TY  - GEN
Y1  - 2018///
TI  - Uncertainty Quantification for a Blood Pump Device with Generalized Polynomial Chaos Expansion
CY  - Heidelberg, Germany
AV  - public
KW  - Numerical Simulation
KW  -  Applied Mathematics
KW  -  Uncertainty Quantification
KW  -  Biomedical Engineering
ID  - heidok24790
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/24790/
A1  - Song, Chen
N2  - Nowadays, an increasing number of numerical modeling techniques, notably by means of the finite element method (FEM), are involved in the industrial design process and play a vital role in the area of the biomedical engineering. Particularly, the computational fluid dynamics (CFD) has become a promising tool for investigating the fluid behavior and has also been used to study the cardiovascular hemodynamics to predict the blood flow in the cardiovascular system over the recent decades.

However, simulating a fluid in rotational frames is not trivial, as the classical fluid calculation considers that the geometry of the fluid domain does not alter along the time. In the meanwhile, due to the high rotating speed and the complex geometry of the ventricular assist device (VAD), a turbulent flow must be developed inside the pump housing. The Navier-Stokes equations are not applicable in respect of our available computing resource, additional assumptions and approaches are often applied as a means to model the eddy formation and cope with numerical instabilities.

For many applications, there is still a big gap between the experimental data and the numerical results. Some of the discrepancies come especially from uncertain data which are used in the physical model, therefore, Uncertainty Quantification (UQ) comes into play. The Galerkin-based polynomial chaos expansion method delivers directly the mean and higher stochastic moments in a closed form. Due to the Galerkin projection?s properties, the spectral convergence is achieved.

This thesis is dedicated to developing an efficient model to simulate the blood pump assuming uncertain parametric input sources. In a first step, we develop the shear layer update approach built on the Shear-Slip Mesh Update Method (SSMUM), our proposition facilitates the update procedure in parallel computing by forcing the local vector to retain the same structure. In a second step, we focus on the Variational Multiscale method (VMS) in order to handle the numerical instability and approximate the turbulent behavior in the blood. As a consequence of utilizing the intrusive Polynomial Chaos formulation, a highly coupled system needs to be solved in an efficient manner. Accordingly, we take advantage of the Multilevel preconditioner to precondition our stochastic Galerkin system, in which the Mean-based preconditioner is prescribed to be the smoother. Besides, the mean block is preconditioned with the Schur-Complement method, which leads to an acceleration of the solution process. Hence, by developing and combining the proposed solvers and preconditioners, dealing with a large coupled stochastic fluid problem on a modern computer architecture is then feasible. Furthermore, based on the stochastic solutions obtained from the previous described system, we obtain valuable information about the blood flow accompanied with certain level of confidence, which is beneficial for designing a new blood-handle device or improving the current model.
ER  -