Monotonicity conditions for multirate and partitioned explicit Runge-Kutta schemes

W. Hundsdorfer, A. Mozartova, V. Savcenco

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

8 Citations (Scopus)
4 Downloads (Pure)


Multirate schemes for conservation laws or convection-dominated problems seem to come in two flavors: schemes that are locally inconsistent, and schemes that lack mass-conservation. In this paper these two defects are discussed for one-dimensional conservation laws. Particular attention will be given to monotonicity properties of the multirate schemes, such as maximum principles and the total variation diminishing (TVD) property. The study of these properties will be done within the framework of partitioned Runge-Kutta methods. It will also be seen that the incompatibility of consistency and mass-conservation holds for ‘genuine’ multirate schemes, but not for general partitioned methods
Original languageEnglish
Title of host publicationRecent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws
EditorsR. Ansorge, H. Bijl, A. Meister, T. Sonar
ISBN (Print)978-364233220-3
Publication statusPublished - 2013

Publication series

NameNotes on Numerical Fluid Mechanics and Multidisciplinary Design
ISSN (Print)0179-9614


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