Next Article in Journal / Special Issue
Control of Triple-Shock Configurations and Vortex Structures Forming in High Speed Flows of Gaseous Media past an AD Body under the Action of External Energy Sources
Previous Article in Journal
Electromagnetic Simulation and Alignment of Dual-Polarized Array Antennas in Multi-Mission Phased Array Radars
Previous Article in Special Issue
A New Gaskinetic Model to Analyze Background Flow Effects on Weak Gaseous Jet Flows from Electric Propulsion Devices
Article Menu
Issue 1 (March) cover image

Export Article

Open AccessArticle
Aerospace 2017, 4(1), 8; doi:10.3390/aerospace4010008

On Multirate GARK Schemes with Adaptive Micro Step Sizes for Fluid–Structure Interaction: Order Conditions and Preservation of the Geometric Conservation Law

Department of Mathematics and Natural Sciences, University of Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
*
Author to whom correspondence should be addressed.
Academic Editors: Hossein Zare-Behtash and Kiran Ramesh
Received: 15 December 2016 / Revised: 23 January 2017 / Accepted: 7 February 2017 / Published: 14 February 2017
(This article belongs to the Special Issue Fluid-Structure Interactions)
View Full-Text   |   Download PDF [682 KB, uploaded 14 February 2017]   |  

Abstract

The application of partitioned schemes to fluid–structure interaction (FSI) allows the use of already developed solvers specifically designed for the efficient solution of the corresponding subproblems. In this work, we propose and describe a loosely coupled partitioned scheme based on the recently introduced generalized-structure additively partitioned Runge-Kutta (GARK) framework. The resulting scheme combines implicit-explicit (IMEX) and multirate approaches while coupling of the subproblems is realized both on the level of the discrete time steps and at the level of interior Runge-Kutta stages. Specifically, we allow for varying micro step sizes for the fluid subproblem and therefore extend the multirate GARK framework based on constant micro steps. Furthermore, we derive the order conditions for this extension allowing for coupled time integration schemes of up to third order and discuss specific choices of the Runge-Kutta coefficients complying with the geometric conservation law. Finally, numerical experiments are carried out for uniform flow on a moving grid as well as the classical FSI test case of a moving piston. View Full-Text
Keywords: multirate schemes; IMEX coupling; time adaptivity; fluid–structure interaction multirate schemes; IMEX coupling; time adaptivity; fluid–structure interaction
Figures

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Bremicker-Trübelhorn, S.; Ortleb, S. On Multirate GARK Schemes with Adaptive Micro Step Sizes for Fluid–Structure Interaction: Order Conditions and Preservation of the Geometric Conservation Law. Aerospace 2017, 4, 8.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Aerospace EISSN 2226-4310 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top