A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D

Pietro Benedusi; Daniel Hupp; Peter Arbenz; Rolf Krause

doi:10.1007/978-3-319-39929-4_26

A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D

Pietro Benedusi^*, Daniel Hupp, Peter Arbenz, Rolf Krause

^*Corresponding author for this work

Applied Mathematics and Computational Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

13 Scopus citations

Abstract

We present a parallel and efficient multilevel solution method for the nonlinear systems arising from the discretization of Navier–Stokes (N-S) equations with finite differences. In particular we study the incompressible, unsteady N-S equations with periodic boundary condition in time. A sequential time integration limits the parallelism of the solver to the spatial variables and can therefore be an obstacle to parallel scalability. Time periodicity allows for a space-time discretization, which adds time as an additional direction for parallelism and thus can improve parallel scalability. To achieve fast convergence, we used a spacetime multigrid algorithm with a SCGS smoothing procedure (symmetrical coupled Gauss–Seidel, a.k.a. box smoothing). This technique, proposed by Vanka (J Comput Phys 65:138–156, 1986), for the steady viscous incompressible Navier–Stokes equations is extended to the unsteady case and its properties are studied using local Fourier analysis. We used numerical experiments to analyze the scalability and the convergence of the solver, focusing on the case of a pulsatile flow.

Original language	English (US)
Title of host publication	Numerical Mathematics and Advanced Applications ENUMATH 2015
Editors	Murat Manguoglu, Bulent Karasozen, Munevver Tezer-Sezgin, Omur Ugur, Munevver Tezer-Sezgin, Murat Manguoglu, Omur Ugur, Serdar Goktepe, Omur Ugur, Munevver Tezer-Sezgin, Murat Manguoglu, Bulent Karasozen, Bulent Karasozen, Serdar Goktepe, Serdar Goktepe
Publisher	Springer Verlag
Pages	265-273
Number of pages	9
ISBN (Print)	9783319399270, 9783319399270, 9783319399270
DOIs	https://doi.org/10.1007/978-3-319-39929-4_26
State	Published - 2016
Event	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2015 - Ankara, Turkey Duration: Sep 14 2015 → Sep 18 2015

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	112
ISSN (Print)	1439-7358

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2015
Country/Territory	Turkey
City	Ankara
Period	09/14/15 → 09/18/15

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016.

ASJC Scopus subject areas

Modeling and Simulation
General Engineering
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

Access to Document

10.1007/978-3-319-39929-4_26

Cite this

Benedusi, P., Hupp, D., Arbenz, P., & Krause, R. (2016). A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D. In M. Manguoglu, B. Karasozen, M. Tezer-Sezgin, O. Ugur, M. Tezer-Sezgin, M. Manguoglu, O. Ugur, S. Goktepe, O. Ugur, M. Tezer-Sezgin, M. Manguoglu, B. Karasozen, B. Karasozen, S. Goktepe, & S. Goktepe (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2015 (pp. 265-273). (Lecture Notes in Computational Science and Engineering; Vol. 112). Springer Verlag. https://doi.org/10.1007/978-3-319-39929-4_26

Benedusi, Pietro ; Hupp, Daniel ; Arbenz, Peter et al. / A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D. Numerical Mathematics and Advanced Applications ENUMATH 2015. editor / Murat Manguoglu ; Bulent Karasozen ; Munevver Tezer-Sezgin ; Omur Ugur ; Munevver Tezer-Sezgin ; Murat Manguoglu ; Omur Ugur ; Serdar Goktepe ; Omur Ugur ; Munevver Tezer-Sezgin ; Murat Manguoglu ; Bulent Karasozen ; Bulent Karasozen ; Serdar Goktepe ; Serdar Goktepe. Springer Verlag, 2016. pp. 265-273 (Lecture Notes in Computational Science and Engineering).

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title = "A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D",

abstract = "We present a parallel and efficient multilevel solution method for the nonlinear systems arising from the discretization of Navier–Stokes (N-S) equations with finite differences. In particular we study the incompressible, unsteady N-S equations with periodic boundary condition in time. A sequential time integration limits the parallelism of the solver to the spatial variables and can therefore be an obstacle to parallel scalability. Time periodicity allows for a space-time discretization, which adds time as an additional direction for parallelism and thus can improve parallel scalability. To achieve fast convergence, we used a spacetime multigrid algorithm with a SCGS smoothing procedure (symmetrical coupled Gauss–Seidel, a.k.a. box smoothing). This technique, proposed by Vanka (J Comput Phys 65:138–156, 1986), for the steady viscous incompressible Navier–Stokes equations is extended to the unsteady case and its properties are studied using local Fourier analysis. We used numerical experiments to analyze the scalability and the convergence of the solver, focusing on the case of a pulsatile flow.",

author = "Pietro Benedusi and Daniel Hupp and Peter Arbenz and Rolf Krause",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2015 ; Conference date: 14-09-2015 Through 18-09-2015",

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doi = "10.1007/978-3-319-39929-4_26",

