On The Acceleration Of Ill-Conditioned Linear Systems: A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow

Gabriela Diaz Cortes, Jan Dirk Jansen, Kees Vuik

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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Abstract

We explore and develop POD-based deflation methods to accelerate the solution of large-scale linear systems resulting from two-phase flow simulation. The techniques here presented collect information from the system in a POD basis, which is later used in a deflation scheme. The snapshots required to obtain the POD basis are captured in two ways: a moving window approach, where the most recently computed solutions are used, and a training phase approach, where a full pre-simulation is run. We test this methodology in highly heterogeneous porous media: a full SPE 10 model containing O(10^6) cells, and in an academic layered problem presenting a contrast in permeability layers up to 10^6. Among the experiments, we study cases including gravity and capillary pressure terms. With the POD-based deflated procedure, we accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method, reducing the required number of iterations to around 10-30 %, i.e., we achieve speed-ups of factors three to ten.
Original languageEnglish
Title of host publicationECMOR XVI
EditorsD. Gunasekera
Place of PublicationBarcelona
PublisherEAGE
Pages1-22
Number of pages22
ISBN (Print)9789462822603
DOIs
Publication statusPublished - 2018
Event16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018: 3–6 September 2018, Barcelona, Spain - Barcelona, Spain
Duration: 3 Sep 20186 Sep 2018
Conference number: 16
https://events.eage.org/en/2018/ecmorxvi

Conference

Conference16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018
Abbreviated titleECMOR 2018
Country/TerritorySpain
CityBarcelona
Period3/09/186/09/18
Internet address

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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  • POD-Based Deflation Method For Reservoir Simulation

    Diaz Cortes, G., 2019, Delft, the Netherlands. 156 p.

    Research output: ThesisDissertation (TU Delft)

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