liu.seSearch for publications in DiVA
Change search
Refine search result
1 - 13 of 13
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • 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.
    Ghasemi, Fatemeh
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    An energy stable coupling procedure for the compressible and incompressible Navier-Stokes equations2019In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 396, p. 280-302Article in journal (Refereed)
    Abstract [en]

    The coupling of the compressible and incompressible Navier-Stokes equations is considered. Our ambition is to take a first step towards a provably well posed and stable coupling procedure. We study a simplified setting with a stationary planar interface and small disturbances from a steady background flow with zero velocity normal to the interface. The simplified setting motivates the use of the linearized equations, and we derive interface conditions such that the continuous problem satisfy an energy estimate. The interface conditions can be imposed both strongly and weakly. It is shown that the weak and strong interface imposition produce similar continuous energy estimates. We discretize the problem in time and space by employing finite difference operators that satisfy a summation-by-parts rule. The interface and initial conditions are imposed weakly using a penalty formulation. It is shown that the results obtained for the weak interface conditions in the continuous case, lead directly to stability of the fully discrete problem.

    The full text will be freely available from 2021-07-16 11:14
  • 2.
    Ghasemi, Fatemeh
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Coupling requirements for multi-physics problems2016Report (Other academic)
    Abstract [en]

    We consider two hyperbolic systems onfirst order form of different size posed on two domains. Our ambition is to derive general conditions for when the two systems can and cannot be coupled.

    The adjoint equations are derived and well-posedness of the primal and dual problems are discussed. By applying the energy method, interface conditions for the primal and dual problems are derived such that the continuous problems are well posed.

    The equations are discretized using a high order finite difference method on summation-by-parts form and the interface conditions are imposed weakly in a stable way, using penalty formulations. It is shown that one specific choice of penalty matrices leads to a dual consistent scheme and superconverging functionals.

    By considering an example, it is shown that the correct physical coupling conditions are contained in the set of well posed coupling conditions. It is also shown that the correct convergence rates are obtained for both the solutions and functionals.

  • 3.
    Ghasemi, Fatemeh
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Coupling Requirements for Multiphysics Problems Posed on Two Domains2017In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 55, no 6, p. 2885-2904Article in journal (Refereed)
    Abstract [en]

    We consider two hyperbolic systems in first order form of different size posed on two domains. Our ambition is to derive general conditions for when the two systems can and cannot be coupled. The adjoint equations are derived and well-posedness of the primal and dual problems is discussed. By applying the energy method, interface conditions for the primal and dual problems are derived such that the continuous problems are well posed. The equations are discretized using a high order finite difference method in summation-by-parts form and the interface conditions are imposed weakly in a stable way, using penalty formulations. It is shown that one specic choice of penalty matrices leads to a dual consistent scheme. By considering an example, it is shown that the correct physical coupling conditions are contained in the set of well posed coupling conditions. It is also shown that dual consistency leads to superconverging functionals and reduced stiffness.

  • 4.
    Ghasemi Zinatabadi, Fatemeh
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Stability, dual consistency and conservation of summation-by-parts formulations for multiphysics problems2019Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, we consider the numerical solution of initial boundary value problems (IBVPs). Boundary and interface conditions are derived such that the IBVP under consideration is well-posed. We also study the dual problem and the related dual boundary/interface conditions. Once the continuous problem is analyzed, we use finite difference operators with the Summation- By-Parts property (SBP) and a weak boundary/interface treatment using the Simultaneous-Approximation-Terms (SAT) technique to construct high-order accurate numerical schemes. We focus in particular on stability, conservation and dual consistency. The energy method is used as our main analysis tool for both the continuous and numerical problems.

    The contributions of this thesis can be divided into two parts. The first part focuses on the coupling of different IBVPs. Interface conditions are derived such that the continuous problem satisfy an energy estimate and such that the discrete problem is stable. In the first paper, two hyperbolic systems of different size posed on two domains are considered. We derive the dual problem and dual interface conditions. It is also shown that a specific choice of penalty matrices leads to dual consistency. As an application, we study the coupling of the Euler and wave equations. In the fourth paper, we examine how to couple the compressible and incompressible Navier-Stokes equations. In order to obtain a sufficient number of interface conditions, the decoupled heat equation is added to the incompressible equations. The interface conditions include mass and momentum balance and two variants of heat transfer. The typical application in this case is the atmosphere-ocean coupling.

