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A stabilized multidomain partition of unity approach to solving incompressible viscous flow

Research output: Contribution to journalArticlepeer-review

Maximilian Balmus, Johan Hoffman, André Massing, David Nordsletten

Original languageEnglish
Article number114656
JournalCOMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume392
Early online date11 Feb 2022
DOIs
Accepted/In press21 Jan 2022
E-pub ahead of print11 Feb 2022
Published15 Mar 2022

Bibliographical note

Funding Information: D.N. acknowledges funding from the Engineering and Physical Sciences Research Council, United Kingdom (EP/N011554/1 and EP/R003866/1). A.M. gratefully acknowledges financial support from the Swedish Research Council under Starting Grant 2017-05038 and from the Wenner-Gren foundation, Sweden under travel grant SSh2017-0013. JH acknowledges the financial support of the Swedish Research Council under Grant 2018-04854. This work is funded by the King's College London and Imperial College London EPSRC Centre for Doctoral Training in Medical Imaging (EP/L015226/1). This work is supported by the Wellcome EPSRC Centre for Medical Engineering at King's College London (WT 203148/Z/16/Z) and by the National Institute for Health Research (NIHR) Biomedical Research Centre award to Guy and St Thomas? NHS Foundation Trust in partnership with King's College London. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health. Funding Information: D.N. acknowledges funding from the Engineering and Physical Sciences Research Council, United Kingdom ( EP/N011554/1 and EP/R003866/1 ). A.M. gratefully acknowledges financial support from the Swedish Research Council under Starting Grant 2017-05038 and from the Wenner-Gren foundation, Sweden under travel grant SSh2017-0013 . JH acknowledges the financial support of the Swedish Research Council under Grant 2018-04854 . This work is funded by the King’s College London and Imperial College London EPSRC Centre for Doctoral Training in Medical Imaging ( EP/L015226/1 ). This work is supported by the Wellcome EPSRC Centre for Medical Engineering at King’s College London ( WT 203148/Z/16/Z ) and by the National Institute for Health Research (NIHR) Biomedical Research Centre award to Guy and St Thomas’ NHS Foundation Trust in partnership with King’s College London. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health. Publisher Copyright: © 2022 The Author(s)

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Abstract

In this work we propose a new stabilized approach for solving the incompressible Navier–Stokes equations on fixed overlapping grids. This new approach is based on the partition of unity finite element method, which defines the solution fields as weighted sums of local fields, supported by the different grids. Here, the discrete weak formulation of the problem is re-set in cG(1)cG(1) stabilized form, which has the dual benefit of lowering grid resolution requirements for convection dominated flows and allowing for the use of velocity and pressure discretizations which do not satisfy the inf–sup condition. Additionally, we provide an outline of our implementation within an existing distributed parallel application and identify four key options to improve the code efficiency namely: the use of cache to store mapped quadrature points and basis function gradients, the intersection volume splitting algorithm, the use of lower order quadrature schemes, and tuning the partition weight associated with the interface elements. The new method is shown to have comparable accuracy to the single mesh boundary-fitted version of the same stabilized solver based on three transient flow tests including both 2D and 3D settings, as well as low and moderate Reynolds number flow conditions. Moreover, we demonstrate how the four implementation options have a synergistic effect lowering the residual assembly time by an order of magnitude compared to a naive implementation, and showing good load balancing properties.

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