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.
| Date of Award | Jul 26 2016 |
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| Original language | English (US) |
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| Awarding Institution | - Computer, Electrical and Mathematical Sciences and Engineering
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| Supervisor | Omar Knio (Supervisor) |
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- stiffness
- low mach number
- numerical integration
- runge-kutta-chebyshev
- non-split scheme