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Coupling Requirements for Multiphysics Problems Posed on Two 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
2017 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 55, no 6, p. 2885-2904Article in journal (Refereed) Published
Abstract [en]

We consider two hyperbolic systems in first order form of different size posed on two domains. Our ambition is to derive general conditions for when the two systems can and cannot be coupled. The adjoint equations are derived and well-posedness of the primal and dual problems is discussed. By applying the energy method, interface conditions for the primal and dual problems are derived such that the continuous problems are well posed. The equations are discretized using a high order finite difference method in summation-by-parts form and the interface conditions are imposed weakly in a stable way, using penalty formulations. It is shown that one specic choice of penalty matrices leads to a dual consistent scheme. By considering an example, it is shown that the correct physical coupling conditions are contained in the set of well posed coupling conditions. It is also shown that dual consistency leads to superconverging functionals and reduced stiffness.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2017. Vol. 55, no 6, p. 2885-2904
Keyword [en]
well posed problems, high order finite diffrences, stability, summation-by-parts, weak interface conditions, dual consistency, stiffness, superconvergence
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-143261DOI: 10.1137/16M1087710ISI: 000418663500015OAI: oai:DiVA.org:liu-143261DiVA, id: diva2:1160741
Available from: 2017-11-28 Created: 2017-11-28 Last updated: 2018-01-26Bibliographically approved

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Ghasemi, FatemehNordström, Jan
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