High order well-balanced schemes
Book
·
OSTI ID:993787
- Institut fur Physikalische Chemie der RWTH
- ORNL
- Brown University
In this paper the authors review some recent work on high-order well-balanced schemes. A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Well-balanced schemes satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. They discuss two classes of schemes, one based on high-order accurate, non-oscillatory finite difference operators which are well-balanced for a general class of equilibria, and the other one based on well-balanced quadratures, which can - in principle - be applied to all equilibria. Applications include equilibria at rest, where the flow velocity vanishes, and also the more challenging moving flow equilibria. Numerical experiments show excellent resolution of unperturbed as well as slightly perturbed equilibria.
- Research Organization:
- Oak Ridge National Laboratory (ORNL)
- Sponsoring Organization:
- SC USDOE - Office of Science (SC); ME USDOE - Office of Management, Budget, and Evaluation; ORNL work for others
- DOE Contract Number:
- AC05-00OR22725
- OSTI ID:
- 993787
- Country of Publication:
- United States
- Language:
- English
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