lnu.sePublications
Change search
Refine search result
1 - 21 of 21
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1.
    Eliasson, Peter
    et al.
    FOI, Swedish Defence Research Agency.
    Eriksson, Sofia
    Uppsala university.
    Nordström, Jan
    Uppsala university ; FOI, Swedish Defence Research Agency.
    The influence of weak and strong solid wall boundary conditions on the convergence to steady-state of the Navier-Stokes equations2009In: 19th AIAA Computational Fluid Dynamics Conference 2009, American Institute of Aeronautics and Astronautics, 2009, article id 3551Conference paper (Refereed)
    Abstract [en]

    In the present paper we study the influence of weak and strong no-slip solid wall boundary conditions on the convergence to steady-state. Our Navier-Stokes solver is edge based and operates on unstructured grids. The two types of boundary conditions are applied to no-slip adiabatic walls. The two approaches are analyzed for a simplified model problem and the reason for the different convergence rates are discussed in terms of the theoretical findings for the model problem. Numerical results for a 2D viscous steady state low Reynolds number problem show that the weak boundary conditions often provide faster convergence. It is shown that strong boundary conditions can prevent the steady state convergence. It is also demonstrated that the two approaches converge to the same solution. Similar results are obtained for high Reynolds number flow in two and three dimensions.

  • 2.
    Eriksson, Sofia
    Technische Universität Darmstadt, Germany.
    A Dual Consistent Finite Difference Method with Narrow Stencil Second Derivative Operators2018In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 75, no 2, p. 906-940Article in journal (Refereed)
    Abstract [en]

    We study the numerical solutions of time-dependent systems of partial differential equations, focusing on the implementation of boundary conditions. The numerical method considered is a finite difference scheme constructed by high order summation by parts operators, combined with a boundary procedure using penalties (SBP-SAT). Recently it was shown that SBP-SAT finite difference methods can yield superconvergent functional output if the boundary conditions are imposed such that the discretization is dual consistent. We generalize these results so that they include a broader range of boundary conditions and penalty parameters. The results are also generalized to hold for narrow-stencil second derivative operators. The derivations are supported by numerical experiments.

  • 3.
    Eriksson, Sofia
    Uppsala University.
    Stable Numerical Methods with Boundary and Interface Treatment for Applications in Aerodynamics2012Doctoral 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.

  • 4.
    Eriksson, Sofia
    et al.
    Uppsala University.
    Abbas, Qaisar
    Uppsala University.
    Nordström, Jan
    Linköping University.
    A stable and conservative method for locally adapting the design order of finite difference schemes2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 11, p. 4216-4231Article in journal (Refereed)
    Abstract [en]

    A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable.

    Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the developed switching procedure is combined with the MUSCL technique.

  • 5.
    Eriksson, Sofia
    et al.
    Uppsala University.
    Abbas, Qaisar
    Uppsala University.
    Nordström, Jan
    Uppsala University ; University of the Witvatersrand, South Africa ; FOI, The Swedish Defence Research Agency .
    A stable and conservative method of locally adapting the design order of finite difference schemes2010In: Proceedings of the 7th South African Conference on Computational and Applied Mechanics / [ed] S. Kok, D. Wilke & H. Inglis, South African Association for Theoretical and Applied Mechanics , 2010, p. 128-136Conference paper (Other academic)
    Abstract [en]

    A procedure to switch the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be stable and accurate.

    Numerical experiments verify the theoretical accuracy for smooth solutions. In addition shock calculations is performed, using a scheme where the developed switching procedure is combined with the MUSCL technique for shock capturing.

  • 6.
    Eriksson, Sofia
    et al.
    Uppsala University.
    Law, Craig
    Gong, Jing
    Uppsala University.
    Nordström, Jan
    Uppsala University.
    Shock Calculations using a Very High Order Accurate Euler and Navier-Stokes Solver2009In: Proceedings of the Sixth South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2009, p. 63-73Conference paper (Other academic)
  • 7.
    Eriksson, Sofia
    et al.
    Uppsala University.
    Nordström, Jan
    FOI, Swedish Defence Research Agency.
    Analysis of mesh and boundary effects on the accuracy of node-centered finite volume schemes2009In: 19th AIAA Computational Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, 2009, article id 3651Conference paper (Refereed)
    Abstract [en]

    The accuracy of the node-centered finite volume method in one-dimension is analyzed. Numerical simulations and analysis are performed for both a hyperbolic and a elliptic case, for various types of grids. The results from the simulations agree with the analysis. The boundary conditions are implemented weakly using penaly technique. For the hyperbolic case we see that the type of grid has large impact on the order of accuracy, whereas the choice of penaly parameter only affect the error constant. For the elliptic case the grid has less impact on the order of accuracy. For both the hyperbolic and elliptic problem we show that the error contribution from the primal and dual grid can be treated separately.

