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Abbas, Qaisar
Publications (10 of 11) Show all publications
Nordström, J., Abbas, Q., Erickson, B. A. & Frenander, H. (2014). A flexible boundary procedure for hyperbolic problems: Multiple penalty terms applied in a domain. Communications in Computational Physics, 16, 541-570
Open this publication in new window or tab >>A flexible boundary procedure for hyperbolic problems: Multiple penalty terms applied in a domain
2014 (English)In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 16, p. 541-570Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-232648 (URN)10.4208/cicp.020313.120314a (DOI)000340786500011 ()
Available from: 2014-06-12 Created: 2014-09-22 Last updated: 2017-12-05Bibliographically 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
Abbas, Q. & Nordström, J. (2011). 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
Abbas, Q. (2011). Weak Boundary and Interface Procedures for Wave and Flow Problems. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis
Open this publication in new window or tab >>Weak Boundary and Interface Procedures for Wave and Flow Problems
2011 (English)Doctoral 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.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2011. p. 42
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 862
Keywords
weak boundary conditions, multiple penalty, finite difference methods, summation-by-parts, high order scheme, hybrid methods, MUSCL scheme, shocks, stability, energy estimate, steady-state, non-reflecting
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-159440 (URN)978-91-554-8176-6 (ISBN)
Public defence
2011-11-07, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2011-10-14 Created: 2011-10-02 Last updated: 2011-11-09Bibliographically approved
Pettersson, P., Abbas, Q., Iaccarino, G. & Nordström, J. (2010). Efficiency of shock capturing schemes for Burgers' equation with boundary uncertainty. In: Numerical Mathematics and Advanced Applications: 2009 (pp. 737-745). Berlin: Springer-Verlag
Open this publication in new window or tab >>Efficiency of shock capturing schemes for Burgers' equation with boundary uncertainty
2010 (English)In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 737-745Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Berlin: Springer-Verlag, 2010
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-132932 (URN)10.1007/978-3-642-11795-4_79 (DOI)000395207900079 ()978-3-642-11794-7 (ISBN)
Available from: 2010-10-29 Created: 2010-10-29 Last updated: 2018-06-16Bibliographically approved
Abbas, Q., van der Weide, E. & Nordström, J. (2010). Energy stability of the MUSCL scheme. In: Numerical Mathematics and Advanced Applications: 2009 (pp. 61-68). Berlin: Springer-Verlag
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
Khan, M., Abbas, Q. & Duru, K. (2010). Magnetohydrodynamic flow of a Sisko fluid in annular pipe: A numerical study. International Journal for Numerical Methods in Fluids, 62, 1169-1180
Open this publication in new window or tab >>Magnetohydrodynamic flow of a Sisko fluid in annular pipe: A numerical study
2010 (English)In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 62, p. 1169-1180Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-137608 (URN)10.1002/fld.2068 (DOI)000276115000006 ()
Available from: 2010-12-16 Created: 2010-12-15 Last updated: 2018-01-12Bibliographically approved
Law, C., Abbas, Q., Nordström, J. & Skews, B. W. (2010). The Effect of Reynolds Number in High Order Accurate Calculations with Shock Diffraction. In: Proc. 7th South African Conference on Computational and Applied Mechanics (pp. 416-423). South African Association for Theoretical and Applied Mechanics
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
Abbas, Q. & Nordström, J. (2010). Weak versus strong no-slip boundary conditions for the Navier-Stokes equations. Engineering Applications of Computational Fluid Mechanics, 4, 29-38
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
Abbas, Q., van der Weide, E. & Nordström, J. (2009). Accurate and stable calculations involving shocks using a new hybrid scheme. In: Proc. 19th AIAA CFD Conference. AIAA
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
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