A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations

Handle URI:
http://hdl.handle.net/10754/597336
Title:
A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations
Authors:
Guermond, J.L.; Minev, P.D.
Abstract:
We introduce in this paper a new direction splitting algorithm for solving the incompressible Navier-Stokes equations. The main originality of the method consists of using the operator (I-∂xx)(I-∂yy)(I-∂zz) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2×109 points. © 2011 Elsevier B.V.
Citation:
Guermond JL, Minev PD (2011) A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations. Computer Methods in Applied Mechanics and Engineering 200: 2083–2093. Available: http://dx.doi.org/10.1016/j.cma.2011.02.007.
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jun-2011
DOI:
10.1016/j.cma.2011.02.007
Type:
Article
ISSN:
0045-7825
Sponsors:
This publication is based on work partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).The work of this author is also supported by fellowships from the Institute of Applied Mathematics and Computational Science and the Institute of Scientific Computing at Texas A&M University, and a Discovery grant of NSERC.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorGuermond, J.L.en
dc.contributor.authorMinev, P.D.en
dc.date.accessioned2016-02-25T12:30:58Zen
dc.date.available2016-02-25T12:30:58Zen
dc.date.issued2011-06en
dc.identifier.citationGuermond JL, Minev PD (2011) A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations. Computer Methods in Applied Mechanics and Engineering 200: 2083–2093. Available: http://dx.doi.org/10.1016/j.cma.2011.02.007.en
dc.identifier.issn0045-7825en
dc.identifier.doi10.1016/j.cma.2011.02.007en
dc.identifier.urihttp://hdl.handle.net/10754/597336en
dc.description.abstractWe introduce in this paper a new direction splitting algorithm for solving the incompressible Navier-Stokes equations. The main originality of the method consists of using the operator (I-∂xx)(I-∂yy)(I-∂zz) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2×109 points. © 2011 Elsevier B.V.en
dc.description.sponsorshipThis publication is based on work partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).The work of this author is also supported by fellowships from the Institute of Applied Mathematics and Computational Science and the Institute of Scientific Computing at Texas A&M University, and a Discovery grant of NSERC.en
dc.publisherElsevier BVen
dc.subjectADIen
dc.subjectDirection splittingen
dc.subjectIncompressible flowsen
dc.subjectNavier-Stokesen
dc.subjectPressure Poisson equationen
dc.subjectTime splittingen
dc.titleA new class of massively parallel direction splitting for the incompressible Navier–Stokes equationsen
dc.typeArticleen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionLIMSI Laobratoire d'Informatique pour la Mecanique et les Sciences de l'Ingenieur, Orsay, Franceen
dc.contributor.institutionUniversity of Alberta, Edmonton, Canadaen
kaust.grant.numberKUS-C1-016-04en
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