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

J.L. Guermond, P.D. Minev

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)2083-2093
Number of pages11
JournalComputer Methods in Applied Mechanics and Engineering
Issue number23-24
StatePublished - Jun 2011
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


Dive into the research topics of 'A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations'. Together they form a unique fingerprint.

Cite this