High Order Well-Balanced Schemes and Applications to Non-Equilibrium Flow with Stiff Source Terms

Journal Article · Wed Jan 14 04:00:00 EST 2009 · Journal of Computational Physics

OSTI ID:970655

Wang, W; Shu, C; Yee, H C; Sjogreen, B

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 Laboratory (LLNL), Livermore, CA
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 970655
• Report Number(s): LLNL-JRNL-409903
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 18 Vol. 228; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
CHEMICAL REACTIONS
CHEMISTRY
COMBUSTION
DESIGN
FLEXIBILITY
NOZZLES
RESOLUTION
SIMULATION
SOURCE TERMS