    The second part of the thesis focuses on the relation between the primal and dual problem and the relation between dual consistency and conservation. In the second and third paper, we show that dual consistency and conservation are equivalent concepts for linear hyperbolic conservation laws. We also show that these concepts are equivalent for symmetric or symmetrizable parabolic problems in the fifth contribution. The relation between the primal and dual boundary conditions for linear hyperbolic systems of equations is investigated in the sixth and last paper. It is shown that for given well-posed primal/dual boundary conditions, the corresponding well-posed dual/primal boundary conditions can be obtained by a simple scaling operation. It is also shown how one can proceed directly from the well-posed weak primal problem to the well-posed weak dual problem.  

    List of papers
    1. Coupling Requirements for Multiphysics Problems Posed on Two Domains
    Open this publication in new window or tab >>Coupling Requirements for Multiphysics Problems Posed on Two Domains
    2017 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 55, no 6, p. 2885-2904Article in journal (Refereed) Published
    Abstract [en]

    We consider two hyperbolic systems in first order form of different size posed on two domains. Our ambition is to derive general conditions for when the two systems can and cannot be coupled. The adjoint equations are derived and well-posedness of the primal and dual problems is discussed. By applying the energy method, interface conditions for the primal and dual problems are derived such that the continuous problems are well posed. The equations are discretized using a high order finite difference method in summation-by-parts form and the interface conditions are imposed weakly in a stable way, using penalty formulations. It is shown that one specic choice of penalty matrices leads to a dual consistent scheme. By considering an example, it is shown that the correct physical coupling conditions are contained in the set of well posed coupling conditions. It is also shown that dual consistency leads to superconverging functionals and reduced stiffness.

    Place, publisher, year, edition, pages
    Society for Industrial and Applied Mathematics, 2017
    Keywords
    well posed problems, high order finite diffrences, stability, summation-by-parts, weak interface conditions, dual consistency, stiffness, superconvergence
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:liu:diva-143261 (URN)10.1137/16M1087710 (DOI)000418663500015 ()
    Available from: 2017-11-28 Created: 2017-11-28 Last updated: 2019-08-01Bibliographically approved
    2. On the relation between conservation and dual consistency for summation-by-parts schemes
    Open this publication in new window or tab >>On the relation between conservation and dual consistency for summation-by-parts schemes
    2017 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 344, p. 3p. 437-439Article in journal (Refereed) Published
    Abstract [en]

    n/a

    Publisher
    p. 3
    Keywords
    Initial boundary value problems Summation-by-parts Conservation, Dual consistent, Multi-block, Multi-element
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-137545 (URN)10.1016/j.jcp.2017.04.072 (DOI)000402481300021 ()
    Note

    Classified in the journal as "Short note"

    Available from: 2017-05-21 Created: 2017-05-21 Last updated: 2019-08-01
    3. Corrigendum to “On the relation between conservation and dual consistency for summation-by-parts schemes”[J. Comput. Phys. 344 (2017) 437–439]
    Open this publication in new window or tab >>Corrigendum to “On the relation between conservation and dual consistency for summation-by-parts schemes”[J. Comput. Phys. 344 (2017) 437–439]
    2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 360, p. 247-247Article in journal (Refereed) Published
    Place, publisher, year, edition, pages
    Academic Press, 2018
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-145718 (URN)10.1016/j.jcp.2018.02.046 (DOI)000428966300014 ()
    Available from: 2018-03-19 Created: 2018-03-19 Last updated: 2019-08-01Bibliographically approved
    4. An energy stable coupling procedure for the compressible and incompressible Navier-Stokes equations
    Open this publication in new window or tab >>An energy stable coupling procedure for the compressible and incompressible Navier-Stokes equations
    2019 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 396, p. 280-302Article in journal (Refereed) Published
    Abstract [en]

    The coupling of the compressible and incompressible Navier-Stokes equations is considered. Our ambition is to take a first step towards a provably well posed and stable coupling procedure. We study a simplified setting with a stationary planar interface and small disturbances from a steady background flow with zero velocity normal to the interface. The simplified setting motivates the use of the linearized equations, and we derive interface conditions such that the continuous problem satisfy an energy estimate. The interface conditions can be imposed both strongly and weakly. It is shown that the weak and strong interface imposition produce similar continuous energy estimates. We discretize the problem in time and space by employing finite difference operators that satisfy a summation-by-parts rule. The interface and initial conditions are imposed weakly using a penalty formulation. It is shown that the results obtained for the weak interface conditions in the continuous case, lead directly to stability of the fully discrete problem.

