Adaptive time stepping for fluid-structure interaction solvers

Mayr, M.; Wall, W. A.; Gee, M. W.

doi:10.1016/j.finel.2017.12.002

Title: Adaptive time stepping for fluid-structure interaction solvers

Abstract

In this work, a novel adaptive time stepping scheme for fluid-structure interaction (FSI) problems is proposed that allows for controlling the accuracy of the time-discrete solution. Furthermore, it eases practical computations by providing an efficient and very robust time step size selection. This has proven to be very useful, especially when addressing new physical problems, where no educated guess for an appropriate time step size is available. The fluid and the structure field, but also the fluid-structure interface are taken into account for the purpose of a posteriori error estimation, rendering it easy to implement and only adding negligible additional cost. The adaptive time stepping scheme is incorporated into a monolithic solution framework, but can straightforwardly be applied to partitioned solvers as well. The basic idea can be extended to the coupling of an arbitrary number of physical models. Accuracy and efficiency of the proposed method are studied in a variety of numerical examples ranging from academic benchmark tests to complex biomedical applications like the pulsatile blood flow through an abdominal aortic aneurysm. Finally, the demonstrated accuracy of the time-discrete solution in combination with reduced computational cost make this algorithm very appealing in all kinds of FSI applications.

Authors:

Mayr, M. ^[1]; Wall, W. A. ^[2]; Gee, M. W. ^[3]

Sandia National Lab. (SNL-CA), Livermore, CA (United States); Technical University of Munich (Germany). Mechanics & High Performance Computing Group
Technical University of Munich (Germany). Institute for Computational Mechanics
Technical University of Munich (Germany). Mechanics & High Performance Computing Group

Publication Date:: 2017-12-22

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1429664

Report Number(s):: SAND-2017-11510J
Journal ID: ISSN 0168-874X; 658108

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Finite Elements in Analysis and Design

Additional Journal Information:: Journal Volume: 141; Journal Issue: C; Journal ID: ISSN 0168-874X

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Fluid-structure interaction; Time integration; Error estimation; Adaptivity

Citation Formats


                    Mayr, M., Wall, W. A., and Gee, M. W.. Adaptive time stepping for fluid-structure interaction solvers.  United States: N. p., 2017. 
Web.  doi:10.1016/j.finel.2017.12.002.

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                    Mayr, M., Wall, W. A., & Gee, M. W.. Adaptive time stepping for fluid-structure interaction solvers.  United States.  https://doi.org/10.1016/j.finel.2017.12.002

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                    Mayr, M., Wall, W. A., and Gee, M. W.. Fri .  
"Adaptive time stepping for fluid-structure interaction solvers".  United States.  https://doi.org/10.1016/j.finel.2017.12.002.  https://www.osti.gov/servlets/purl/1429664.

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@article{osti_1429664,

  title        = {Adaptive time stepping for fluid-structure interaction solvers},

  author       = {Mayr, M. and Wall, W. A. and Gee, M. W.},

  abstractNote = {In this work, a novel adaptive time stepping scheme for fluid-structure interaction (FSI) problems is proposed that allows for controlling the accuracy of the time-discrete solution. Furthermore, it eases practical computations by providing an efficient and very robust time step size selection. This has proven to be very useful, especially when addressing new physical problems, where no educated guess for an appropriate time step size is available. The fluid and the structure field, but also the fluid-structure interface are taken into account for the purpose of a posteriori error estimation, rendering it easy to implement and only adding negligible additional cost. The adaptive time stepping scheme is incorporated into a monolithic solution framework, but can straightforwardly be applied to partitioned solvers as well. The basic idea can be extended to the coupling of an arbitrary number of physical models. Accuracy and efficiency of the proposed method are studied in a variety of numerical examples ranging from academic benchmark tests to complex biomedical applications like the pulsatile blood flow through an abdominal aortic aneurysm. Finally, the demonstrated accuracy of the time-discrete solution in combination with reduced computational cost make this algorithm very appealing in all kinds of FSI applications.},

  doi          = {10.1016/j.finel.2017.12.002},

  journal      = {Finite Elements in Analysis and Design},

  number       = C,

  volume       = 141,

  place        = {United States},

  year         = {2017},

  month        = {12}

}

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https://doi.org/10.1016/j.finel.2017.12.002

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Cited by: 18 works

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Figures / Tables:

Figure 1: Problem statement adopted from [38] — Left: The domain Ω is subdivided into a fluid domain Ω^F and a structural domain Ω^S by the fluid-structure interface Γ_FSI. Both subdomains are bounded by Dirichlet boundaries Γ^F_D and Γ ^S _D, Neumann boundaries Γ ^F _N and Γ ^S _N,more »

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