NUMERICAL ANALYSIS AND SIMULATIONS OF COUPLED PROBLEMS FOR THE CARDIOVASCULAR SYSTEM

Saverio Smaldone 1
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : In this thesis we present the numerical analysis and the development of partitioned algorithms in order to couple the blood dynamics in different cardiovascular compartments (3D-3D, 3D-0D). In the first par t a fluid-fluid coupled problem is introduced. On the interface between the domains Robin-Robin boundary conditions, derived from the Nitsche’s interface formulation, are considered. We suggest different staggered explicit schemes whose stability is analyzed in the energy norm. Extensive numerical experiments illustrate the accuracy of the methods presented. The second par t deals with more realistic cardiovascular applications. First a reduced order model for the hear t valves is described. Without dealing with fluid-structure interaction with the blood flow, the valves are replaced by immersed surfaces acting as resistances on the fluid. Numerical simulations show the efficiency and the robustness of this model in the framework of a fluid-fluid interaction scheme. In the end, an ALE formulation is used to solve a fluid model in a moving domain. We show that adding a suitable consistent term, a stable energy inequality can be obtained without considering any Geometric Conservation Laws. The work ends with numerical simulations on blood dynamics in the left ventricle coupled with the blood flowing in the aorta
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Contributor : Saverio Smaldone <>
Submitted on : Sunday, March 13, 2016 - 4:22:52 PM
Last modification on : Tuesday, May 14, 2019 - 10:15:08 AM
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Saverio Smaldone. NUMERICAL ANALYSIS AND SIMULATIONS OF COUPLED PROBLEMS FOR THE CARDIOVASCULAR SYSTEM. Mathematics [math]. L’UNIVERSITÉ PIERRE ET MARIE CURIE - Paris VI 2014. English. ⟨tel-01287506⟩

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