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

  • Hasnaa H. Alzahrani

Student thesis: Master's Thesis


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 AwardJul 26 2016
Original languageEnglish (US)
Awarding Institution
  • Computer, Electrical and Mathematical Sciences and Engineering
SupervisorOmar Knio (Supervisor)


  • stiffness
  • low mach number
  • numerical integration
  • runge-kutta-chebyshev
  • non-split scheme

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