On acceleration of krylov-subspace-based newton and arnoldi iterations for incompressible CFD: Replacing time steppers and generation of initial guess

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Abstract

We propose two techniques aimed at improving the convergence rate of steady state and eigenvalue solvers preconditioned by the inverse Stokes operator and realized via time-stepping. First, we suggest a generalization of the Stokes operator so that the resulting preconditioner operator depends on several parameters and whose action preserves zero divergence and boundary conditions. The parameters can be tuned for each problem to speed up the convergence of a Krylov-subspace-based linear algebra solver. This operator can be inverted by the Uzawa-like algorithm, and does not need a time-stepping. Second, we propose to generate an initial guess of steady flow, leading eigenvalue and eigenvector using orthogonal projection on a divergence-free basis satisfying all boundary conditions. The approach, including the two proposed techniques, is illustrated on the solution of the linear stability problem for laterally heated square and cubic cavities.

Original languageEnglish
Title of host publicationComputational Methods in Applied Sciences
PublisherSpringer Netherland
Pages147-167
Number of pages21
DOIs
StatePublished - 2019

Publication series

NameComputational Methods in Applied Sciences
Volume50
ISSN (Print)1871-3033

Keywords

  • CFD
  • Eigenvalue solver
  • Krylov methods
  • Linear stability
  • Newton solver

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