uu.seUppsala University Publications
Change search
Link to record
Permanent link

Direct link
BETA
Pettersson, Per
Publications (10 of 14) Show all publications
Pettersson, P., Iaccarino, G. & Nordström, J. (2014). A stochastic Galerkin method for the Euler equations with Roe variable transformation. Journal of Computational Physics, 257, 481-500
Open this publication in new window or tab >>A stochastic Galerkin method for the Euler equations with Roe variable transformation
2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 257, p. 481-500Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-213890 (URN)10.1016/j.jcp.2013.10.011 (DOI)000327483200023 ()
Available from: 2013-10-11 Created: 2014-01-05 Last updated: 2017-12-06Bibliographically approved
Pettersson, P., Iaccarino, G. & Nordström, J. (2013). An intrusive hybrid method for discontinuous two-phase flow under uncertainty. Computers & Fluids, 86, 228-239
Open this publication in new window or tab >>An intrusive hybrid method for discontinuous two-phase flow under uncertainty
2013 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 86, p. 228-239Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-207700 (URN)10.1016/j.compfluid.2013.07.009 (DOI)000325834300021 ()
Available from: 2013-07-18 Created: 2013-09-17 Last updated: 2017-12-06Bibliographically approved
Pettersson, P., Doostan, A. & Nordström, J. (2013). On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity. Computer Methods in Applied Mechanics and Engineering, 258, 134-151
Open this publication in new window or tab >>On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity
2013 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 258, p. 134-151Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-202381 (URN)10.1016/j.cma.2013.02.009 (DOI)000319180800011 ()
Available from: 2013-02-28 Created: 2013-06-24 Last updated: 2017-12-06Bibliographically approved
Pettersson, P. (2013). Uncertainty Quantification and Numerical Methods for Conservation Laws. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis
Open this publication in new window or tab >>Uncertainty Quantification and Numerical Methods for Conservation Laws
2013 (English)Doctoral 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.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2013. p. 39
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1008
Keywords
uncertainty quantification, polynomial chaos, stochastic Galerkin methods, conservation laws, hyperbolic problems, finite difference methods, finite volume methods
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-188348 (URN)978-91-554-8569-6 (ISBN)
Public defence
2013-02-08, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2013-01-11 Created: 2012-12-16 Last updated: 2013-04-02Bibliographically approved
Pettersson, P., Iaccarino, G. & Nordström, J. (2012). A Roe variable based chaos method for the Euler equations under uncertainty.
Open this publication in new window or tab >>A Roe variable based chaos method for the Euler equations under uncertainty
2012 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-021
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-179498 (URN)
Available from: 2012-08-16 Created: 2012-08-17Bibliographically approved
Pettersson, P., Iaccarino, G. & Nordström, J. (2012). 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
Pettersson, P., Iaccarino, G. & Nordström, J. (2012). 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
Pettersson, P., Doostan, A. & Nordström, J. (2012). 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
Pettersson, P., Nordström, J. & Iaccarino, G. (2010). Boundary procedures for the time-dependent Burgers' equation under uncertainty. Acta Mathematica Scientia, 30, 539-550
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
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
Organisations

Search in DiVA

Show all publications