    Place, publisher, year, edition, pages
    Elsevier, 2019
    Keywords
    Compressible fluid, Incompressible fluid, Navier-Stokes equations, Energy estimate, Interface conditions, Stability
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-159116 (URN)10.1016/j.jcp.2019.07.022 (DOI)000481732600015 ()
    Available from: 2019-07-29 Created: 2019-07-29 Last updated: 2019-09-09
    5. On conservation and dual consistency for summation-by-parts based approximations of parabolic problems
    Open this publication in new window or tab >>On conservation and dual consistency for summation-by-parts based approximations of parabolic problems
    2019 (English)Report (Other academic)
    Abstract [en]

    We consider the coupling of parabolic problems discretized using difference operators on summation-by-parts (SBP) form with interface conditions imposed weakly. In, it was shown that conservation and dual consistency are equivalent concepts for linear conservation laws. Here, we show that these concepts are equivalent also for symmetric or symmetrizable parabolic problems, exemplified by the heat equation. We rewrite the heat equation as first order system as in the local discontinuous Galerkin method and show the equivalence of dual consistency and conservation for both the first and second order forms.

    Place, publisher, year, edition, pages
    Linköping: Linköping University Electronic Press, 2019. p. 9
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 2019:5
    National Category
    Computational Mathematics Mathematics
    Identifiers
    urn:nbn:se:liu:diva-158903 (URN)LiTH-MAT-R--2019/05--SE (ISRN)
    Available from: 2019-07-17 Created: 2019-07-17 Last updated: 2019-08-12Bibliographically approved
    6. The relation between primal and dual boundary conditions for hyperbolic systems of equations
    Open this publication in new window or tab >>The relation between primal and dual boundary conditions for hyperbolic systems of equations
    2020 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 401, article id 109032Article in journal (Refereed) Published
    Abstract [en]

    In this paper we study boundary conditions for linear hyperbolic systems of equations and the corresponding dual problem. In particular, we show that the primal and dual boundary conditions are related by a simple scaling relation. It is also shown that the weak dual problem can be derived directly from the weak primal problem. Based on the continuous analysis, we discretize and perform computations with a high-order finite difference scheme on summation- by-parts form with weak boundary conditions. It is shown that the results obtained in the continuous analysis lead directly to stability results for the primal and dual discrete problems. Numerical experiments corroborate the theoretical results.

    Place, publisher, year, edition, pages
    Elsevier, 2020
    Keywords
    Hyperbolic systems, Boundary conditions, Primal problem, Dual problem, Well-posedness, Dual consistency
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-161459 (URN)10.1016/j.jcp.2019.109032 (DOI)
    Available from: 2019-11-01 Created: 2019-11-01 Last updated: 2019-12-05Bibliographically approved
  • 5.
    Ghasemi Zinatabadi, Fatemeh
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    An Energy Stable Coupling Procedure for the Compressible and Incompressible Navier-Stokes Equations2019Report (Other academic)
    Abstract [en]

    The coupling of the compressible and incompressible Navier-Stokes equations is considered. Our ambition is to take a first step towards a provably well posed and stable coupling procedure. We study a simplified setting with a stationary planar interface and small disturbances from a steady background ow with zero velocity normal to the interface.

    The simplified setting motivates the use of the linearized equations, and we derive interface conditions such that the continuous problem satisfy an energy estimate. The interface conditions can be imposed both strongly and weakly. It is shown that the weak and strong interface imposition produce similar continuous energy estimates.

    We discretize the problem in time and space by employing finite difference operators that satisfy a summation-by-parts rule. The interface and initial conditions are imposed weakly using a penalty formulation. It is shown that the results obtained for the weak interface conditions in the continuous case, lead directly to stability of the fully discrete problem.

  • 6.
    Ghasemi Zinatabadi, Fatemeh
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    An Energy Stable Coupling Procedure for the Compressible and Incompressible Navier-Stokes Equations2019Report (Other academic)
    Abstract [en]

    The coupling of the compressible and incompressible Navier-Stokes equations is considered. Our ambition is to take a first step towards a provably well posed and stable coupling procedure. We study a simplified setting with a stationary planar interface and small disturbances from a steady background ow with zero velocity normal to the interface.

    The simplified setting motivates the use of the linearized equations, and we derive interface conditions such that the continuous problem satisfy an energy estimate. The interface conditions can be imposed both strongly and weakly. It is shown that the weak and strong interface imposition produce similar continuous energy estimates.

