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\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}