A dual consistent summation-by-parts formulation for the linearized incompressible Navier-Stokes equations posed on deforming domains
2016 (English)Report (Other academic)
In this article, well-posedness and dual consistency of the linearized incompressible Navier-Stokes equations posed on time-dependent spatial domains are studied. To simplify the derivation of the dual problem, the second order formulation is transformed to rst order form. Boundary conditions that simultaneously lead to well-posedness of the primal and dual problems are derived.
We construct fully discrete nite di erence schemes on summation-byparts form, in combination with the simultaneous approximation technique. We prove energy stability and discrete dual consistency. Moreover, we show how to construct the penalty operators such that the scheme automatically adjusts to the variations of the spatial domain, and as a result, stability and discrete dual consistency follow simultaneously.
The method is illustrated by considering a deforming time-dependent spatial domain in two dimensions. The numerical calculations are performed using high order operators in space and time. The results corroborate the stability of the scheme and the accuracy of the solution. We also show that linear functionals are superconverging. Additionally, we investigate the convergence of non-linear functionals and the divergence of the solution.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. , 26 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2016:10
Incompressible Navier-Stokes equations, Deforming domain, Stability, Dual consistency, High order accuracy, Superconvergence
IdentifiersURN: urn:nbn:se:liu:diva-130584ISRN: LiTH-MAT-R--2016/10--SEOAI: oai:DiVA.org:liu-130584DiVA: diva2:953289