This thesis uses the Immersed Boundary Method (IBM) to simulate the movement of a human heart. The IBM was developed by Charles Peskin in the 70’s to solve Fluid-Structure Interaction models (FSI). The heart is embedded inside a fluid (blood) which moves according to the Navier-Stokes equation. The Navier-Stokes equation is solved by the Spectral Method. Forces on the heart muscle can be divided into two kinds: Active Force and Passive Force. Passive includes the effect of curvature (Peskin’s model), spring model, and the torsional spring (or beam) model. Active force is modeled by the 3-element Hill model, which was used in the 30’s to model skeletal muscle. We performed simulations with different combinations of these four forces. Numerical simulations are performed using MATLAB. We downloaded Peskin’s code from the Internet and modified the Force.m file to include the above four forces. This thesis only considers heart muscle movement in the organ (macroscopic) scale.

State-of-the-art deep learning methods for outlier detection make the assumption that outliers will appear far away from inlier data in the latent space produced by distribution mapping deep networks. However, this assumption fails in practice,because the divergence penalty adopted for this purpose encourages mapping outliers into the same high-probability regions as inliers. To overcome this shortcoming,we introduce a novel deep learning outlier detection method, called Outlier Preserving Distribution Mapping Autoencoder (OP-DMA), which succeeds to map outliers to low probability regions in the latent space of an autoencoder. For this we leverage the insight that outliers are likely to have a higher reconstruction error than inliers. We thus achieve outlier-preserving distribution mapping through weighting the reconstruction error of individual points by the value of a multivariate Gaussian probability density function evaluated at those points. This weighting implies that outliers will result in an overall penalty if they are mapped to low-probability regions. We show that if the global minimum of our newly proposed loss function is achieved,then our OP-DMA maps inliers to regions with a Mahalanobis distance less than \delta, and outliers to regions past this \delta, \delta being the inverse ChiSquared CDF evaluated at 1−\alpha with \alpha the percentage of outliers in the dataset. We evaluated OP-DMA on 11 benchmark real-world datasets and compared its performance against 7 different state-of-the-art outlier detection methods, including ALOCC and MO-GAAL. Our experiments show that OP-DMA outperforms the state-of-the-art methods on 7 of the datasets, and performs second best on 3 of the remaining 4 datasets, while no other method won on more than 1 dataset.

Most realistic fluid flow problems are characterised by high Reynolds numbers and complex boundaries. Over the last ten years, immersed boundary methods (IBM) that are able to cope with realistic geometries have been applied to Lattice- Boltzmann methods (LBM). These methods, however, have normally been applied to low Reynolds number problems. In the present work, an iterative direct forcing IBM has been successfully coupled with a multi-domain cascaded LBM in order to investigate viscous flows around rigid, moving and wilfully deformed boundaries at a wide range of Reynolds numbers. The iterative force-correction immersed boundary method of (Zhang et al., 2016) has been selected due to the improved accuracy of the computation, while the cascaded LB formulation is used due to its superior stability at high Reynolds numbers. The coupling is shown to improve both the stability and numerical accuracy of the solution. The resulting solver has been applied to viscous flow (up to a Reynolds number of 100000) passed a NACA-0012 airfoil at a 10 degree angle of attack. Good agreement with results obtained using a body-fitted Navier-Stokes solver has been obtained. At moving or deformable boundary applications, emphasis should be given on the influence of the internal mass on the computation of the aerodynamic forces, focusing on deforming boundary motions where the rigid body approximation is no longer valid. Both the rigid body and the internal Lagrangian points approximations are examined. The resulting solver has been applied to viscous flows around an in-line oscillating cylinder, a pitching foil, a plunging SD7003 airfoil and a plunging and flapping NACA-0014 airfoil. Good agreement with experimental results and other numerical schemes has been obtained. It is shown that the internal Lagrangian points approximation accurately captures the internal mass effects in linear and angular motions, as well as in deforming motions, at Reynolds numbers up to 4 • 104. Finally, an expanded higher-order immersed boundary method which addresses two major drawbacks of the conventional IBM will be presented. First, an expanded velocity profile scheme has been developed, in order to compensate for the discontinuities caused by the gradient of the velocity across the boundary. Second, a numerical method derived from the Navier-Stokes equations in order to correct the pressure distribution across the boundary has been examined. The resulting hybrid solver has been applied to viscous flows around stationary and oscillating cylinders and examined the hovering flight of elliptical wings at low Reynolds numbers. It is shown that the proposed scheme smoothly expands the velocity profile across the boundary and increases the accuracy of the immersed boundary method. In addition, the pressure correction algorithm correctly expands the pressure profile across the boundary leading to very accurate pressure coefficient values along the boundary surface. The proposed numerical schemes are shown to be very efficient in terms of computational cost. The majority of the presented results are obtained within a few hours of CPU time on a 2.8 GHz Intel Core i7 MacBook Pro computer with a 16GB memory.

