Contribution to a conference proceedings/Contribution to a book

FZJ-2015-00034

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Convergence of Parareal for the Navier-Stokes Equations Depending on the Reynolds Number

Steiner, J. (Corresponding Author) ; Ruprecht, D. ; Speck, R.FZJ* ; Krause, R.

2015
Springer International Publishing Cham
ISBN: 978-3-319-10704-2 (print), 978-3-319-10705-9 (electronic)

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Please use a persistent id in citations: doi:10.1007/978-3-319-10705-9_19

Abstract: 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.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)
2. DFG project 450829162 - Raum-Zeit-parallele Simulation multimodale Energiesystemen (450829162) (450829162)

Appears in the scientific report 2015

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