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Pettersson, Per
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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
Öppna denna publikation i ny flik eller fönster >>A stochastic Galerkin method for the Euler equations with Roe variable transformation
2014 (Engelska)Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 257, s. 481-500Artikel i tidskrift (Refereegranskat) Published
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:uu:diva-213890 (URN)10.1016/j.jcp.2013.10.011 (DOI)000327483200023 ()
Tillgänglig från: 2013-10-11 Skapad: 2014-01-05 Senast uppdaterad: 2017-12-06Bibliografiskt granskad
Pettersson, P., Iaccarino, G. & Nordström, J. (2013). An intrusive hybrid method for discontinuous two-phase flow under uncertainty. Computers & Fluids, 86, 228-239
Öppna denna publikation i ny flik eller fönster >>An intrusive hybrid method for discontinuous two-phase flow under uncertainty
2013 (Engelska)Ingår i: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 86, s. 228-239Artikel i tidskrift (Refereegranskat) Published
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:uu:diva-207700 (URN)10.1016/j.compfluid.2013.07.009 (DOI)000325834300021 ()
Tillgänglig från: 2013-07-18 Skapad: 2013-09-17 Senast uppdaterad: 2017-12-06Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity
2013 (Engelska)Ingår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 258, s. 134-151Artikel i tidskrift (Refereegranskat) Published
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:uu:diva-202381 (URN)10.1016/j.cma.2013.02.009 (DOI)000319180800011 ()
Tillgänglig från: 2013-02-28 Skapad: 2013-06-24 Senast uppdaterad: 2017-12-06Bibliografiskt granskad
Pettersson, P. (2013). Uncertainty Quantification and Numerical Methods for Conservation Laws. (Doctoral dissertation). Uppsala: Acta Universitatis Upsaliensis
Öppna denna publikation i ny flik eller fönster >>Uncertainty Quantification and Numerical Methods for Conservation Laws
2013 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Uppsala: Acta Universitatis Upsaliensis, 2013. s. 39
Serie
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1008
Nyckelord
uncertainty quantification, polynomial chaos, stochastic Galerkin methods, conservation laws, hyperbolic problems, finite difference methods, finite volume methods
Nationell ämneskategori
Beräkningsmatematik
Forskningsämne
Beräkningsvetenskap med inriktning mot numerisk analys
Identifikatorer
urn:nbn:se:uu:diva-188348 (URN)978-91-554-8569-6 (ISBN)
Disputation
2013-02-08, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2013-01-11 Skapad: 2012-12-16 Senast uppdaterad: 2013-04-02Bibliografiskt granskad
Pettersson, P., Iaccarino, G. & Nordström, J. (2012). A Roe variable based chaos method for the Euler equations under uncertainty.
Öppna denna publikation i ny flik eller fönster >>A Roe variable based chaos method for the Euler equations under uncertainty
2012 (Engelska)Rapport (Övrigt vetenskapligt)
Serie
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-021
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:uu:diva-179498 (URN)
Tillgänglig från: 2012-08-16 Skapad: 2012-08-17Bibliografiskt granskad
Pettersson, P., Iaccarino, G. & Nordström, J. (2012). A stochastic Galerkin method for the Euler equations with Roe variable transformation.
Öppna denna publikation i ny flik eller fönster >>A stochastic Galerkin method for the Euler equations with Roe variable transformation
2012 (Engelska)Rapport (Övrigt vetenskapligt)
Serie
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-033
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:uu:diva-184967 (URN)
Tillgänglig från: 2012-11-15 Skapad: 2012-11-15 Senast uppdaterad: 2013-01-11Bibliografiskt granskad
Pettersson, P., Iaccarino, G. & Nordström, J. (2012). An intrusive hybrid method for discontinuous two-phase flow under uncertainty.
Öppna denna publikation i ny flik eller fönster >>An intrusive hybrid method for discontinuous two-phase flow under uncertainty
2012 (Engelska)Rapport (Övrigt vetenskapligt)
Serie
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-035
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:uu:diva-188347 (URN)
Tillgänglig från: 2012-12-16 Skapad: 2012-12-16 Senast uppdaterad: 2013-01-11Bibliografiskt granskad
Pettersson, P., Doostan, A. & Nordström, J. (2012). On stability and monotonicity requirements of discretized stochastic conservation laws with random viscosity.
Öppna denna publikation i ny flik eller fönster >>On stability and monotonicity requirements of discretized stochastic conservation laws with random viscosity
2012 (Engelska)Rapport (Övrigt vetenskapligt)
Serie
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-028
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:uu:diva-182195 (URN)
Tillgänglig från: 2012-09-30 Skapad: 2012-10-04 Senast uppdaterad: 2013-01-11Bibliografiskt granskad
Pettersson, P., Nordström, J. & Iaccarino, G. (2010). Boundary procedures for the time-dependent Burgers' equation under uncertainty. Acta Mathematica Scientia, 30, 539-550
Öppna denna publikation i ny flik eller fönster >>Boundary procedures for the time-dependent Burgers' equation under uncertainty
2010 (Engelska)Ingår i: Acta Mathematica Scientia, ISSN 0252-9602, E-ISSN 1003-3998, Vol. 30, s. 539-550Artikel i tidskrift (Refereegranskat) Published
Nationell ämneskategori
Beräkningsmatematik Datavetenskap (datalogi)
Identifikatorer
urn:nbn:se:uu:diva-123426 (URN)10.1016/S0252-9602(10)60061-6 (DOI)000276112800009 ()
Tillgänglig från: 2010-04-02 Skapad: 2010-04-27 Senast uppdaterad: 2018-01-12Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>Efficiency of shock capturing schemes for Burgers' equation with boundary uncertainty
2010 (Engelska)Ingår i: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, s. 737-745Konferensbidrag, Publicerat paper (Refereegranskat)
Ort, förlag, år, upplaga, sidor
Berlin: Springer-Verlag, 2010
Nationell ämneskategori
Beräkningsmatematik Datavetenskap (datalogi)
Identifikatorer
urn:nbn:se:uu:diva-132932 (URN)10.1007/978-3-642-11795-4_79 (DOI)000395207900079 ()978-3-642-11794-7 (ISBN)
Tillgänglig från: 2010-10-29 Skapad: 2010-10-29 Senast uppdaterad: 2018-06-16Bibliografiskt granskad
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