We present an immersed interface algorithm for the incompressible Navier Stokes equations. The interface is represented by cubic splines which are interpolated through a set of Lagrangian control points. The position of the control points is implicitly updated using the fluid velocity. The forces that the interface exerts on the fluid are computed from the constitutive relation of the interface and are applied to the fluid through jumps in the pressure and jumps in the derivatives of pressure and velocity. A projection method is used to time advance the Navier-Stokes equations on a uniform cartesian mesh. The Poisson-like equations required for the implicit solution of the diffusive and pressure terms are solved using a fast Fourier transform algorithm. The position of the interface is updated implicitly using a quasi-Newton method (BFGS) within each timestep. Several examples are presented to illustrate the flexibility of the presented approach. / Singapore-MIT Alliance (SMA)

Diffusion imaging is a relatively recent branch of magnetic resonance imaging that produces images of human physiology through diffusion of water molecules within the body. One difficulty in calculating diffusion coefficients, particularly in the brain, is the multitude of natural barriers to water diffusion, such as cell membranes, myelin sheaths, and fiber tracts. These barriers mean that water diffusion is not a homogeneous random process. Due to the complexity of modeling these structures, a simplifying assumption made in some methods of data analysis is that there are no barriers to water diffusion. We develop tools to simulate the diffusion of water in an inhomogeneous medium, which may then be used to test the accuracy of this assumption. The inherent difficulty (and computational cost) of including barriers (e.g., cell membranes) can be lessened by employing the immersed boundary (IB) method to represent these structures without the need for complicated computational grids. The contribution of this thesis is the implementation and validation of an IB method that allows for diffusion across semi-permeable membranes. The method is tested for a square interface aligned with the computational grid by comparing it to a second numerical scheme that uses standard finite differences. We also calculate the rate of convergence for the IB method to assess the numerical accuracy. To demonstrate the flexibility of the IB method to simulate diffusion with any interface shape, we also present simulations for irregular interfaces. / UOIT

Atherosclerosis is a systemic disease occurring in specific sections of the cardiovascular tree such as the carotid and the coronary arteries. Previous studies proposed a strong correlation between plaque localization and blood flow patterns in specific sections of the arteries. In order to elucidate cellular mechanisms that contribute to atherosclerosis, standard cone-and-plate devices are widely used in experiments to reproduce in vitro the effect of different hemodynamic conditions on endothelial cells. In this study, a novel computational fluid dynamic (CFD) numerical code based on the immersed boundary method is developed to simulate this microscopic flow field under different geometries and flow conditions. A comprehensive validation of the CFD code is performed. Once validated, the code is used to analyze the flow field in the cone-and-plate device simulating conditions typically employed in endothelial cell experiments. No previous studies have yet been performed on the fluid dynamics of the cone-and-plate device when surfaces representing actual endothelial cell contours are modeled on the plate surface. This represents a great opportunity to correlate the fluid dynamics in the experimental device and the biochemical properties of the cells under specific flow conditions. The challenging aspect of the problem is represented by its different length scales. While the size of the cone-and-plate device is of the order of millimeters, the endothelial cells laying on the plate surface have size of the order of microns. The goal is to obtain a spatial resolution smaller than the height of the single cell. This allows us to investigate the biological features of the endothelial cells under shear stress in different areas of their membrane surface. This feature must be incorporated in the numerical grid, representing a challenging computational problem and is expected to be a major contribution of the research.

This thesis investigates a horizontal water turbine blade designed to suit the periodical ocean current in Penghu sea region. Blade element momentum theory is exploited to design blade profiles. Then, CFD software, Fluent, is used to obtain such simulation result for torque, power, and efficiency. Firstly, performance of turbines with various cross-sectional profiles is discussed. Then, we use quasi-steady method to simulate power output of turbines from periodical ocean current and estimate how much ocean current energy we can obtain per day. Further, the performance of a turbine installed for different immersed depth from the surface is investigated. Our studies show that airfoil profile NACA6409 can outperform others in terms of high lift/drag ratio under low Reynolds number, and better hydrodynamic properties help the water turbine obtain higher torque and power output. A water turbine designed by using NACA6409, at R=1 m, at uniform velocity=2 m/s is estimated to generate 5KW output power. On condition of periodical current flow, the ebb tidal current can rotate water turbine, but power output is only 0.54 times of flood tidal current. The water turbine can generate more power when it is sited in deeper water, and less torque when it is sited near the water surface.

