Energy stability of the MUSCL scheme

Qaisar Abas; Edwin van der Weide; Jan Nordström

doi:10.1007/978-3-642-11795-4_5

Energy stability of the MUSCL scheme

Qaisar Abas^*, Edwin van der Weide, Jan Nordström

^*Corresponding author for this work

Engineering Fluid Dynamics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

We analyze the energy stability of the standard MUSCL scheme. The analysis is possible by reformulating the MUSCL scheme in the framework of summation-by-parts (SBP) operators including an artificial dissipation. The effect of different slope limiters is studied. It is found that all the slope limiters do not lead to the correct sign of the entries in the dissipation matrix. The implication of that is discussed. The analysis is done for both linear and nonlinear scalar problems.

Original language	Undefined
Title of host publication	Numerical Mathematics and Advanced Applications 2009
Subtitle of host publication	Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, July 2009
Editors	Gunilla Kreiss, Per Lötstedt, Axel Màlqvist, Maya Neytcheva
Place of Publication	Berlin
Publisher	Springer
Pages	61-68
ISBN (Electronic)	978-3-642-11795-4
ISBN (Print)	978-3-642--11794-7, 978-3-662-51953-0
DOIs	https://doi.org/10.1007/978-3-642-11795-4_5
Publication status	Published - 29 Jun 2010
Event	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2009 - Uppsala, Sweden Duration: 29 Jun 2009 → 3 Jul 2009

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2009
Abbreviated title	ENUMATH
Country/Territory	Sweden
City	Uppsala
Period	29/06/09 → 3/07/09

Keywords

NLA

Access to Document

10.1007/978-3-642-11795-4_5

Cite this

Abas, Q., van der Weide, E., & Nordström, J. (2010). Energy stability of the MUSCL scheme. In G. Kreiss, P. Lötstedt, A. Màlqvist, & M. Neytcheva (Eds.), Numerical Mathematics and Advanced Applications 2009: Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, July 2009 (pp. 61-68). Springer. https://doi.org/10.1007/978-3-642-11795-4_5

Abas, Qaisar ; van der Weide, Edwin ; Nordström, Jan. / Energy stability of the MUSCL scheme. Numerical Mathematics and Advanced Applications 2009: Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, July 2009. editor / Gunilla Kreiss ; Per Lötstedt ; Axel Màlqvist ; Maya Neytcheva. Berlin : Springer, 2010. pp. 61-68

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title = "Energy stability of the MUSCL scheme",

abstract = "We analyze the energy stability of the standard MUSCL scheme. The analysis is possible by reformulating the MUSCL scheme in the framework of summation-by-parts (SBP) operators including an artificial dissipation. The effect of different slope limiters is studied. It is found that all the slope limiters do not lead to the correct sign of the entries in the dissipation matrix. The implication of that is discussed. The analysis is done for both linear and nonlinear scalar problems.",

keywords = "NLA",

author = "Qaisar Abas and \{van der Weide\}, Edwin and Jan Nordstr{\"o}m",

year = "2010",

month = jun,

day = "29",

doi = "10.1007/978-3-642-11795-4\_5",

language = "Undefined",

isbn = "978-3-642--11794-7",

pages = "61--68",

editor = "Gunilla Kreiss and Per L{\"o}tstedt and Axel M{\`a}lqvist and Maya Neytcheva",

booktitle = "Numerical Mathematics and Advanced Applications 2009",

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note = "European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2009 ; Conference date: 29-06-2009 Through 03-07-2009",

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Abas, Q, van der Weide, E & Nordström, J 2010, Energy stability of the MUSCL scheme. in G Kreiss, P Lötstedt, A Màlqvist & M Neytcheva (eds), Numerical Mathematics and Advanced Applications 2009: Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, July 2009. Springer, Berlin, pp. 61-68, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2009, Uppsala, Sweden, 29/06/09. https://doi.org/10.1007/978-3-642-11795-4_5

Energy stability of the MUSCL scheme. / Abas, Qaisar; van der Weide, Edwin; Nordström, Jan.
Numerical Mathematics and Advanced Applications 2009: Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, July 2009. ed. / Gunilla Kreiss; Per Lötstedt; Axel Màlqvist; Maya Neytcheva. Berlin: Springer, 2010. p. 61-68.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Energy stability of the MUSCL scheme

AU - Abas, Qaisar

AU - van der Weide, Edwin

AU - Nordström, Jan

PY - 2010/6/29

Y1 - 2010/6/29

N2 - We analyze the energy stability of the standard MUSCL scheme. The analysis is possible by reformulating the MUSCL scheme in the framework of summation-by-parts (SBP) operators including an artificial dissipation. The effect of different slope limiters is studied. It is found that all the slope limiters do not lead to the correct sign of the entries in the dissipation matrix. The implication of that is discussed. The analysis is done for both linear and nonlinear scalar problems.

AB - We analyze the energy stability of the standard MUSCL scheme. The analysis is possible by reformulating the MUSCL scheme in the framework of summation-by-parts (SBP) operators including an artificial dissipation. The effect of different slope limiters is studied. It is found that all the slope limiters do not lead to the correct sign of the entries in the dissipation matrix. The implication of that is discussed. The analysis is done for both linear and nonlinear scalar problems.

KW - NLA

U2 - 10.1007/978-3-642-11795-4_5

DO - 10.1007/978-3-642-11795-4_5

M3 - Conference contribution

SN - 978-3-642--11794-7

SN - 978-3-662-51953-0

SP - 61

EP - 68

BT - Numerical Mathematics and Advanced Applications 2009

A2 - Kreiss, Gunilla

A2 - Lötstedt, Per

A2 - Màlqvist, Axel

A2 - Neytcheva, Maya

PB - Springer

CY - Berlin

T2 - European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2009

Y2 - 29 June 2009 through 3 July 2009

ER -

Abas Q, van der Weide E, Nordström J. Energy stability of the MUSCL scheme. In Kreiss G, Lötstedt P, Màlqvist A, Neytcheva M, editors, Numerical Mathematics and Advanced Applications 2009: Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, July 2009. Berlin: Springer. 2010. p. 61-68 doi: 10.1007/978-3-642-11795-4_5