1. RKC time-stepping for advection-diffusion-reaction problems
- Author
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Jan Verwer, Ben Sommeijer, Willem Hundsdorfer, and Analysis (KDV, FNWI)
- Subjects
Numerical Analysis ,Physics and Astronomy (miscellaneous) ,Differential equation ,Applied Mathematics ,Mathematical analysis ,Parabolic partial differential equation ,Computer Science Applications ,Numerical integration ,Computational Mathematics ,Runge–Kutta methods ,Modeling and Simulation ,Reaction–diffusion system ,Diffusion (business) ,Convection–diffusion equation ,Hyperbolic partial differential equation ,Mathematics - Abstract
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.
- Published
- 2004