Convergence of parareal for the Navier-Stokes equations depending on the Reynolds number

Publikationstyp
Conference Paper
Date Issued
2014-10-31
Sprache
English
Author(s)
Steiner, Johannes  
Ruprecht, Daniel  orcid-logo
Speck, Robert  
Krause, Rolf  
TORE-URI
http://hdl.handle.net/11420/10538
First published in
Lecture notes in computational science and engineering  
Number in series
103
Start Page
195
End Page
202
Citation
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)
Contribution to Conference
10th European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2013  
Publisher DOI
10.1007/978-3-319-10705-9_19
Scopus ID
2-s2.0-84919789607
Publisher
Springer
Peer Reviewed
true
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.
Subjects
Reynolds Number
Linear Stability Analysis
Stability Domain
Domain Decomposition Method
Drive Cavity
DDC Class
510: Mathematik