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  • 1.
    Abbas, Qaisar
    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.
    Weak Boundary and Interface Procedures for Wave and Flow Problems2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems.

    The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case.

    The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach.

    Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks.

    Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability.

    Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.

    List of papers
    1. Weak versus strong no-slip boundary conditions for the Navier-Stokes equations
    Open this publication in new window or tab >>Weak versus strong no-slip boundary conditions for the Navier-Stokes equations
    2010 (English)In: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, p. 29-38Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-112977 (URN)000276898600003 ()
    Available from: 2010-01-24 Created: 2010-01-24 Last updated: 2018-01-12Bibliographically approved
    2. A weak boundary procedure for high order finite difference approximations of hyperbolic problems
    Open this publication in new window or tab >>A weak boundary procedure for high order finite difference approximations of hyperbolic problems
    2011 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2011-019
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-159353 (URN)
    Available from: 2011-09-23 Created: 2011-09-28 Last updated: 2011-11-04Bibliographically approved
    3. Accurate and stable calculations involving shocks using a new hybrid scheme
    Open this publication in new window or tab >>Accurate and stable calculations involving shocks using a new hybrid scheme
    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 ; 2009-3985
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-110133 (URN)
    Available from: 2009-11-04 Created: 2009-11-04 Last updated: 2018-01-12Bibliographically approved
    4. A stable and conservative method for locally adapting the design order of finite difference schemes
    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
    5. Energy stability of the MUSCL scheme
    Open this publication in new window or tab >>Energy stability of the MUSCL scheme
    2010 (English)In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 61-68Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    Berlin: Springer-Verlag, 2010
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-132925 (URN)10.1007/978-3-642-11795-4_5 (DOI)000395207900005 ()978-3-642-11794-7 (ISBN)
    Available from: 2010-10-29 Created: 2010-10-29 Last updated: 2018-06-16Bibliographically approved
    6. The Effect of Reynolds Number in High Order Accurate Calculations with Shock Diffraction
    Open this publication in new window or tab >>The Effect of Reynolds Number in High Order Accurate Calculations with Shock Diffraction
    2010 (English)In: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, p. 416-423Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    South African Association for Theoretical and Applied Mechanics, 2010
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-113571 (URN)978-0-620-49192-1 (ISBN)
    Available from: 2010-01-29 Created: 2010-01-29 Last updated: 2018-01-12Bibliographically approved
  • 2.
    Abbas, Qaisar
    et al.
    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.
    Nordström, Jan
    A weak boundary procedure for high order finite difference approximations of hyperbolic problems2011Report (Other academic)
  • 3.
    Abbas, Qaisar
    et al.
    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.
    Nordström, Jan
    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.
    Weak versus strong no-slip boundary conditions for the Navier-Stokes equations2010In: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, p. 29-38Article in journal (Refereed)
  • 4.
    Abbas, Qaisar
    et al.
    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.
    Nordström, Jan
    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.
    Weak versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations2008In: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, p. 52-62Conference paper (Other academic)
  • 5.
    Abbas, Qaisar
    et al.
    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.
    van der Weide, Edwin
    Nordström, Jan
    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.
    Accurate and stable calculations involving shocks using a new hybrid scheme2009In: Proc. 19th AIAA CFD Conference, AIAA , 2009Conference paper (Refereed)
  • 6.
    Abbas, Qaisar
    et al.
    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.
    van der Weide, Edwin
    Nordström, Jan
    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.
    Energy stability of the MUSCL scheme2010In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 61-68Conference paper (Refereed)
  • 7.
    Eriksson, Sofia
    et al.
    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.
    Abbas, Qaisar
    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.
    Nordström, Jan
    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, p. 4216-4231Article in journal (Refereed)
  • 8. Khan, Masood
    et al.
    Abbas, Qaisar
    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.
    Duru, Kenneth
    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.
    Magnetohydrodynamic flow of a Sisko fluid in annular pipe: A numerical study2010In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 62, p. 1169-1180Article in journal (Refereed)
  • 9. Law, Craig
    et al.
    Abbas, Qaisar
    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.
    Nordström, Jan
    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.
    Skews, Beric W.
    The Effect of Reynolds Number in High Order Accurate Calculations with Shock Diffraction2010In: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, p. 416-423Conference paper (Refereed)
  • 10. Nordström, Jan
    et al.
    Abbas, Qaisar
    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.
    Erickson, Brittany A.
    Frenander, Hannes
    A flexible boundary procedure for hyperbolic problems: Multiple penalty terms applied in a domain2014In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 16, p. 541-570Article in journal (Refereed)
  • 11.
    Pettersson, Per
    et al.
    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.
    Abbas, Qaisar
    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.
    Iaccarino, Gianluca
    Nordström, Jan
    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.
    Efficiency of shock capturing schemes for Burgers' equation with boundary uncertainty2010In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 737-745Conference paper (Refereed)
1 - 11 of 11
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