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On the convergence rate of the Dirichlet-Neumann iteration for unsteady thermal fluid structure interaction

Monge, Azahar LU and Birken, Philipp LU (2017) In Computational Mechanics
Abstract
We consider the Dirichlet-Neumann iteration for partitioned simulation of thermal fluid-structure interaction, also called conjugate heat transfer. We analyze its convergence rate for two coupled fully discretized 1D linear heat equations with jumps in the material coefficients across these. These are discretized using implicit Euler in time, a finite element method on one domain, a finite volume method on the other one and variable aspect ratio. We provide an exact formula for the spectral radius of the iteration matrix. This shows that for large time steps, the convergence rate is the aspect ratio times the quotient of heat conductivities and that decreasing the time step will improve the convergence rate. Numerical results... (More)
We consider the Dirichlet-Neumann iteration for partitioned simulation of thermal fluid-structure interaction, also called conjugate heat transfer. We analyze its convergence rate for two coupled fully discretized 1D linear heat equations with jumps in the material coefficients across these. These are discretized using implicit Euler in time, a finite element method on one domain, a finite volume method on the other one and variable aspect ratio. We provide an exact formula for the spectral radius of the iteration matrix. This shows that for large time steps, the convergence rate is the aspect ratio times the quotient of heat conductivities and that decreasing the time step will improve the convergence rate. Numerical results confirm
the analysis and show that the 1D formula is a good estimator in 2D and even for nonlinear thermal FSI applications. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
in
Computational Mechanics
pages
29 pages
publisher
Springer
external identifiers
  • scopus:85034740185
ISSN
0178-7675
DOI
10.1007/s00466-017-1511-3
language
English
LU publication?
yes
id
0260cfd2-2747-4a38-a38b-d601979bedb8
date added to LUP
2017-05-11 17:03:07
date last changed
2018-01-07 12:03:13
@article{0260cfd2-2747-4a38-a38b-d601979bedb8,
  abstract     = {We consider the Dirichlet-Neumann iteration for partitioned simulation of thermal fluid-structure interaction, also called conjugate heat transfer. We analyze its convergence rate for two coupled fully discretized 1D linear heat equations with jumps in the material coefficients across these. These are discretized using implicit Euler in time, a finite element method on one domain, a finite volume method on the other one and variable aspect ratio. We provide an exact formula for the spectral radius of the iteration matrix. This shows that for large time steps, the convergence rate is the aspect ratio times the quotient of heat conductivities and that decreasing the time step will improve the convergence rate. Numerical results confirm<br/>the analysis and show that the 1D formula is a good estimator in 2D and even for nonlinear thermal FSI applications.},
  author       = {Monge, Azahar and Birken, Philipp},
  issn         = {0178-7675},
  language     = {eng},
  month        = {11},
  pages        = {29},
  publisher    = {Springer},
  series       = {Computational Mechanics},
  title        = {On the convergence rate of the Dirichlet-Neumann iteration for unsteady thermal fluid structure interaction},
  url          = {http://dx.doi.org/10.1007/s00466-017-1511-3},
  year         = {2017},
}