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

by Hasnaa H Alzahrani

Institution: King Abdullah University of Science and Technology
Year: 2016
Keywords: stiffness; low mach number; numerical integration; runge-kutta-chebyshev; non-split scheme
Posted: 02/05/2017
Record ID: 2135406
Full text PDF: http://hdl.handle.net/10754/617606


Abstract

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. 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. Advisors/Committee Members: Knio, Omar M., Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, Gomes, Diogo, Laleg-Kirati, Taous-Meriem, Parsani, Matteo.

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