From 68b6232e1f62b8879de2a23453725836f879202f Mon Sep 17 00:00:00 2001
From: reidmen
Date: Sat, 9 Apr 2022 14:50:17 +0200
Subject: [PATCH] updated cmbe21 tex
---
cbme2022/CMBE21_ale.tex | 7 ++++---
1 file changed, 4 insertions(+), 3 deletions(-)
diff --git a/cbme2022/CMBE21_ale.tex b/cbme2022/CMBE21_ale.tex
index 7782bd8..0a80ffe 100644
--- a/cbme2022/CMBE21_ale.tex
+++ b/cbme2022/CMBE21_ale.tex
@@ -95,11 +95,12 @@
\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}. 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 an alternative option when requirements such a low time computations are needed, specially for future industrial applications.
-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.
+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}. The main result to show will be that under appropiate conditions on the rate of domain deformation, a first order time discretization scheme for the CT scheme is unconditionally stable.
+
+Our finding will be supplemented with an application case of fluid-solid interactions problem in an idealize geometry, exploiting the splitting nature of the CT scheme with a well-known coupling approach \cite{bertoglio2013sisc}.
\bibliography{biblio_merged.bib}