A staggered‐grid multilevel incomplete LU for steady incompressible flows

Sven Baars, Mark van der Klok, Jonas Thies, Fred W. Wubs

Research output: Contribution to journalArticleAcademicpeer-review


Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully implicit time integration, also require very robust solvers for this type of linear system. We present a parallel fully coupled multilevel incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed by Wubs and Thies. In this article, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the well-known 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner.
Original languageEnglish
Pages (from-to)909-926
JournalInternational Journal for Numerical Methods in Fluids
Issue number4
Publication statusPublished - 29 Apr 2021


  • incomplete factorization
  • incompressible Navier-Stokes
  • lid-driven cavity
  • multilevel
  • paralle
  • -matrix


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