    We discretize the problem in time and space by employing finite difference operators that satisfy a summation-by-parts rule. The interface and initial conditions are imposed weakly using a penalty formulation. It is shown that the results obtained for the weak interface conditions in the continuous case, lead directly to stability of the fully discrete problem.

  • 7.
    Ghasemi Zinatabadi, Fatemeh
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    On conservation and dual consistency for summation-by-parts based approximations of parabolic problems2019Report (Other academic)
    Abstract [en]

    We consider the coupling of parabolic problems discretized using difference operators on summation-by-parts (SBP) form with interface conditions imposed weakly. In, it was shown that conservation and dual consistency are equivalent concepts for linear conservation laws. Here, we show that these concepts are equivalent also for symmetric or symmetrizable parabolic problems, exemplified by the heat equation. We rewrite the heat equation as first order system as in the local discontinuous Galerkin method and show the equivalence of dual consistency and conservation for both the first and second order forms.

  • 8.
    Ghasemi Zinatabadi, Fatemeh
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    On conservation and dual consistency for summation-by-parts based approximations of parabolic problems2019Report (Other academic)
    Abstract [en]

    We consider the coupling of parabolic problems discretized using difference operators on summation-by-parts (SBP) form with interface conditions imposed weakly. In [1, 2], it was shown that conservation and dual consistency are equivalent concepts for linear conservation laws. Here, we show that these concepts are equivalent also for symmetric or symmetrizable parabolic problems, exemplified by the heat equation. We rewrite the heat equation as first order system as in the local discontinuous Galerkin method and show the equivalence of dual consistency and conservation for both the first and second order forms.

  • 9.
    Ghasemi Zinatabadi, Fatemeh
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    The Relation Between Primal and Dual Boundary Conditions for Hyperbolic Systems of Equations2019Report (Other academic)
    Abstract [en]

    In this paper we study boundary conditions for linear hyperbolic systems of equations and the corresponding dual problems. In particular, we show that the primal and dual boundary conditions are related by a simple scaling relation. It is also shown that the weak dual problem can be derived directly from the weak primal problem.

    Based on the continuous analysis, we discretize and perform computations with a high-order finite difference scheme on summation-by-parts form with weak boundary conditions. It is shown that the results obtained in the continuous analysis lead directly to stability results for the primal and dual discrete problems. Numerical experiments corroborate the theoretical results.

  • 10.
    Nordström, Jan
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Ghasemi, Fatemeh
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Corrigendum to “On the relation between conservation and dual consistency for summation-by-parts schemes”[J. Comput. Phys. 344 (2017) 437–439]2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 360, p. 247-247Article in journal (Refereed)
  • 11.
    Nordström, Jan
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Ghasemi, Fatemeh
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    On the relation between conservation and dual consistency for summation-by-parts schemes2017In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 344, p. 3p. 437-439Article in journal (Refereed)
    Abstract [en]

    n/a

  • 12.
    Nordström, Jan
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Ghasemi, Fatemeh
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    The relation between primal and dual boundary conditions for hyperbolic systems of equations2020In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 401, article id 109032Article in journal (Refereed)
    Abstract [en]

    In this paper we study boundary conditions for linear hyperbolic systems of equations and the corresponding dual problem. In particular, we show that the primal and dual boundary conditions are related by a simple scaling relation. It is also shown that the weak dual problem can be derived directly from the weak primal problem. Based on the continuous analysis, we discretize and perform computations with a high-order finite difference scheme on summation- by-parts form with weak boundary conditions. It is shown that the results obtained in the continuous analysis lead directly to stability results for the primal and dual discrete problems. Numerical experiments corroborate the theoretical results.

    The full text will be freely available from 2021-10-16 00:00
  • 13.
    Nordström, Jan
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Ghasemi Zinatabadi, Fatemeh
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Coupling Requirements for Well Posed and Stable Multi-physics Problems2015In: Coupled Problems in Science and Engineering VI, International Center for Numerical Methods in Engineering (CIMNE), 2015, p. 464-476Conference paper (Other academic)
    Abstract [en]

    We discuss well-posedness and stability of multi-physics problems by studying a model problem. By applying the energy method, boundary and interface conditions are derived such that the continuous and semi-discrete problem are well-posed and stable. The numerical scheme is implemented using high order finite difference operators on summation-by-parts (SBP) form and weakly imposed boundary and interface conditions. Numerical experiments involving a spectral analysis corroborate the theoretical findings.

1 - 13 of 13
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • 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