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Oscillatory instabilities of high‐resolution TVD central schemes for hyperbolic conservation laws
Author(s) -
Breuß Michael
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510355
Subject(s) - conservation law , total variation diminishing , maxima and minima , variation (astronomy) , scheme (mathematics) , high resolution , resolution (logic) , order (exchange) , mathematics , law , geology , mathematical analysis , physics , computer science , economics , political science , remote sensing , artificial intelligence , astrophysics , finance
Even if a numerical scheme for hyperbolic conservation laws is total variation diminishing, it can create oscillations at data extrema. We show that such oscillations can reduce the overall accuracy of a method considerably, effectively reducing a high‐resolution scheme to first order accuracy. The phenomenon is investigated and we derive accurate non‐staggered accurate central schemes not featuring this weakness. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)