Summation-by-parts operators for non-simply connected domains
2016 (English)Report (Other academic)
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 multi-block technique. Finally, an application using the linearized Euler equations for sound propagation is presented.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. , 32 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2016:11
Initial boundary value problems, Stability, Well-posedness, Boundary conditions, Non-simply connected domains, Complex geometries
IdentifiersURN: urn:nbn:se:liu:diva-130585ISRN: LiTH-MAT-R--2016/11--SEOAI: oai:DiVA.org:liu-130585DiVA: diva2:953296