Convergence of Parareal for the Navier-Stokes Equations Depending on the Reynolds Number

  • Johannes Steiner
  • Daniel Ruprecht
  • Robert Speck
  • Rolf Krause
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 103)


The paper presents first a linear stability analysis for the time-parallel Parareal method, using an IMEX Euler as coarse and a Runge-Kutta-3 method as fine propagator, confirming that dominant imaginary eigenvalues negatively affect Parareal’s convergence. This suggests that when Parareal is applied to the nonlinear Navier-Stokes equations, problems for small viscosities could arise. Numerical results for a driven cavity benchmark are presented, confirming that Parareal’s convergence can indeed deteriorate as viscosity decreases and the flow becomes increasingly dominated by convection. The effect is found to strongly depend on the spatial resolution.


Reynolds Number Linear Stability Analysis Stability Domain Domain Decomposition Method Drive Cavity 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Johannes Steiner
    • 1
  • Daniel Ruprecht
    • 1
  • Robert Speck
    • 2
  • Rolf Krause
    • 1
  1. 1.Institute of Computational ScienceUniversità della Svizzera italianaLuganoSwitzerland
  2. 2.Jülich Supercomputing CentreForschungszentrum JülichJülichGermany

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