Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
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 di...
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| Language: | en |
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2016
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| 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 |
| Summary: | 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. |
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