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Volume 12, Issue 1
Stability of the Kinematically Coupled β-Scheme for Fluid-Structure Interaction Problems in Hemodynamics

Sunčica Čanić, Boris Muha & Martina Bukač

Int. J. Numer. Anal. Mod., 12 (2015), pp. 54-80.

Published online: 2015-12

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  • Abstract

It is well-known that classical Dirichlet-Neumann loosely coupled partitioned schemes for fluid-structure interaction (FSI) problems are unconditionally unstable for certain combinations of physical and geometric parameters that are relevant in hemodynamics. It was shown in [18] on a simple test problem, that these instabilities are associated with the so called “added-mass effect”. By considering the same test problem as in [18], the present work shows that a novel, partitioned, loosely coupled scheme, recently introduced in [11], called the kinematically coupled β-scheme, does not suffer from the added mass effect for any β ∈ [0; 1], and is unconditionally stable for all the parameters in the problem. Numerical results showing unconditional stability are presented for a full, nonlinearly coupled benchmark FSI problem, first considered in [31].

  • Keywords

Fluid-structure interaction, Partitioned schemes, Stability analysis, Added-mass effect.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-54, author = {Sunčica Čanić, Boris Muha and Martina Bukač}, title = {Stability of the Kinematically Coupled β-Scheme for Fluid-Structure Interaction Problems in Hemodynamics}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {1}, pages = {54--80}, abstract = {

It is well-known that classical Dirichlet-Neumann loosely coupled partitioned schemes for fluid-structure interaction (FSI) problems are unconditionally unstable for certain combinations of physical and geometric parameters that are relevant in hemodynamics. It was shown in [18] on a simple test problem, that these instabilities are associated with the so called “added-mass effect”. By considering the same test problem as in [18], the present work shows that a novel, partitioned, loosely coupled scheme, recently introduced in [11], called the kinematically coupled β-scheme, does not suffer from the added mass effect for any β ∈ [0; 1], and is unconditionally stable for all the parameters in the problem. Numerical results showing unconditional stability are presented for a full, nonlinearly coupled benchmark FSI problem, first considered in [31].

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/478.html} }
TY - JOUR T1 - Stability of the Kinematically Coupled β-Scheme for Fluid-Structure Interaction Problems in Hemodynamics AU - Sunčica Čanić, Boris Muha & Martina Bukač JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 54 EP - 80 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/478.html KW - Fluid-structure interaction, Partitioned schemes, Stability analysis, Added-mass effect. AB -

It is well-known that classical Dirichlet-Neumann loosely coupled partitioned schemes for fluid-structure interaction (FSI) problems are unconditionally unstable for certain combinations of physical and geometric parameters that are relevant in hemodynamics. It was shown in [18] on a simple test problem, that these instabilities are associated with the so called “added-mass effect”. By considering the same test problem as in [18], the present work shows that a novel, partitioned, loosely coupled scheme, recently introduced in [11], called the kinematically coupled β-scheme, does not suffer from the added mass effect for any β ∈ [0; 1], and is unconditionally stable for all the parameters in the problem. Numerical results showing unconditional stability are presented for a full, nonlinearly coupled benchmark FSI problem, first considered in [31].

Sunčica Čanić, Boris Muha and Martina Bukač. (2015). Stability of the Kinematically Coupled β-Scheme for Fluid-Structure Interaction Problems in Hemodynamics. International Journal of Numerical Analysis and Modeling. 12 (1). 54-80. doi:
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