uu.seUppsala universitets publikationer
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
An intrusive hybrid method for discontinuous two-phase flow under uncertainty
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
2012 (Engelska)Rapport (Övrigt vetenskapligt)
Ort, förlag, år, upplaga, sidor
2012.
Serie
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-035
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
URN: urn:nbn:se:uu:diva-188347OAI: oai:DiVA.org:uu-188347DiVA, id: diva2:577674
Tillgänglig från: 2012-12-16 Skapad: 2012-12-16 Senast uppdaterad: 2013-01-11Bibliografiskt granskad
Ingår i avhandling
1. Uncertainty Quantification and Numerical Methods for Conservation Laws
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

Open Access i DiVA

Fulltext saknas i DiVA

Övriga länkar

http://www.it.uu.se/research/publications/reports/2012-035/

Personposter BETA

Pettersson, PerNordström, Jan

Sök vidare i DiVA

Av författaren/redaktören
Pettersson, PerNordström, Jan
Av organisationen
Avdelningen för beräkningsvetenskapNumerisk analys
Beräkningsmatematik

Sök vidare utanför DiVA

GoogleGoogle Scholar

urn-nbn

Altmetricpoäng

urn-nbn
Totalt: 416 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf