Issue |
Math. Model. Nat. Phenom.
Volume 16, 2021
Fluid-structure interaction
|
|
---|---|---|
Article Number | 20 | |
Number of page(s) | 19 | |
DOI | https://doi.org/10.1051/mmnp/2021005 | |
Published online | 25 March 2021 |
Parallel time-stepping for fluid–structure interactions
1
Helmut Schmidt University,
Hamburg, Germany.
2
Otto-von-Guericke Universität Magdeburg,
Magdeburg, Germany.
* Corresponding author: thomas.richter@ovgu.de
Received:
2
July
2019
Accepted:
11
January
2021
We present a parallel time-stepping method for fluid–structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space is based on equal order finite element for all variables and a variant of the Crank-Nicolson scheme is used as second order time integrator. To accelerate the solution of the systems, we analyze a parallel-in time method. For different numerical test cases in 2d and in 3d we present the efficiency of the resulting solution approach. We also discuss some challenges and limitations that are connected to the special structure of fluid–structure interaction problem. In particular, we will investigate stability and dissipation effects of the time integration and their influence on the convergence of the parareal method. It turns out that especially processes based on an internal dynamics (e.g. driven by the vortex street around an elastic obstacle) cause great difficulties. Configurations however, which are driven by oscillatory problem data, are well-suited for parallel time stepping and allow for substantial speedups.
Mathematics Subject Classification: 65L05 / 65M22 / 65Y05 / 76D05 / 74F10
Key words: Fluid-structure interactions / parallel time stepping / finite elements / monolithic / parareal
© The authors. Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.