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Summation-by-Parts Operators for Non-Simply Connected Domains
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2018 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 40, no 3, p. 1250-1273Article in journal (Refereed) Published
Abstract [en]

We construct fully discrete stable and accurate numerical schemes for solving partial differential equations posed on non-simply connected spatial domains. The schemes are constructed using summation-by-parts operators in combination with a weak imposition of initial and boundary conditions using the simultaneous approximation term technique. In the theoretical part, we consider the two-dimensional constant coefficient advection equation posed on a rectangular spatial domain with a hole. We construct the new scheme and study well-posedness and stability. Once the theoretical development is done, the technique is extended to more complex non-simply connected geometries. Numerical experiments corroborate the theoretical results and show the applicability of the new approach and its advantages over the standard multiblock technique. Finally, an application using the linearized Euler equations for sound propagation is presented.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2018. Vol. 40, no 3, p. 1250-1273
Keywords [en]
initial boundary value problems, stability, well-posedness, boundary conditions, non-simply connected domains, complex geometries
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-147651DOI: 10.1137/18M1163671ISI: 000436986000022OAI: oai:DiVA.org:liu-147651DiVA, id: diva2:1203300
Available from: 2018-05-03 Created: 2018-05-03 Last updated: 2018-07-20

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Nikkar, SamiraNordström, Jan

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