Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes

Willem Hundsdorfer; Anna Mozartova; Valeriu Savcenco

doi:10.1007/978-3-642-33221-0_11

Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes

Willem Hundsdorfer, Anna Mozartova, Valeriu Savcenco

Research output: Chapter in Book/Report/Conference proceeding › Chapter

9 Scopus citations

Abstract

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 language	English (US)
Title of host publication	Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws
Publisher	Springer Nature
Pages	177-195
Number of pages	19
ISBN (Print)	9783642332203
DOIs	https://doi.org/10.1007/978-3-642-33221-0_11
State	Published - 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): FIC/2010/05
Acknowledgements: The work of W. Hundsdorfer is supported by Award No. FIC/2010/05from King Abdullah University of Science and Technology (KAUST). The work ofA. Mozartova has been supported by a grant from the Netherlands Organisation for ScientificResearch NWO.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1007/978-3-642-33221-0_11

Cite this

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title = "Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes",

abstract = "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 {\textquoteleft}genuine{\textquoteright} multirate schemes, but not for general partitioned methods.",

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note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): FIC/2010/05 Acknowledgements: The work of W. Hundsdorfer is supported by Award No. FIC/2010/05from King Abdullah University of Science and Technology (KAUST). The work ofA. Mozartova has been supported by a grant from the Netherlands Organisation for ScientificResearch NWO. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1007/978-3-642-33221-0_11",

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AU - Hundsdorfer, Willem

AU - Mozartova, Anna

AU - Savcenco, Valeriu

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): FIC/2010/05 Acknowledgements: The work of W. Hundsdorfer is supported by Award No. FIC/2010/05from King Abdullah University of Science and Technology (KAUST). The work ofA. Mozartova has been supported by a grant from the Netherlands Organisation for ScientificResearch NWO. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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N2 - 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.

AB - 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.

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UR - http://link.springer.com/10.1007/978-3-642-33221-0_11

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EP - 195

BT - Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws

PB - Springer Nature

ER -

Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes

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