A numerical algorithm for computational modelling of coupled advection-diffusion-reaction systems

Purpose: This paper aims to capture the effective behaviour of nonlinear coupled advection-diffusion-reaction systems and develop a new computational scheme based on differential quadrature method. Design/methodology/approach: The developed scheme converts the coupled system into a system of ordinary differential equations. Finally, the obtained system is solved by a four-stage RK4 scheme. Findings: The developed scheme helped to capture the different types of patterns of nonlinear time-dependent coupled advection-diffusion-reaction systems such as Brusselator model, Chemo-taxis model and linear model which are similar to the existing patterns of the models. Originality/value: The originality lies in the fact that the developed scheme is new for coupled advection-diffusion-reaction systems such as Brusselator model, Chemo-taxis model and linear models. Second, the captured pattern is similar to the existing patterns of the models.