uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2012 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, 4867-4884 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2012. Vol. 231, 4867-4884 p.
National Category
Computational Mathematics
URN: urn:nbn:se:uu:diva-173565DOI: 10.1016/j.jcp.2012.04.007ISI: 000304257600021OAI: oai:DiVA.org:uu-173565DiVA: diva2:523909
Available from: 2012-04-18 Created: 2012-04-26 Last updated: 2013-01-23Bibliographically approved
In thesis
1. Stable Numerical Methods with Boundary and Interface Treatment for Applications in Aerodynamics
Open this publication in new window or tab >>Stable Numerical Methods with Boundary and Interface Treatment for Applications in Aerodynamics
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In numerical simulations, problems stemming from aerodynamics pose many challenges for the method used. Some of these are addressed in this thesis, such as the fluid interacting with objects, the presence of shocks, and various types of boundary conditions.

Scenarios of the kind mentioned above are described mathematically by initial boundary value problems (IBVPs). We discretize the IBVPs using high order accurate finite difference schemes on summation by parts form (SBP), combined with weakly imposed boundary conditions, a technique called simultaneous approximation term (SAT). By using the energy method, stability can be shown.

The weak implementation is compared to the more commonly used strong implementation, and it is shown that the weak technique enhances the rate of convergence to steady state for problems with solid wall boundary conditions. The analysis is carried out for a linear problem and supported numerically by simulations of the fully non-linear Navier–Stokes equations.

Another aspect of the boundary treatment is observed for fluid structure interaction problems. When exposed to eigenfrequencies, the coupled system starts oscillating, a phenomenon called flutter. We show that the strong implementation sometimes cause instabilities that can be mistaken for flutter.

Most numerical schemes dealing with flows including shocks are first order accurate to avoid spurious oscillations in the solution. By modifying the SBP-SAT technique, a conservative and energy stable scheme is derived where the order of accuracy can be lowered locally. The new scheme is coupled to a shock-capturing scheme and it retains the high accuracy in smooth regions.

For problems with complicated geometry, one strategy is to couple the finite difference method to the finite volume method. We analyze the accuracy of the latter on unstructured grids. For grids of bad quality the truncation error can be of zeroth order, indicating that the method is inconsistent, but we show that some of the accuracy is recovered.

We also consider artificial boundary closures on unbounded domains. Non-reflecting boundary conditions for an incompletely parabolic problem are derived, and it is shown that they yield well-posedness. The SBP-SAT methodology is employed, and we prove that the discretized problem is stable.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. 26 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 985
summation by parts, simultaneous approximation term, accuracy, stability, finite difference methods
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
urn:nbn:se:uu:diva-182953 (URN)978-91-554-8509-2 (ISBN)
Public defence
2012-12-07, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Available from: 2012-11-16 Created: 2012-10-19 Last updated: 2013-01-23Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Nordström, JanEriksson, Sofia
By organisation
Division of Scientific ComputingNumerical Analysis
In the same journal
Journal of Computational Physics
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 330 hits
ReferencesLink to record
Permanent link

Direct link