Doctor's Theses (authored and supervised):
"Lattice Boltzmann Modeling and Simulation of Incompressible Flows in Distensible Tubes for Applications in Hemodynamics";
Supervisor, Reviewer: G. Pontrelli, F. Breitenecker;
Institut für Analysis und Scientific Computing,
oral examination: 2012-11-30.
Due to the increase of cardiovascular diseases in industrialized countries in the past years, there is a strong interest in understanding the hemodynamic processes in the cardiovascular system. A lot of research has been done to study the characteristics of the blood flow and to correlate these to the development of vascular diseases. Since experimental methods are difficult, limited, and often invasive, mathematical modeling and numerical simulations are used to better understand the effects of several hemo-dynamic factors on the blood flow. Most studies in computational fluid dynamics assume that the vessel walls are rigid. However, especially when studying the blood flow in large arteries, it is of particular importance to incorporate the elasticity of the vessel and its interaction with the fluid. The treatment of such fluid-structure interaction problems is a real challenge. This thesis presents an accurate and computationally efficient approach for modeling and simulating incompressible flow in distensible tubes and its interaction with the tube wall, with particular focus on applications in hemodynamics. The developed lattice Boltzmann method has been used as a competitive alternative approach to conventional numerical methods. A novel boundary condition is introduced allowing a continuous displacement of the wall, which reduces discretization errors. The method has been extended to model the blood flow through stents and to study the effect of different stent properties. The overall algorithm has been implemented in the programming language C and numerical experiments on artificial vessel segments have been extensively carried out providing qualitative results. The results show the expected physical behavior and prove the feasibility and the efficacy of the methodology. In the simulations, a constant outflow boundary condition has been used. Even if this condition is reasonable for steady-state problems, in time-dependent flows it may cause spurious reflections spoiling the solution. In order to circumvent this problem, a more realistic boundary condition coupling the lattice
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