Relations Between WENO3 and Third-Order Limiting in Finite Volume Methods
Genre
Journal ArticleDate
2016-08-01Author
Schmidtmann, BSeibold, B
Torrilhon, M
Subject
Non-linear and non-polynomial limiterWENO
Finite volume
Hyperbolic conservation laws
Shock capturing
Permanent link to this record
http://hdl.handle.net/20.500.12613/5756
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Show full item recordDOI
10.1007/s10915-015-0151-zAbstract
© 2015, Springer Science+Business Media New York. Weighted essentially non-oscillatory (WENO) and finite volume (FV) methods employ different philosophies in their way to perform limiting. We show that a generalized view on limiter functions, which considers a two-dimensional, rather than a one-dimensional dependence on the slopes in neighboring cells, allows to write WENO3 and 3rd-order FV schemes in the same fashion. Within this framework, it becomes apparent that the classical approach of FV limiters to only consider ratios of the slopes in neighboring cells, is overly restrictive. The hope of this new perspective is to establish new connections between WENO3 and FV limiter functions, which may give rise to improvements for the limiting behavior in both approaches.Citation to related work
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Journal of Scientific ComputingADA compliance
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http://dx.doi.org/10.34944/dspace/5738