Axisymmetric and Three-Dimensional Lattice Boltzmann Models and Their Applications in Fluid Flows

Ph.DDOCTOR OF PHILOSOPH

Transport in complex systems : a lattice Boltzmann approach

Celem niniejszej pracy jest zbadanie możliwości efektywnego modelowania procesów transportu w złożonych systemach z zakresu dynamiki płynów za pomocą metody siatkowej Boltzmanna (LBM). Złożoność systemu została potraktowana wieloaspektowo i konkretne układy, które poddano analizie pokrywały szeroki zakres zagadnień fizycznych, m.in. przepływy wielofazowe, hemodynamikę oraz turbulencje. We wszystkich przypadkach szczególna uwaga została zwrócona na aspekty numeryczne — dokładność używanych modeli, jak również szybkość z jaką pozwalają one uzyskać zadowalające rozwiązanie. W ramach pracy rozwinięty został pakiet oprogramowania Sailfish, będący otwarta implementacja metody siatkowej Boltzmanna na procesory kart graficznych (GPU). Po analizie szybkości jego działania, walidacji oraz omówieniu założeń projektowych, pakiet ten został użyty do symulacji trzech typów przepływów. Pierwszym z nich były przepływy typu Brethertona/Taylora w dwu- i trójwymiarowych geometriach, do symulacji których zastosowano model energii swobodnej. Analiza otrzymanych wyników pokazała dobra zgodność z danymi dostępnymi w literaturze, zarówno eksperymentalnymi, jak i otrzymanymi za pomocą innych metod numerycznych. Drugim badanym problemem były przepływy krwi w realistycznych geometriach tętnic dostarczających krew do ludzkiego mózgu. Wyniki symulacji zostały dokładnie porównane z rozwiązaniem otrzymanym metoda objętości skończonych z wykorzystaniem pakietu OpenFOAM, przyspieszonego komercyjna biblioteka pozwalająca na wykonywanie obliczeń na GPU. Otrzymano dobra zgodność między badanymi metodami oraz pokazano, że metoda siatkowa Boltzmanna pozwala na wykonywanie symulacji do ok. 20 razy szybciej. Trzecim przeanalizowanym zagadnieniem były turbulentne przepływy w prostych geometriach. Po zwalidowaniu wszystkich zaimplementowanych modeli relaksacji na przypadku wiru Kidy, zbadano przepływy w pustym kanale oraz w obecności przeszkód. Do symulacji wykorzystano zarówno siatki zapewniające pełną rozdzielczość aż do skal Kolmogorova, jak i siatki o mniejszej rozdzielczości. Również w tym kontekście pokazano dobrą zgodność wyników otrzymanych metodą siatkową Boltzmanna z wynikami innych symulacji oraz badaniami eksperymentalnymi. Pokazano również, że implementacja LBM w pakiecie Sailfish zapewnia większą stabilność obliczeń niż ta opisana w literaturze dla tych samych przepływów i modeli relaksacji

Lattice-Boltzmann simulations of cerebral blood flow

Computational haemodynamics play a central role in the understanding of blood behaviour in the cerebral vasculature, increasing our knowledge in the onset of vascular diseases and their progression, improving diagnosis and ultimately providing better patient prognosis. Computer simulations hold the potential of accurately characterising motion of blood and its interaction with the vessel wall, providing the capability to assess surgical treatments with no danger to the patient. These aspects considerably contribute to better understand of blood circulation processes as well as to augment pre-treatment planning. Existing software environments for treatment planning consist of several stages, each requiring significant user interaction and processing time, significantly limiting their use in clinical scenarios. The aim of this PhD is to provide clinicians and researchers with a tool to aid in the understanding of human cerebral haemodynamics. This tool employs a high performance fluid solver based on the lattice-Boltzmann method (coined HemeLB), high performance distributed computing and grid computing, and various advanced software applications useful to efficiently set up and run patient-specific simulations. A graphical tool is used to segment the vasculature from patient-specific CT or MR data and configure boundary conditions with ease, creating models of the vasculature in real time. Blood flow visualisation is done in real time using in situ rendering techniques implemented within the parallel fluid solver and aided by steering capabilities; these programming strategies allows the clinician to interactively display the simulation results on a local workstation. A separate software application is used to numerically compare simulation results carried out at different spatial resolutions, providing a strategy to approach numerical validation. This developed software and supporting computational infrastructure was used to study various patient-specific intracranial aneurysms with the collaborating interventionalists at the National Hospital for Neurology and Neuroscience (London), using three-dimensional rotational angiography data to define the patient-specific vasculature. Blood flow motion was depicted in detail by the visualisation capabilities, clearly showing vortex fluid ow features and stress distribution at the inner surface of the aneurysms and their surrounding vasculature. These investigations permitted the clinicians to rapidly assess the risk associated with the growth and rupture of each aneurysm. The ultimate goal of this work is to aid clinical practice with an efficient easy-to-use toolkit for real-time decision support