  • 8.
    Eriksson, Sofia
    et al.
    Uppsala University .
    Nordström, Jan
    Uppsala University ; The Swedish Defence Research Agency.
    Analysis of the order of accuracy for node-centered finite volume schemes2009In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 59, no 10, p. 2659-2676Article in journal (Refereed)
    Abstract [en]

    The order of accuracy of the node-centered finite volume methods is analyzed, and the analysis is based on an exact derivation of the numerical errors in one dimension. The accuracy for various types of grids are considered. Numerical simulations and analysis are performed for both a hyperbolic and a elliptic case, and the results agree. The impact of weakly imposed boundary conditions is analyzed and verified numerically. We show that the error contribution from the primal and dual grid can be treated separately.

  • 9.
    Eriksson, Sofia
    et al.
    Uppsala University.
    Nordström, Jan
    Uppsala University.
    Analysis of the order of accuracy for node-centered finite volume schemes2009Report (Other academic)
    Abstract [en]

    The order of accuracy of the node-centered finite volume methods is analyzed, and the analysis is based on an exact derivation of the numerical errors in one dimension. The accuracy for various types of grids are considered. Numerical simulations and analysis are performed for both a hyperbolic and a eliptic case, and the results agree. The impact of weakly imposed boundary conditions is analyzed and verified numerically. We show that the error contribution from the primal and dual grid can be treated separately.

  • 10.
    Eriksson, Sofia
    et al.
    Technische Universität Darmstadt, Germany.
    Nordström, Jan
    Linköping University.
    Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability2017In: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, Vol. 17, no 4, p. 957-986Article in journal (Refereed)
    Abstract [en]

    Exact non-reflecting boundary conditions for a linear incompletely parabolic system in one dimension have been studied. The system is a model for the linearized compressible Navier-Stokes equations, but is less complicated which allows for a detailed analysis without approximations. It is shown that well-posedness is a fundamental property of the exact non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, it is also shown that energy stability follows automatically.

  • 11.
    Eriksson, Sofia
    et al.
    Uppsala University, Sweden.
    Nordström, Jan
    Linköping University, Sweden.
    Exact non-reflecting boundary conditions revisited: well-posedness and stability2012Report (Other academic)
    Abstract [en]

    Exact non-reflecting boundary conditions for an incompletely parabolic system have been studied. It is shown that well-posedness is a fundamental property of the non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, energy stability follows automatically. The stability in combination with the high order accuracy results in a reliable, efficient and accurate method. The theory is supported by numerical simulations.

  • 12.
    Eriksson, Sofia
    et al.
    University of Linköping.
    Nordström, Jan
    Linköping University.
    Finite difference schemes with transferable interfaces for parabolic problems2018Report (Other academic)
    Abstract [en]

    We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent.

  • 13.
    Eriksson, Sofia
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Nordström, Jan
    Linköping University.
    Finite difference schemes with transferable interfaces for parabolic problems2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, p. 935-949Article in journal (Refereed)
    Abstract [en]

    We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent. (C) 2018 Elsevier Inc. All rights reserved.

  • 14.
    Eriksson, Sofia
    et al.
    Uppsala University.
    Nordström, Jan
    Linköping University.
    Well-posedness and stability of exact non-reflecting boundary conditions2013In: 21st AIAA Computational Fluid Dynamics Conference, Fluid Dynamics and Co-located Conferences, American Institute of Aeronautics and Astronautics, 2013, article id 2960Conference paper (Refereed)
  • 15.
    Eriksson, Sofia
    et al.
    Uppsala University.
    Svärd, Magnus
    Nordström, Jan
    Uppsala University.
    Simulations of Ground Effects on Wake Vortices at Runways2009In: Proceedings of the Sixth South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2009, p. 101-108Conference paper (Refereed)
  • 16.
    Eriksson, Sofia
    et al.
    Uppsala University.
    Svärd, Magnus
    University of Oslo.
    Nordström, Jan
    Uppsala University.
    Simulations of Ground Effects on Wake Vortices at Runways2007Report (Other academic)
    Abstract [en]

    n this paper the interaction between two counter-rotating vortices is examined, and the performance of a newly developed finite difference code is discussed. The Reynolds numbers considered are low to medium, and the flow is compressible. Most of the computations are performed in a two dimensional domain, with different grid sizes, Reynolds number and order of accuracy of the scheme. Finally, a three dimensional computation is made in order to examine the relevance of the two dimensional model.

