corrections

.gitignore

@@ -9,7 +9,6 @@ __pypackages__/
 build/
 develop-eggs/
 dist/
-downloads/
 eggs/
 .eggs/
 lib/
@@ -40,9 +39,6 @@ MANIFEST
 *.ipynb
 .ipynb_checkpoints/
 
-# Numerical results
-tests/
-
 # Paraview state files
 *.pvsm
 
@@ -55,5 +51,9 @@ tests/
 # published article exception and
 # TeX exceptions
 !/tex/**/*.png
+!conferences/**/*
+conferences/**/*.synctex.gz
+conferences/**/*.aux
+conferences/**/*.log
+
 !article_published.pdf
-!conferences/

cbme2022/CMBE21_ale.tex

@@ -23,10 +23,11 @@
 % comment if not needed
 \usepackage[hyphens]{url}
 \usepackage{hyperref}
+\usepackage{color}
 
 
 % TITLE: replace text with your abstract title WITHOUT full stop
-\title{On monolithic and Chorin-Temam schemes for incompressible flows in moving domains.}
+\title{On monolithic and Chorin-Temam schemes for incompressible flows in moving domains}
 % AUTHOR/AFFILIATION: handled by authblk. 
 % Use only one of the two following methods for author listing. Delete or comment out the other.
 % Add/remove authors/affiliations as necessary, complete following the template without adding additional superscript/footnotes  
@@ -88,18 +89,36 @@
 
 
 % SUMMARY: replace text with a short summary
-\summary{Several time discretized domain for the incompressible Navier-Stokes equations (iNSE) in moving domains have been proposed in literature. Here, we introduce a unified formulation that combines different approaches found in literature, allowing a common well posedness and time stability analysis. It can be therefore shown that only a particular choice of numerical schemes ensure such properties under some restrictions. The analysis will be shown for Chorin-Temam schemes using the insight found in the monolithic case. Results are supported from numerical simulations and its usage in fluid-solid interaction problems will be presented.}
+\summary{Several time discretized domain for the incompressible Navier-Stokes equations (iNSE) in moving domains have been proposed in literature. Here, we introduce a unified formulation that combines different approaches found in literature, allowing a common well posedness and time stability analysis. It can be therefore shown that only a particular choice of numerical schemes ensure such properties under some restrictions. The analysis will be shown for Chorin-Temam schemes using the insight found in the monolithic case. Results are supported from numerical simulations and its usage in fluid-solid interaction problems in cardiac geometries will be presented.}
 
 % KEYWORDS: replace text with 2-4 keywords, not capitalised, separated by comma, and without a full stop at the end.
 \keywords{numerical schemes, stability analysis, incompressible flows, fluid-structure interaction}
 
 
 \begin{document}
-Estimating parameters from heart contraction data, using e.g. magnetic resonance imaging \cite{imperiale2021tagged, markl20124d, marchesseau2013fast, marchesseau2013regionalvols}, requires several techniques such as the estimation algorithms, e.g. \cite{pfaller2020pod}, fluid-solid coupling schemes modeling the physics itself e.g. \cite{astorino-chouly-fernandez-09, bertoglio2013sisc} and in particular, the discretization of fluid problem arising from the blood movement e.g. \cite{bevan2016comparative}.
 
-In such a context, several works have been reported dealing with numerical solutions of the iNSE in moving domains within the Arbitrary Lagrangian Eulerian formulation (ALE). Different choices of time discretization have been reported , e.g. \cite{Basting2017}, \cite{Hessenthaler2017}. To the best of the authors knowledge, only a few monolithic schemes have been throughly analyzed, e.g. \cite{Lozovskiy2018, smaldone2014, le-tallec-mouro-01, Burtschell2017} while no analysis has been reported for Chorin-Temam (CT) methods, being an alternative option when requirements such a low time computations are needed, specially for future industrial applications.
+Several works have been reported dealing with numerical solutions of the iNSE in moving domains within the Arbitrary Lagrangian Eulerian formulation (ALE), primarily in the context of fluid-solid coupling, e.g. \cite{astorino-chouly-fernandez-09, bertoglio2013sisc}. 
 
-The goal of this talk is to present the finding of well-posedness and unconditional energy balance of the iNSE-ALE for several reported CT discretization schemes within a single formulation, published in \cite{arostica2021monolithic}. It will be supplemented with an usage case for fluid-solid interaction problems.
+Different choices of time discretization schemes have been reported e.g. \cite{Basting2017, Hessenthaler2017}, nevertheless to the best of the authors knowledge, only a few monolithic schemes have been throughly analyzed, e.g. \cite{Lozovskiy2018, smaldone2014, le-tallec-mouro-01, Burtschell2017} while no analysis has been reported for Chorin-Temam (CT) schemes, being a feasible alternative when requirements such a low time computations are needed.
+
+The goal of this talk is to present the finding of well-posedness and unconditional energy balance of the iNSE-ALE for several reported monolithic discretization schemes within a single formulation, recently published in \cite{arostica2021monolithic}. The main result is that under appropriate conditions on the rate of domain deformation, only some of first order time discretization schemes are unconditionally stable. 
+
+We will show the extension to a CT scheme. Namely, in that case the following inequality can be shown:
+\begin{equation}
+\int_{\Omega^0} \frac{\rho J^{n+1}}{2\tau} \vert \tilde{\mathbf{u}}^{n+1} \vert^2 \, \text{d}\mathbf{X} -\int_{\Omega^0} \frac{\rho J^{n}}{2\tau} \vert \tilde{\mathbf{u}}^{n} \vert^2 \, \text{d}\mathbf{X} \leq - \int_{\Omega^0} J^{\star} 2 \mu \vert \epsilon^{\star} (\tilde{\mathbf{u}}) \vert^2 \, \text{d}\mathbf{X} - \int_{\Omega^0} \frac{\tau J^n}{2 \rho} \vert Grad(p^n) H^n \vert^2 \, \text{d} \mathbf{X}
+\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}, 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{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}
+
+\newpage
 
 
 \bibliography{biblio_merged.bib}

cbme2022/biblio_merged.bib

@@ -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},