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In this master thesis, a 2D/3D free surface flow solver based on the PFEM method is developed. While an existing 2D implicit incompressible solver developed in a previous work by Marco-Lucio Cerquaglia is available at the MTFC and MN2L lab of Uliège, an explicit solver is developed especially in the goal of simulating 3D flows efficiently. To do so, the incompressible Navier-Stokes equations are replaced by weakly-compressible Navier-Stokes equations using a Tait-Murnaghan equation of state. The Computational Geometry Algorithms Library (CGAL) is used to handle everything related to Delaunay triangulation and alpha-shapes algorithm in 2D and 3D. The simulations results are then compared to analytical solutions and to Cerquaglia’s solver. The solvers seems able to correctly represent flow not to far from incompressibility, and 3D simulations are working.

PFEM --- CGAL --- GMSH --- c++ --- free surface flows --- fluid simulations --- Ingénierie, informatique & technologie > Multidisciplinaire, généralités & autres

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Cardiovascular diseases are a leading cause of mortality in Belgium and worldwide, with projections indicating a concerning rise in related deaths. Understanding the hemodynamics and biomechanical mechanisms underlying vascular failure is essential for advancing diagnostic and therapeutic strategies. In this context, computational models offer a promising tool that can really improve patient care. In particular, fluid-structure interaction algorithms have found significant applications in cardiovascular engineering, in coupling simulations of blood flows with the mechanical responses of blood vessels.
This thesis focuses on the computational modeling of the fluid-structure interaction of artery walls and blood flows as a means of assessing different biomechanical aspects. For this, the flow-structure interaction problem is addressed using a partitioned approach with a strong coupling of PFEM (for the fluid) and FEM (for the solid) models. This work relies on the PFEM3D and Metafor codes and exploits the synchronization and communication framework FSPC, all developed in the LTAS-MN2L lab of ULiège. This marks the first application of the PFEM to such biomechanical simulations.
Axisymmetric models of arteries are developed by incorporating both the Newtonian and Casson fluid models, as well as linear elastic, Neo-Hookean, and Mooney-Rivlin hyperelastic models for the deformation of blood vessels. The numerical simulations successfully describe a wide range of situations and problems, from the ejection of blood from the left ventricle and the blood flow in the healthy aortic artery to the dynamics of an abdominal aortic aneurysm and, ultimately, its rupture. The different models provide valuable insights into the corresponding dynamics and help to identify the different aspects that still need to be improved. In particular, the results explain why local defects of the artery wall must be compensated by biological remodeling processes, with the replacement of elastin by stiffer collagen, to avoid further development and rupture of an aneurysm.
Overall, this work underscores the potential of PFEM3D, Metafor, and their coupling within the FSPC framework to advance our understanding of hemodynamics and biomechanical processes, and to contribute to the improved handling of cardiovascular diseases.

cardiovascular diseases --- biomechanics --- hemodynamics --- PFEM --- fluid-structure interaction --- Ingénierie, informatique & technologie > Multidisciplinaire, généralités & autres