Oscillatory instabilities of high‐resolution TVD central schemes for hyperbolic conservation laws | Zendy

Breuß Michael | Zendy

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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)

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