High Order Well-Balanced Schemes and Applications to Non-Equilibrium Flow with Stiff Source Terms
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 solving non-reacting flows. A well-balanced scheme, which can preserve certain non-trivial steady state solutions exactly, may help to resolve 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 high order finite difference weighted essentially non-oscillatory (WENO) scheme, modified balanced WENO schemes and various TVD schemes. The advantages of using a well-balanced scheme in preserving steady states and in resolving small perturbations of such states will be shown. Additional numerical examples are provided to verify the good resolution, in addition to the well-balancedness, for both smooth and discontinuous solutions as well.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 970655
- Report Number(s):
- LLNL-JRNL-409903; JCTPAH; TRN: US201003%%23
- Journal Information:
- Journal of Computational Physics, Vol. 228, Issue 18; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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