Publisher DOI: 10.1007/978-3-319-10705-9_19
Title: Convergence of parareal for the Navier-Stokes equations depending on the Reynolds number
Language: English
Authors: Steiner, Johannes 
Ruprecht, Daniel  
Speck, Robert 
Krause, Rolf 
Keywords: Reynolds Number; Linear Stability Analysis; Stability Domain; Domain Decomposition Method; Drive Cavity
Issue Date: 31-Oct-2014
Publisher: Springer
Source: ENUMATH 2013 : Proceedings of ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013. - Cham, 2015. - (Lecture Notes in Computational Science and Engineering ; 103). - Pp. 195-202 (2015)
Abstract (english): 
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.
Conference: 10th European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2013 
ISBN: 978-3-319-10704-2
Document Type: Chapter/Article (Proceedings)
Peer Reviewed: Yes
Part of Series: Lecture notes in computational science and engineering 
Volume number: 103
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