2) and third-order variants (IMEX3s3). Their corresponding stability regions are also presented. Numerical simulations demonstrate the capability of these schemes to capture pollutant transport dynamics with high accuracy under varying advection and diffusion parameters. Furthermore, the accuracy of the proposed IMEX-RK methods are assessed, and results show that both IMEX2s2 and IMEX3s3 methods accurately reproduce pollutant concentration profiles, with the IMEX3s3 scheme exhibiting superior accuracy compared to the IMEX2s2 and a diagonal implicit Runge-Kutta method in the literature.