The use of accelerator technology, particularly Graphics Processing Units (GPUs), for scientific computing has increased greatly over the last decade. While this technology allows larger and more complicated problems to be solved faster than before it also presents another opportunity: the real-time and interactive solution of problems. This work aims to investigate the progress that GPU technology has made towards allowing fluid-structure interaction (FSI) problems to be solved in real-time, and to facilitate user interaction with such a solver. A mesoscopic scale fluid flow solver is implemented on third generation nVidia ‘Kepler’ GPUs in two and three dimensions, and its performance studied and compared with existing literature. Following careful optimisation the solvers are found to be at least as efficient as existing work, reaching peak efficiencies of 93% compared with theoretical values. These solvers are then coupled with a novel immersed boundary method, allowing boundaries defined at arbitrary coordinates to interact with the structured fluid domain through a set of singular forces. The limiting factor of the performance of this method is found to be the integration of forces and velocities over the fluid and boundaries; the arbitrary location of boundary markers makes the memory accesses during these integrations largely random, leading to poor utilisation of the available memory bandwidth. In sample cases, the efficiency of the method is found to be as low as 2.7%, although in most scenarios this inefficiency is masked by the fact that the time taken to evolve the fluid flow dominates the overall execution time of the solver. Finally, techniques to visualise the fluid flow in-situ are implemented, and used to allow user interaction with the solvers. Initially this is achieved via keyboard and mouse to control the fluid properties and create boundaries within the fluid, and later by using an image based depth sensor to import real world geometry into the fluid. The work concludes that, for 2D problems, real-time interactive FSI solvers can be implemented on a single laptop-based GPU. In 3D the memory (both size and bandwidth) of the GPU limits the solver to relatively simple cases. Recommendations for future work to allow larger and more complicated test cases to be solved in real-time are then made to complete the work.

Surface charging is a fundamental interaction process in space plasma engineering. A three-dimensional Immersed Finite Element Particle-In-Cell (IFE-PIC) method is developed to model surface charging involving complex boundary conditions. This method extends the previous IFE-PIC algorithm to explicitly include charge deposition on a dielectric surface for charging calculations. Three simulation studies are carried out using the new algorithm to model current collection and charging in both the orbital motion limited (OML) and space charge limited regime. The first one is a full particle simulation of the charging process of single small sphere and clusters of multiple small spheres in plasma. We find that while single sphere charging agrees well with the predictions of the OML theory, the charging of a sphere in a cluster is significantly, indicating that the often used OML charging model is not an accurate one to model charging in dusty plasma. The second one concerns a secondary electron emission experiment. The simulation includes detailed experimental setup in a vacuum chamber and the results are compared against experimental data. The simulation is used to determine the facility error in experiments. The third one is a full particle simulation of charging on lunar surface. The simulation concerns both flat and non-flat surface, and spacecraft on lunar surface, in the lunar polar region. The surface sees a mesothermal solar wind plasma flow and the emission of photoelectrons and secondary electrons. At a small sun elevation angle, the surface landscape generates a complex plasma flow field and local differential charging on surface. The results will be useful for further study of charging and levitation of lunar dust. / Ph. D.

Gas-solid flow is fundamental to many industrial processes. Extensive experimental and numerical studies have been devoted to understand the interphase momentum and heat transfer in these systems. Most of the studies have focused on spherical particle shapes, however, in most natural and industrial processes, the particle shape is seldom spherical. In fact, particle shape is one of the important parameters that can have a significant impact on momentum, heat and mass transfer, which are fundamental to all processes. In this study particle-resolved simulations are performed to study momentum and heat transfer in flow through a fixed random assembly of ellipsoidal particles with sphericity of 0.887. The incompressible Navier-Stokes equations are solved using the Immersed Boundary Method (IBM). A Framework for generating particle assembly is developed using physics engine PhysX. High-order boundary conditions are developed for immersed boundary method to resolve the heat transfer in the vicinity of fluid/particle boundary with better accuracy. A complete framework using particle-resolved simulation study assembly of particles with any shape is developed. The drag force of spherical particles and ellipsoid particles are investigated. Available correlations are evaluated based on simulation results and recommendations are made regarding the best combinations. The heat transfer in assembly of ellipsoidal particle is investigated, and a correlation is proposed for the particle shape studied. The lift force, lateral force and torque of ellipsoid particles in assembly and their variations are quantitatively presented and it is shown that under certain conditions these forces and torques cannot be neglected as is done in the larger literature. / Ph. D.