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Evaluation of a new implicit coupling algorithm for the partitioned fluid-structure interaction simulation of bileaflet mechanical heart valves

Sebastiaan Annerel (UGent) , Joris Degroote (UGent) and Jan Vierendeels (UGent)
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Abstract
The movement of the leaflets of Bileaflet Mechanical Heart Valves (BMHVs) strongly interacts with the surrounding fluid motion and therefore it needs to be modeled through a Fluid-Structure Interaction (FSI) scheme with implicit coupling. Therefore, when using partitioned solvers, a subiteration loop within each time step is needed. The stability of such a scheme depends on the value of the under-relaxation factor. For the simulation of a BMHV, several methods can be used to find such an appropriate under-relaxation factor, like fixed under-relaxation or the dynamically changing Aitken Δ2 under-relaxation. Also, a stable scheme can be achieved with a newly developed algorithm which uses the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with resprect to the angular accelerations of the leaflets. In this paper, this new algorithm is presented and compared to existing coupling schemes. It is shown through numerical experiments that our newly developed algorithm outperforms these existing coupling schemes.
Keywords
Bileaflet Mechanical Heart Valve, Fluid-structure interaction, partitioned solvers

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Chicago
Annerel, Sebastiaan, Joris Degroote, and Jan Vierendeels. 2010. “Evaluation of a New Implicit Coupling Algorithm for the Partitioned Fluid-structure Interaction Simulation of Bileaflet Mechanical Heart Valves.” In Computational Fluid Dynamics, 6th International Conference, Proceedings, ed. A Kuzmin, 43–44. St. Petersburg, Russia: VVM Publishing Co.
APA
Annerel, S., Degroote, J., & Vierendeels, J. (2010). Evaluation of a new implicit coupling algorithm for the partitioned fluid-structure interaction simulation of bileaflet mechanical heart valves. In A Kuzmin (Ed.), Computational Fluid Dynamics, 6th International conference, Proceedings (pp. 43–44). Presented at the 6th International conference on Computational Fluid Dynamics (ICCFD 6), St. Petersburg, Russia: VVM Publishing Co.
Vancouver
1.
Annerel S, Degroote J, Vierendeels J. Evaluation of a new implicit coupling algorithm for the partitioned fluid-structure interaction simulation of bileaflet mechanical heart valves. In: Kuzmin A, editor. Computational Fluid Dynamics, 6th International conference, Proceedings. St. Petersburg, Russia: VVM Publishing Co; 2010. p. 43–4.
MLA
Annerel, Sebastiaan, Joris Degroote, and Jan Vierendeels. “Evaluation of a New Implicit Coupling Algorithm for the Partitioned Fluid-structure Interaction Simulation of Bileaflet Mechanical Heart Valves.” Computational Fluid Dynamics, 6th International Conference, Proceedings. Ed. A Kuzmin. St. Petersburg, Russia: VVM Publishing Co, 2010. 43–44. Print.
@inproceedings{1044974,
  abstract     = {The movement of the leaflets of Bileaflet Mechanical Heart Valves (BMHVs) strongly interacts with the surrounding fluid motion and therefore it needs to be modeled through a Fluid-Structure Interaction (FSI) scheme with implicit coupling. Therefore, when using partitioned solvers, a subiteration loop within each time step is needed. The stability of such a scheme depends on the value of the under-relaxation factor. For the simulation of a BMHV, several methods can be used to find such an appropriate under-relaxation factor, like fixed under-relaxation or the dynamically changing Aitken \ensuremath{\Delta}2 under-relaxation. Also, a stable scheme can be achieved with a newly developed algorithm which uses the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with resprect to the angular accelerations of the leaflets. In this paper, this new algorithm is presented and compared to existing coupling schemes. It is shown through numerical experiments that our newly developed algorithm outperforms these existing coupling schemes.},
  author       = {Annerel, Sebastiaan and Degroote, Joris and Vierendeels, Jan},
  booktitle    = {Computational Fluid Dynamics, 6th International conference, Proceedings},
  editor       = {Kuzmin, A},
  isbn         = {9785965104710},
  keyword      = {Bileaflet Mechanical Heart Valve,Fluid-structure interaction,partitioned solvers},
  language     = {eng},
  location     = {St. Petersburg, Russia},
  pages        = {43--44},
  publisher    = {VVM Publishing Co},
  title        = {Evaluation of a new implicit coupling algorithm for the partitioned fluid-structure interaction simulation of bileaflet mechanical heart valves},
  year         = {2010},
}