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Fully Discrete Energy Stable High Order Finite Difference Methods for Hyperbolic Problems in Deforming Domains
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2014 (English)Report (Other academic)
Abstract [en]

A time-dependent coordinate transformation of a constant coefficient hyperbolic system of equations which results in a variable coecient system of equations is considered. By applying the energy method, well-posed boundary conditions for the continuous problem are derived. Summation-by-Parts (SBP) operators for the space and time discretization, together with a weak imposition of boundary and initial conditions using Simultaneously Approximation Terms (SATs) lead to a provable fully-discrete energy-stable finite difference scheme.   We show how to construct a time-dependent SAT formulation that automatically imposes boundary conditions, when and where they are required. We also prove that a uniform flow field is preserved, i.e. the numerical Geometric Conservation Law holds automatically by using SBP-SAT in time. The developed technique is illustrated by considering an application using the linearized Euler equations: the sound generated by moving boundaries. Numerical calculations corroborate the stability and accuracy of the new fully discrete approximations.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2014. , 31 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2014:15
Keyword [en]
deforming domain, initial boundary value problems, high order accuracy, well-posed boundary conditions, summation-by-parts operators, stability, convergence, conservation, numerical geometric conservation law, Euler equation, sound propagation
National Category
Computational Mathematics Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-111336ISRN: LiTH-MAT-R--2014/15--SEOAI: oai:DiVA.org:liu-111336DiVA: diva2:755469
Available from: 2014-10-14 Created: 2014-10-14 Last updated: 2015-03-26

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Nikkar, SamiraNordström, Jan

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • Other style
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Language
  • de-DE
  • en-GB
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  • nn-NB
  • sv-SE
  • Other locale
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Output format
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