Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations

• Main Author: Alzahrani, Hasnaa H.
• Other Authors: Knio, Omar
• Language: en
• Published: 2016
• Subjects: stiffness; low mach number; numerical integration; runge-kutta-chebyshev; non-split scheme
• Online Access: Alzahrani, H. H. (2016). Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations. KAUST Research Repository. https://doi.org/10.25781/KAUST-070XM; http://hdl.handle.net/10754/617606

A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.