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High Order Well-Balanced Schemes And Applications To Non-Equilibrium Flow With Stiff Source Terms, Wei Wang, Chi-Wang Shu, H. C. Yee, Björn Sjögreen

United States National Aeronautics and Space Administration: Publications

The stiffness of the source terms in modeling non-equilibrium ow problems containing finite-rate chemistry or combustion poses additional numerical difficulties beyond that for solving 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 advantages …