Identifier: 2009-6
Author(s): W. Wang, C.-W. Shu, H.C. Yee, and B. Sjogreen
Title: High-order well-balanced schemes and applications to non-equilibrium flow with stiff source terms
Page count: 31 pp.
Date: 2009-02-15
Abstract:
The stiffness of the source terms in modeling non-equilibrium flow problems containing finite-rate chemistry or combustion poses additional numerical difficulties beyond that for solv- ing non-reacting flows. A well-balanced scheme, which can preserve certain non-trivial steady state solutions exactly, may help minimize some of these difficulties. In this paper, a simple one dimensional non-equilibrium model with one temperature is considered. We first describe a general strategy to design high order well-balanced finite difference schemes and then study the well-balanced properties of the high order finite difference weighted essentially non-oscillatory (WENO) scheme, modified balanced WENO schemes and various TVD schemes. The ad- vantages of using a well-balanced scheme in preserving steady states and in resolving small perturbations of such states will be shown. Numerical examples containing both smooth and discontinuous solutions are included to verify the improved accuracy, in addition to the well- balanced behavior.
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