A second order directional split exponential integrator for systems of advection-diffusion-reaction equations

We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection-diffusion-reaction equations in two and three space dimensions. It is based on a directional splitting of the involved matrix functions, which allows for a simple yet efficient implementation through the computation of small sized exponential-like functions and tensor-matrix products. The procedure straightforwardly extends to the case of an arbitrary num-ber of components and to any space dimension. Several numerical examples in 2D and 3D with physically relevant (advective) Schnakenberg, FitzHugh-Nagumo, DIB, and advective Brusselator models clearly show the advantage of the approach against state-of-the-art techniques.

Automated summary

In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.