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Eriksson, Sofia
Publications (10 of 15) Show all publications
Eriksson, S. & Nordström, J. (2013). Well-posedness and stability of exact non-reflecting boundary conditions. In: Proc. 21st AIAA CFD Conference: . AIAA
Open this publication in new window or tab >>Well-posedness and stability of exact non-reflecting boundary conditions
2013 (English)In: Proc. 21st AIAA CFD Conference, AIAA , 2013Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
AIAA, 2013
Series
Conference Proceeding Series ; 2013-2960
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-207703 (URN)10.2514/6.2013-2960 (DOI)
Available from: 2013-06-26 Created: 2013-09-17 Last updated: 2013-09-17Bibliographically approved
Eriksson, S. & Nordström, J. (2012). Exact non-reflecting boundary conditions revisited: well-posedness and stability.
Open this publication in new window or tab >>Exact non-reflecting boundary conditions revisited: well-posedness and stability
2012 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-032
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-183131 (URN)
Available from: 2012-10-19 Created: 2012-10-22 Last updated: 2013-01-23Bibliographically approved
Eriksson, S. (2012). Stable Numerical Methods with Boundary and Interface Treatment for Applications in Aerodynamics. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis
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. p. 26
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 985
Keywords
summation by parts, simultaneous approximation term, accuracy, stability, finite difference methods
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
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)
Opponent
Supervisors
Available from: 2012-11-16 Created: 2012-10-19 Last updated: 2013-01-23Bibliographically approved
Nordström, J., Eriksson, S. & Eliasson, P. (2012). Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations. Journal of Computational Physics, 231, 4867-4884
Open this publication in new window or tab >>Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations
2012 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, p. 4867-4884Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-173565 (URN)10.1016/j.jcp.2012.04.007 (DOI)000304257600021 ()
Available from: 2012-04-18 Created: 2012-04-26 Last updated: 2017-12-07Bibliographically approved
Eriksson, S., Abbas, Q. & Nordström, J. (2011). A stable and conservative method for locally adapting the design order of finite difference schemes. Journal of Computational Physics, 230, 4216-4231
Open this publication in new window or tab >>A stable and conservative method for locally adapting the design order of finite difference schemes
2011 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, p. 4216-4231Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-134055 (URN)10.1016/j.jcp.2010.11.020 (DOI)000290185000007 ()
Available from: 2010-11-20 Created: 2010-11-21 Last updated: 2018-01-12Bibliographically approved
Nordström, J. & Eriksson, S. (2010). Fluid structure interaction problems: the necessity of a well posed, stable and accurate formulation. Communications in Computational Physics, 8, 1111-1138
Open this publication in new window or tab >>Fluid structure interaction problems: the necessity of a well posed, stable and accurate formulation
2010 (English)In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 8, p. 1111-1138Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-126723 (URN)10.4208/cicp.260409.120210a (DOI)000284672100007 ()
Available from: 2010-06-23 Created: 2010-06-23 Last updated: 2017-12-12Bibliographically approved
Eriksson, S. & Nordström, J. (2009). Analysis of mesh and boundary effects on the accuracy of node-centered finite volume schemes. In: Proc. 19th AIAA CFD Conference. AIAA
Open this publication in new window or tab >>Analysis of mesh and boundary effects on the accuracy of node-centered finite volume schemes
2009 (English)In: Proc. 19th AIAA CFD Conference, AIAA , 2009Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
AIAA, 2009
Series
Conference Proceeding Series ; 2009-3651
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-110132 (URN)
Available from: 2009-11-04 Created: 2009-11-04 Last updated: 2018-01-12Bibliographically approved
Eriksson, S. & Nordström, J. (2009). Analysis of the order of accuracy for node-centered finite volume schemes. Applied Numerical Mathematics, 59, 2659-2676
Open this publication in new window or tab >>Analysis of the order of accuracy for node-centered finite volume schemes
2009 (English)In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 59, p. 2659-2676Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-105956 (URN)10.1016/j.apnum.2009.06.001 (DOI)000268513700023 ()
Available from: 2009-06-10 Created: 2009-06-10 Last updated: 2018-01-13Bibliographically approved
Eriksson, S. & Nordström, J. (2009). Analysis of the order of accuracy for node-centered finite volume schemes.
Open this publication in new window or tab >>Analysis of the order of accuracy for node-centered finite volume schemes
2009 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2009-009
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-99695 (URN)
Available from: 2009-03-18 Created: 2009-03-18 Last updated: 2018-01-13Bibliographically approved
Nordström, J., Eriksson, S., Law, C. & Gong, J. (2009). Shock and vortex calculations using a very high order accurate Euler and Navier-Stokes solver. Journal of Mechanics and MEMS, 1(1), 19-26
Open this publication in new window or tab >>Shock and vortex calculations using a very high order accurate Euler and Navier-Stokes solver
2009 (English)In: Journal of Mechanics and MEMS, ISSN 0974-8407, Vol. 1, no 1, p. 19-26Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-103805 (URN)
Available from: 2009-05-20 Created: 2009-05-20 Last updated: 2018-01-13Bibliographically approved
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