Numerical Simulation of Particle Deposition in the Human Lungs

We model, simulate and calculate breathing and particle depositions in the human lungs. We review the theory and discretization of fluid mechanics, the anatomy, physiology and measuring methods of lungs. A new model is introduced and investigated with a sensitivity analysis using the singular value decomposition. Particle depositions are simulated in patient-specific and schematized human lungs and compared to the particle deposition in a multiplicative model of subsequent bifurcations

A Coupled Stochastic-Deterministic Method for the Numerical Solution of Population Balance Systems

In this thesis, a new algorithm for the numerical solution of population balance systems is proposed and applied within two simulation projects. The regarded systems stem from chemical engineering. In particular, crystallization processes in fluid environment are regarded. The descriptive population balance equations are extensions of the classical Smoluchowski coagulation equation, of which they inherit the numerical difficulties introduced with the coagulation integral, especially in regard of higher dimensional particle models. The new algorithm brings together two different fields of numerical mathematics and scientific computing, namely a stochastic particle simulation based on a Markov process Monte—Carlo method, and (deterministic) finite element schemes from computational fluid dynamics. Stochastic particle simulations are approved methods for the solution of population balance equations. Their major advantages are the inclusion of microscopic information into the model while offering convergence against solutions of the macroscopic equation, as well as numerical efficiency and robustness. The embedding of a stochastic method into a deterministic flow simulation offers new possibilities for the solution of coupled population balance systems, especially in regard of the microscopic details of the interaction of particles. In the thesis, the new simulation method is first applied to a population balance system that models an experimental tube crystallizer which is used for the production of crystalline aspirin. The device is modeled in an axisymmetric two-dimensional fashion. Experimental data is reproduced in moderate computing time. Thereafter, the method is extended to three spatial dimensions and used for the simulation of an experimental, continuously operated fluidized bed crystallizer. This system is fully instationary, the turbulent flow is computed on-the-fly. All the used methods from the simulation of the Navier—Stokes equations, the simulation of convection-diffusion equations, and of stochastic particle simulation are introduced, motivated and discussed extensively. Coupling phenomena in the regarded population balance systems and the coupling algorithm itself are discussed in great detail. Furthermore, own results about the efficient numerical solution of the Navier—Stokes equations are presented, namely an assessment of fast solvers for discrete saddle point problems, and an own interpretation of the classical domain decompositioning method for the parallelization of the finite element method

Uncertainty Quantification for a Blood Pump Device with Generalized Polynomial Chaos Expansion

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

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Aeronautical engineering: A continuing bibliography with indexes (supplement 289)

This bibliography lists 792 reports, articles, and other documents introduced into the NASA scientific and technical information system in Mar. 1993. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Aeronautical engineering: A continuing bibliography with indexes (supplement 218)

This bibliography lists 469 reports, articles, and other documents introduced into the NASA scientific and technical information system in September, 1987