On conservation and stability properties for summation-by-parts schemes

Jan Nordström; Andrea A. Ruggiu

doi:10.1016/j.jcp.2017.05.002

On conservation and stability properties for summation-by-parts schemes

Jan Nordström, Andrea A. Ruggiu

Linköping University

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

We discuss conservative and stable numerical approximations in summation-by-parts form for linear hyperbolic problems with variable coefficients. An extended setting, where the boundary or interface may or may not be included in the grid, is considered. We prove that conservative and stable formulations for variable coefficient problems require a boundary and interface conforming grid and exact numerical mimicking of integration-by-parts. Finally, we comment on how the conclusions from the linear analysis carry over to the nonlinear setting.

Original language	English
Pages (from-to)	451-464
Number of pages	14
Journal	Journal of Computational Physics
Volume	344
DOIs	https://doi.org/10.1016/j.jcp.2017.05.002
Publication status	Published - 1 Sept 2017
Externally published	Yes

Keywords

Boundary conditions
Conservation
Hyperbolic problems
Interface conditions
Stability
Summation-by-parts

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2017.05.002

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AU - Ruggiu, Andrea A.

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AB - We discuss conservative and stable numerical approximations in summation-by-parts form for linear hyperbolic problems with variable coefficients. An extended setting, where the boundary or interface may or may not be included in the grid, is considered. We prove that conservative and stable formulations for variable coefficient problems require a boundary and interface conforming grid and exact numerical mimicking of integration-by-parts. Finally, we comment on how the conclusions from the linear analysis carry over to the nonlinear setting.

KW - Boundary conditions

KW - Conservation

KW - Hyperbolic problems

KW - Interface conditions

KW - Stability

KW - Summation-by-parts

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SP - 451

EP - 464

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

On conservation and stability properties for summation-by-parts schemes

Abstract

Keywords

ASJC Scopus subject areas

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