TY  - CONF
AU  - Steiner, Johannes
AU  - Ruprecht, Daniel
AU  - Speck, Robert
AU  - Krause, Rolf
TI  - Convergence of Parareal for the Navier-Stokes Equations Depending on the Reynolds Number
VL  - 103
CY  - Cham
PB  - Springer International Publishing
M1  - FZJ-2015-00034
SN  - 978-3-319-10704-2 (print)
T2  - Lecture Notes in Computational Science and Engineering
SP  - 195 - 202
PY  - 2015
AB  - 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.
T2  - European Numerical Mathematics and Advanced Applications
CY  - 26 Aug 2013 - 30 Aug 2013, Lausanne (Switzerland)
Y2  - 26 Aug 2013 - 30 Aug 2013
M2  - Lausanne, Switzerland
LB  - PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
DO  - DOI:10.1007/978-3-319-10705-9_19
UR  - https://juser.fz-juelich.de/record/185897
ER  -