This title appears in the Scientific Report :
2015
Please use the identifier:
http://dx.doi.org/10.1007/978-3-319-10705-9_19 in citations.
Convergence of Parareal for the Navier-Stokes Equations Depending on the Reynolds Number
Convergence of Parareal for the Navier-Stokes Equations Depending on the Reynolds Number
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 applie...
Saved in:
Personal Name(s): | Steiner, Johannes (Corresponding Author) |
---|---|
Ruprecht, Daniel / Speck, Robert / Krause, Rolf | |
Contributing Institute: |
Jülich Supercomputing Center; JSC |
Published in: |
Numerical Mathematics and Advanced Applications - ENUMATH 2013 |
Imprint: |
Cham
Springer International Publishing
2015
|
Physical Description: |
195 - 202 |
ISBN: |
978-3-319-10705-9 (electronic) 978-3-319-10704-2 (print) |
DOI: |
10.1007/978-3-319-10705-9_19 |
Conference: | European Numerical Mathematics and Advanced Applications, Lausanne (Switzerland), 2013-08-26 - 2013-08-30 |
Document Type: |
Contribution to a book Contribution to a conference proceedings |
Research Program: |
Raum-Zeit-parallele Simulation multimodale Energiesystemen Computational Science and Mathematical Methods |
Series Title: |
Lecture Notes in Computational Science and Engineering
103 |
Publikationsportal JuSER |
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. |