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cbme2022/CMBE21_ale.tex
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@ -109,12 +109,12 @@ We will show the extension to a CT scheme. Namely, in that case the following in
\end{equation}
for $(\mathbf{u}^n, p^n)$ the velocity/pressure pair solution at time $t^n$, in the reference domain $\Omega^0$, for operators to be specified in the talk.
Our finding will be supplemented with an application to fluid-solid interaction in an idealized cardiac geometry, exploiting the splitting nature of the CT scheme with a well-known coupling approach \cite{bertoglio2013sisc, fernandez-gerbeau-grandmont-06}.
Our finding will be supplemented with an application to fluid-solid interaction in an idealized cardiac geometry, exploiting the splitting nature of the CT scheme with a well-known coupling approach \cite{bertoglio2013sisc, fernandez-gerbeau-grandmont-06}, see example in Figure \ref{fig:comparison_figure}.
%In such a case, we will exploit the fluid pressure projection step, coupling it with the solid problem in an efficient fashion. Simulations of such a case will be provided, as well as the current research done in more realistic geometries.
\begin{figure}[!hbtp]
\centering
\includegraphics[width=0.8\textwidth]{figs/comparison_two_ways_to_one_way.png}
\caption{Comparison two-ways (left) to one-way (right) approach, with $\mathbb{P}_1$ lagrange elements. In arrows the fluid magnitude and direction, driven by an hyperelastic solid actively contracting (grey, with decreased opacity).}
\caption{Two-ways FSI (left) and one-way FSI (right), on an ellipsoid. In arrows the fluid velocity magnitude and direction, driven by an hyperelastic active solid (in grey, with decreased opacity).}
\label{fig:comparison_figure}
\end{figure}

14
cbme2022/biblio_merged.bib
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@ -29,7 +29,7 @@
publisher = {Elsevier {BV}},
volume = {182},
pages = {313--324},
author = {Bruno Burtschell and Dominique Chapelle and Philippe Moireau},
author = {B. Burtschell and D. Chapelle and P. Moireau},
title = {Effective and energy-preserving time discretization for a general nonlinear poromechanical formulation},
journal = {Computers {\&} Structures}
}
@ -37,7 +37,7 @@
@phdthesis{smaldone2014,
TITLE = {{Numerical analysis and simulations of coupled problems for the cariovascular system}},
AUTHOR = {Smaldone, Saverio},
AUTHOR = {Smaldone, S.},
SCHOOL = {{L'universit{\'e} Pierre et Marie Curie - Paris VI }},
YEAR = {2014},
MONTH = Oct,
@ -52,7 +52,7 @@
publisher = {Elsevier {BV}},
volume = {333},
pages = {55--73},
author = {Alexander Lozovskiy and Maxim A. Olshanskii and Yuri V. Vassilevski},
author = {A. Lozovskiy and M. Olshanskii and Y. Vassilevski},
title = {A quasi-Lagrangian finite element method for the Navier{\textendash}Stokes equations in a time-dependent domain},
journal = {Computer Methods in Applied Mechanics and Engineering}
}
@ -64,7 +64,7 @@
volume = {33},
number = {8},
pages = {e2845},
author = {Andreas Hessenthaler and Oliver R\"{o}hrle and David Nordsletten},
author = {A. Hessenthaler and O. R\"{o}hrle and D. Nordsletten},
title = {Validation of a non-conforming monolithic fluid-structure interaction method using phase-contrast {MRI}},
journal = {International Journal for Numerical Methods in Biomedical Engineering}
}
@ -75,7 +75,7 @@
publisher = {Elsevier {BV}},
volume = {331},
pages = {312--336},
author = {Steffen Basting and Annalisa Quaini and Sun{\v{c}}ica {\v{C}}ani{\'{c}} and Roland Glowinski},
author = {S. Basting and A. Quaini and S. {\v{C}}ani{\'{c}} and Roland Glowinski},
title = {Extended {ALE} Method for fluid{\textendash}structure interaction problems with large structural displacements},
journal = {Journal of Computational Physics}
}
@ -126,7 +126,7 @@
@article{marchesseau2013regionalvols,
title={Personalization of a cardiac electromechanical model using reduced order unscented Kalman filtering from regional volumes},
author={Marchesseau, St{\'e}phanie and Delingette, Herv{\'e} and Sermesant, Maxime and Cabrera-Lozoya, R and Tobon-Gomez, Catalina and Moireau, Philippe and i Ventura, RM Figueras and Lekadir, Karim and Hernandez, Alfredo and Garreau, Mireille and others},
author={Marchesseau, St{\'e}phanie and Delingette, Herv{\'e} and Sermesant, Maxime and Cabrera-Lozoa, R and Tobon-Gomez, Catalina and Moireau, Philippe and i Ventura, RM Figueras and Lekadir, Karim and Hernandez, Alfredo and Garreau, Mireille and others},
journal={Medical image analysis},
volume={17},
number={7},
@ -177,7 +177,7 @@
@article{arostica2021monolithic,
title={On monolithic and Chorin--Temam schemes for incompressible flows in moving domains},
author={Ar{\'o}stica, Reidmen and Bertoglio, Crist{\'o}bal},
author={Ar{\'o}stica, R. and Bertoglio, C.},
journal={Applied Mathematics Letters},
volume={112},
pages={106830},