New RK type time-integration methods for stiff convection–diffusion–reaction systems

Abstract

Convection–diffusion–reaction equations (CDREs) are extensively used to model the various physical processes, which are generally stiff in both reaction and diffusion terms. This paper discusses a new class of implicit–explicit Runge–Kutta (IMEX RK) type methods for numerical simulations of the convection–diffusion–reaction systems. The developed approach does not need to invert the coefficient matrix, despite being implicit in nature. The Fourier stability analysis is performed to gauge the properties of the developed methods using one- and two-dimensional scalar CDRE as model systems. Additionally, numerical simulation of the one-dimensional inhomogeneous linear CDRE, contaminant transport with kinetic Langmuir sorption model, and two-dimensional chemotaxis model that incorporates volume-filling effect and nonlinear diffusion are used to validate the effectiveness and robustness of the developed methods. The numerical solutions match the exact solutions discussed in the literature very well.