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editor = "Murat Manguoglu and Bulent Karasozen and Munevver Tezer-Sezgin and Omur Ugur and Munevver Tezer-Sezgin and Murat Manguoglu and Omur Ugur and Serdar Goktepe and Omur Ugur and Munevver Tezer-Sezgin and Murat Manguoglu and Bulent Karasozen and Bulent Karasozen and Serdar Goktepe and Serdar Goktepe",

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Benedusi, P, Hupp, D, Arbenz, P & Krause, R 2016, A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D. in M Manguoglu, B Karasozen, M Tezer-Sezgin, O Ugur, M Tezer-Sezgin, M Manguoglu, O Ugur, S Goktepe, O Ugur, M Tezer-Sezgin, M Manguoglu, B Karasozen, B Karasozen, S Goktepe & S Goktepe (eds), Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol. 112, Springer Verlag, pp. 265-273, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2015, Ankara, Turkey, 09/14/15. https://doi.org/10.1007/978-3-319-39929-4_26

A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D. / Benedusi, Pietro; Hupp, Daniel; Arbenz, Peter et al.
Numerical Mathematics and Advanced Applications ENUMATH 2015. ed. / Murat Manguoglu; Bulent Karasozen; Munevver Tezer-Sezgin; Omur Ugur; Munevver Tezer-Sezgin; Murat Manguoglu; Omur Ugur; Serdar Goktepe; Omur Ugur; Munevver Tezer-Sezgin; Murat Manguoglu; Bulent Karasozen; Bulent Karasozen; Serdar Goktepe; Serdar Goktepe. Springer Verlag, 2016. p. 265-273 (Lecture Notes in Computational Science and Engineering; Vol. 112).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D

AU - Benedusi, Pietro

AU - Hupp, Daniel

AU - Arbenz, Peter

AU - Krause, Rolf

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - We present a parallel and efficient multilevel solution method for the nonlinear systems arising from the discretization of Navier–Stokes (N-S) equations with finite differences. In particular we study the incompressible, unsteady N-S equations with periodic boundary condition in time. A sequential time integration limits the parallelism of the solver to the spatial variables and can therefore be an obstacle to parallel scalability. Time periodicity allows for a space-time discretization, which adds time as an additional direction for parallelism and thus can improve parallel scalability. To achieve fast convergence, we used a spacetime multigrid algorithm with a SCGS smoothing procedure (symmetrical coupled Gauss–Seidel, a.k.a. box smoothing). This technique, proposed by Vanka (J Comput Phys 65:138–156, 1986), for the steady viscous incompressible Navier–Stokes equations is extended to the unsteady case and its properties are studied using local Fourier analysis. We used numerical experiments to analyze the scalability and the convergence of the solver, focusing on the case of a pulsatile flow.

AB - We present a parallel and efficient multilevel solution method for the nonlinear systems arising from the discretization of Navier–Stokes (N-S) equations with finite differences. In particular we study the incompressible, unsteady N-S equations with periodic boundary condition in time. A sequential time integration limits the parallelism of the solver to the spatial variables and can therefore be an obstacle to parallel scalability. Time periodicity allows for a space-time discretization, which adds time as an additional direction for parallelism and thus can improve parallel scalability. To achieve fast convergence, we used a spacetime multigrid algorithm with a SCGS smoothing procedure (symmetrical coupled Gauss–Seidel, a.k.a. box smoothing). This technique, proposed by Vanka (J Comput Phys 65:138–156, 1986), for the steady viscous incompressible Navier–Stokes equations is extended to the unsteady case and its properties are studied using local Fourier analysis. We used numerical experiments to analyze the scalability and the convergence of the solver, focusing on the case of a pulsatile flow.

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DO - 10.1007/978-3-319-39929-4_26

M3 - Conference contribution

AN - SCOPUS:84998893199

SN - 9783319399270

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BT - Numerical Mathematics and Advanced Applications ENUMATH 2015

A2 - Manguoglu, Murat

A2 - Karasozen, Bulent

A2 - Tezer-Sezgin, Munevver

A2 - Ugur, Omur

A2 - Tezer-Sezgin, Munevver

A2 - Manguoglu, Murat

A2 - Ugur, Omur

A2 - Goktepe, Serdar

A2 - Ugur, Omur

A2 - Tezer-Sezgin, Munevver

A2 - Manguoglu, Murat

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ER -

Benedusi P, Hupp D, Arbenz P, Krause R. A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D. In Manguoglu M, Karasozen B, Tezer-Sezgin M, Ugur O, Tezer-Sezgin M, Manguoglu M, Ugur O, Goktepe S, Ugur O, Tezer-Sezgin M, Manguoglu M, Karasozen B, Karasozen B, Goktepe S, Goktepe S, editors, Numerical Mathematics and Advanced Applications ENUMATH 2015. Springer Verlag. 2016. p. 265-273. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-39929-4_26

A parallel multigrid solver for time-periodic incompressible Navier–Stokes equations in 3D

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