  • 17.
    Nordström, Jan
    et al.
    Uppsala university ; University Witwatersrand, South Africa ; Swedish Def Res Agcy.
    Eriksson, Sofia
    Uppsala university.
    Fluid structure interaction problems: the necessity of a well posed, stable and accurate formulation2010In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 8, no 5, p. 1111-1138Article in journal (Refereed)
    Abstract [en]

    We investigate problems of fluid structure interaction type and aim for a formulation that leads to a well posed problem and a stable numerical procedure. Our first objective is to investigate if the generally accepted formulations of the fluid structure interaction problem are the only possible ones. Our second objective is to derive a stable numerical coupling. To accomplish that we will use a weak coupling procedure and employ summation-by-parts operators and penalty terms. We compare the weak coupling with other common procedures. We also study the effect of high order accurate schemes. In multiple dimensions this is a formidable task and we start by investigating the simplest possible model problem available. As a flow model we use the linearized Euler equations in one dimension and as the structure model we consider a spring.

  • 18.
    Nordström, Jan
    et al.
    Uppsala University.
    Eriksson, Sofia
    Uppsala University.
    Well Posed, Stable and Weakly Coupled Fluid Structure Interaction Problems2009Report (Other academic)
    Abstract [en]

    We investigate problems of fluid structure interaction type and aim for a formulation that leads to a well posed problem and a stable numerical procedure. Our first objective is to investigate if the generally accepted formulations of the FSI problems are the only possible ones.

    Our second objective is to derive a numerical coupling which is truly stable. To accomplish that we will use a weak coupling procedure and employ summation- by-parts operators and penalty terms. We compare the weak coupling with other common procedures. We also study the effect of high order accurate schemes.

    In multiple dimensions this is a formidable task and for that reason we start by investigating the simplest possible model problem available. As a flow model we use the linearized Euler equations in one dimension and as the structure model we consider a spring.

  • 19.
    Nordström, Jan
    et al.
    University of Linköping.
    Eriksson, Sofia
    Uppsala University.
    Eliasson, Peter
    The Swedish Defence Research Agency.
    Weak and Strong Wall Boundary Procedures and Convergence to Steady-State of the Navier-Stokes Equations2011Report (Refereed)
    Abstract [en]

    We study the influence of different implementations of no-slip solid wall boundary conditions on the convergence to steady-state of the Navier-Stokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steady-state for coarse meshes. It is also demonstrated that all the stable approaches produce the same convergence rate as the mesh size goes to zero. The numerical results obtained by using a fully nonlinear finite volume solver support the theoretical findings from the linear analysis.

  • 20.
    Nordström, Jan
    et al.
    Linköping University.
    Eriksson, Sofia
    Uppsala University.
    Eliasson, Peter
    The Swedish Defense Research Agency.
    Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations2012In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, no 14, p. 4867-4884Article in journal (Refereed)
    Abstract [en]

    We study the influence of different implementations of no-slip solid wall boundary conditions on the convergence to steady-state of the Navier–Stokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steady-state for coarse meshes. It is also demonstrated that all the stable approaches produce the same convergence rate as the mesh size goes to zero. The numerical results obtained by using a fully nonlinear finite volume solver support the theoretical findings from the linear analysis.

  • 21.
    Nordström, Jan
    et al.
    Uppsala University.
    Eriksson, Sofia
    Uppsala University.
    Law, Craig
    Gong, Jing
    Uppsala University.
    Shock and vortex calculations using a very high order accurate Euler and Navier-Stokes solver2009In: Journal of Mechanics and MEMS, ISSN 0974-8407, Vol. 1, no 1, p. 19-26Article in journal (Refereed)
1 - 21 of 21
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf