Coupling Requirements for Multi-physics Problems
2016 (English)Report (Other academic)
We consider two hyperbolic systems onfirst 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 are 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 on summation-by-parts form and the interface conditions are imposed weakly in a stable way, using penalty formulations. It is shown that one specific choice of penalty matrices leads to a dual consistent scheme and superconverging functionals.
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 the correct convergence rates are obtained for both the solutions and functionals.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. , 19 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2016:08
Well posed problems, high order finite differences, stability, summation-by-parts, weak interface conditions, dual consistency
IdentifiersURN: urn:nbn:se:liu:diva-130817ISRN: LiTH-MAT-R--2016/08--SEOAI: oai:DiVA.org:liu-130817DiVA: diva2:955580