Progress in particle-based multiscale and hybrid methods for flow applications

This work focuses on the review of particle-based multiscale and hybrid methods that have surfaced in the field of fluid mechanics over the last 20 years. We consider five established particle methods: molecular dynamics, direct simulation Monte Carlo, lattice Boltzmann method, dissipative particle dynamics and smoothed-particle hydrodynamics. A general description is given on each particle method in conjunction with multiscale and hybrid applications. An analysis on the length scale separation revealed that current multiscale methods only bridge across scales which are of the order of O(102)−O(103) and that further work on complex geometries and parallel code optimisation is needed to increase the separation. Similarities between methods are highlighted and combinations discussed. Advantages, disadvantages and applications of each particle method have been tabulated as a reference

Towards patient-speci�fic modelling of cerebral blood flow using lattice-Boltzmann methods

Patient-specifi�c Computational fluid dynamics (CFD) studies of cerebral blood flow have the potential to help plan neurosurgery, but developing realistic simulation methods that deliver results quickly enough presents a major challenge. The majority of CFD studies assume that the arterial walls are rigid. Since the lattice-Boltzmann method (LBM) is computationally efficient on multicore machines, some methods for carrying out lattice-Boltzmann simulations of time-dependent fluid flow in elastic vessels are developed. They involve integrating the equations of motion for a number of points on the wall. The calculations at every lattice site and point on the wall depend only on information from neighbouring lattice sites or wall points, so they are suitable for efficient computation on multicore machines. The �first method is suitable for three-dimensional axisymmetric vessels. The steady-state solutions for the wall displacement and flow �fields in a cylinder at realistic parameters for cerebral blood ow agree closely with the analytical solutions. Compared to simulations with rigid walls, simulations with elastic walls require 13% more computational e�ffort at the parameters chosen in this study. A scheme is then developed for a more complex geometry in two dimensions, which applies the full theory of linear elasticity. The steady-state wall pro�files obtained from simulations of a Starling resistor agree closely with those from existing computational studies. I �find that it is essential to change the lattice sites from solid to fluid and vice versa if the wall crosses any of them during the simulation. Simple tests of the dynamics show that when the mass of the wall is much greater than that of the fluid, the period of oscillation of the wall agrees within 7% of the expected period. This method could be extended to three dimensions for use in cerebral blood ow simulations

Numerical studies on complex axisymmetric flows using axisymmetric lattice Boltzmann method

The lattice Boltzmann method (LBM) has proven to be an effective numerical technique for computational fluid dynamics (CFD). It has numerous advantages over traditional computational methods such as finite element and finite difference approaches. The method’s simplicity, easy treatment of boundary conditions, and parallel programming features make it ideal for solving large-scale real-world problems. In this thesis, the development and use of a lattice Boltzmann model for both steady and unsteady two-dimensional axisymmetric flows are presented. Three-dimensional (3D) Navier-Stokes equations describe axisymmetric flows, which can be solved using the three-dimensional (3D) lattice Boltzmann method. Such 3D equations become 2D axisymmetric flow equations when cylindrical coordinates are used. The cavity flow benchmark has been used in our study to verify the axisymmetric lattice Boltzmann revised model(AxLAB®) for more complex axisymmetric flows in a cylindrical container. Also, systematic research on vortex breakdown has been done in a closed cylindrical container with one or two rotating lids. Furthermore, an investigation was carried out into unsteady-periodic flow in the cavity to see how the flow behaviour can be predicted. To the author’s knowledge, this is the first numerical study to determine the periodicity of such flows. The formation of vortex breakdowns, their frequency, and the locations of stagnation points as the flow pattern enlarges are all explained in depth. In addition, the second-order bounce-back technique is introduced to the model for no-slip boundary conditions to increase the accuracy of the AxLAB®. The magnitude of the maximum axial velocities along the cylinder axis, their locations, and the locations of stagnation points have all been analysed to demonstrate the advantages of the described method. The most recent experimental and numerical approaches are then used to compare the results, indicating that the new method provides more accurate results in detail. Also, a more advanced version of AxLAB® is developed to model turbulent flows. By incorporating the conventional subgrid-scale stress (SGS) model into the axisymmetric lattice Boltzmann equation in a way that is consistent with lattice gas dynamics, the turbulent flow is effectively and naturally represented. By using the model to simulate two common engineering scenarios, (i) pipe flow through an abrupt axisymmetric constriction, and (ii) axisymmetric separated-reattached flow, the model is proven to be accurate. Analysis of the axial velocity profile and the reattachment length reveals how much more comparable the outcomes are to other experimental and computational methods, particularly in the region close to the wall domain, as a result of using the second-order bounce back method for the wall boundary conditions. The result demonstrates that the second-order bounce-back method in the upgraded AxLAB® is straightforward and has a higher level of accuracy than AxLAB® in its ability to predict axisymmetric turbulent flows as well as laminar flows

A Numerical Study on the Deformation of Liquid-Filled Capsules with Elastic Membranes in Simple Shear Flow

Ph.DDOCTOR OF PHILOSOPH