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Eulerian finite element method for the numerical modeling of fluid dynamics of natural and pathological aortic valves

Aymen Laadhari, Gábor Székely
Journal of Computational and Applied Mathematics, doi: http://dx.doi.org/10.1016/j.cam.2016.11.042
Vol. 319, pp. 236-261, August 2017

Abstract

Eulerian Finite Element Method for the numerical modeling of fluid dynamics of natural and pathological aortic valves Aymen Laadhari*, Gabor Székely We present a finite element methodology tailored for the simulation of pulsatile flow in the full aorta and sinus of Valsalva interacting with highly deformable thin leaflets. We describe an extension of the so-called "Resistive Immersed Surface" method. To circumvent stability issues resulting from the bad conditioning of the linear system, especially when flow and geometry become complex after the inclusion of the aorta, we use a Lagrange multiplier technique that couples the dynamics of valve and flow. A banded level set variant allows to address the singularity of the resulting linear system while featuring, in addition to the parallel implementation of a monolithic solver, higher accuracy and an affordable computational burden. Several numerical experiments illustrate the ability of the model to capture the basic fluidic phenomena in both healthy and pathological configurations. We finally examine numerically the hemodynamics in the sinus of Valsalva after Transcatheter Aortic Valve Implantation. We show numerically that blood flow may be subject to stagnation in the lower part of the sinuses, and we highlight the far-reaching consequences of this phenomenon.


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@Article{eth_biwi_01347,
  author = {Aymen Laadhari and Gábor Székely},
  title = {Eulerian finite element method for the numerical modeling of fluid dynamics of natural and pathological aortic valves},
  journal = {Journal of Computational and Applied Mathematics, doi: http://dx.doi.org/10.1016/j.cam.2016.11.042},
  year = {2017},
  month = {August},
  pages = {236-261},
  volume = {319},
  number = {},
  keywords = {Computational hemodynamics, Finite Element Method, Exact Lagrange multiplier, Damped Newton, Aortic valve, Aorta; Transcatheter Aortic Valve Implantation.}
}