uu.seUppsala University Publications
Change search
Refine search result
1 - 14 of 14
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • 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. Iaccarino, Gianluca
    et al.
    Pettersson, Per
    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.
    Witteveen, Jeroen
    Numerical methods for uncertainty propagation in high speed flows2010In: Proc. ECCOMAS CFD Conference 2010, Portugal: Tech. Univ. Lisbon , 2010, p. 11-Conference paper (Refereed)
  • 2.
    Pettersson, Per
    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.
    Uncertainty Quantification and Numerical Methods for Conservation Laws2013Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Conservation laws with uncertain initial and boundary conditions are approximated using a generalized polynomial chaos expansion approach where the solution is represented as a generalized Fourier series of stochastic basis functions, e.g. orthogonal polynomials or wavelets. The stochastic Galerkin method is used to project the governing partial differential equation onto the stochastic basis functions to obtain an extended deterministic system.

    The stochastic Galerkin and collocation methods are used to solve an advection-diffusion equation with uncertain viscosity. We investigate well-posedness, monotonicity and stability for the stochastic Galerkin system. High-order summation-by-parts operators and weak imposition of boundary conditions are used to prove stability. We investigate the impact of the total spatial operator on the convergence to steady-state. 

    Next we apply the stochastic Galerkin method to Burgers' equation with uncertain boundary conditions. An analysis of the truncated polynomial chaos system presents a qualitative description of the development of the solution over time. An analytical solution is derived and the true polynomial chaos coefficients are shown to be smooth, while the corresponding coefficients of the truncated stochastic Galerkin formulation are shown to be discontinuous. We discuss the problematic implications of the lack of known boundary data and possible ways of imposing stable and accurate boundary conditions.

    We present a new fully intrusive method for the Euler equations subject to uncertainty based on a Roe variable transformation. The Roe formulation saves computational cost compared to the formulation based on expansion of conservative variables. Moreover, it is more robust and can handle cases of supersonic flow, for which the conservative variable formulation fails to produce a bounded solution. A multiwavelet basis that can handle  discontinuities in a robust way is used.

    Finally, we investigate a two-phase flow problem. Based on regularity analysis of the generalized polynomial chaos coefficients, we present a hybrid method where solution regions of varying smoothness are coupled weakly through interfaces. In this way, we couple smooth solutions solved with high-order finite difference methods with non-smooth solutions solved for with shock-capturing methods.

    List of papers
    1. Numerical analysis of the Burgers' equation in the presence of uncertainty
    Open this publication in new window or tab >>Numerical analysis of the Burgers' equation in the presence of uncertainty
    2009 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 228, p. 8394-8412Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-108561 (URN)10.1016/j.jcp.2009.08.012 (DOI)000271342600011 ()
    Available from: 2009-09-22 Created: 2009-09-22 Last updated: 2018-01-13Bibliographically approved
    2. Boundary procedures for the time-dependent Burgers' equation under uncertainty
    Open this publication in new window or tab >>Boundary procedures for the time-dependent Burgers' equation under uncertainty
    2010 (English)In: Acta Mathematica Scientia, ISSN 0252-9602, E-ISSN 1003-3998, Vol. 30, p. 539-550Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-123426 (URN)10.1016/S0252-9602(10)60061-6 (DOI)000276112800009 ()
    Available from: 2010-04-02 Created: 2010-04-27 Last updated: 2018-01-12Bibliographically approved
    3. On stability and monotonicity requirements of discretized stochastic conservation laws with random viscosity
    Open this publication in new window or tab >>On stability and monotonicity requirements of discretized stochastic conservation laws with random viscosity
    2012 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-028
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-182195 (URN)
    Available from: 2012-09-30 Created: 2012-10-04 Last updated: 2013-01-11Bibliographically approved
    4. A stochastic Galerkin method for the Euler equations with Roe variable transformation
    Open this publication in new window or tab >>A stochastic Galerkin method for the Euler equations with Roe variable transformation
    2012 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-033
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-184967 (URN)
    Available from: 2012-11-15 Created: 2012-11-15 Last updated: 2013-01-11Bibliographically approved
    5. An intrusive hybrid method for discontinuous two-phase flow under uncertainty
    Open this publication in new window or tab >>An intrusive hybrid method for discontinuous two-phase flow under uncertainty
    2012 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-035
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-188347 (URN)
    Available from: 2012-12-16 Created: 2012-12-16 Last updated: 2013-01-11Bibliographically approved
  • 3.
    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)
  • 4.
    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.
    Doostan, Alireza
    Nordström, Jan
    On stability and monotonicity requirements of discretized stochastic conservation laws with random viscosity2012Report (Other academic)
  • 5.
    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.
    Doostan, Alireza
    Nordström, Jan
    On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity2013In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 258, p. 134-151Article in journal (Refereed)
  • 6.
    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.
    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.
    A Roe variable based chaos method for the Euler equations under uncertainty2012Report (Other academic)
  • 7.
    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.
    Iaccarino, Gianluca
    Nordström, Jan
    A stochastic Galerkin method for the Euler equations with Roe variable transformation2012Report (Other academic)
  • 8.
    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.
    Iaccarino, Gianluca
    Nordström, Jan
    A stochastic Galerkin method for the Euler equations with Roe variable transformation2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 257, p. 481-500Article in journal (Refereed)
  • 9.
    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.
    Iaccarino, Gianluca
    Nordström, Jan
    An intrusive hybrid method for discontinuous two-phase flow under uncertainty2012Report (Other academic)
  • 10.
    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.
    Iaccarino, Gianluca
    Nordström, Jan
    An intrusive hybrid method for discontinuous two-phase flow under uncertainty2013In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 86, p. 228-239Article 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.
    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.
    Boundary procedures for the time-dependent stochastic Burgers' equation2009In: Proc. 19th AIAA CFD Conference, AIAA , 2009Conference paper (Refereed)
  • 12.
    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.
    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.
    Numerical analysis of Burgers' equation with uncertain boundary conditions using the stochastic Galerkin method2008Report (Other academic)
  • 13.
    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.
    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.
    Numerical analysis of the Burgers' equation in the presence of uncertainty2009In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 228, p. 8394-8412Article in journal (Refereed)
  • 14.
    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.
    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.
    Iaccarino, Gianluca
    Boundary procedures for the time-dependent Burgers' equation under uncertainty2010In: Acta Mathematica Scientia, ISSN 0252-9602, E-ISSN 1003-3998, Vol. 30, p. 539-550Article in journal (Refereed)
1 - 14 of 14
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • 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