RKC time-stepping for advection–diffusion–reaction problems

The original explicit Runge–Kutta–Chebyshev (RKC) method is a stabilized second-order integration method for pure diffusion problems. Recently, it has been extended in an implicit–explicit manner to also incorporate highly stiff reaction terms. This implicit–explicit RKC method thus treats diffusion terms explicitly and the highly stiff reaction terms implicitly. The current paper deals with the incorporation of advection terms for the explicit method, thus aiming at the implicit–explicit RKC integration of advection–diffusion–reaction equations in a manner that advection and diffusion terms are treated simultaneously and explicitly and the highly stiff reaction terms implicitly.