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.

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.

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.

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.

Solid-fluid two-phase flows, where the solid volume fraction is large either by geometry or by population (as in slurry flows), are ubiquitous in nature and industry. The interaction between the fluid and the suspended solids, in such flows, are too strongly coupled rendering the assumption of a single-way interaction (flow influences particle motion alone but not vice-versa) invalid and inaccurate. Most commercial flow solvers do not account for twoway interactions between fluid and immersed solids. The current state-of-art is restricted to two-way coupling between spherical particles (of very small diameters, such that the particlediameter to the characteristic flow domain length scale ratio is less than 0.01) and flow. These solvers are not suitable for solving several industrial slurry flow problems such as those of hydrates which is crucial to the oil-gas industry and rheology of slurries, flows in highly constrained geometries like microchannels or sessile drops that are laden with micro-PIV beads at concentrations significant for two-way interactions to become prominent. It is therefore necessary to develop direct numerical simulation flow solvers employing rigorous two-way coupling in order to accurately characterise the flow profiles between large immersed solids and fluid. It is necessary that such a solution takes into account the full 3D governing equations of flow (Navier-Stokes and continuity equations), solid translation (Newton’s second law) and solid rotation (equation of angular momentum) while simultaneously enabling interaction at every time step between the forces in the fluid and solid domains. This thesis concerns with development and rigorous validation of a 3D solid-fluid solver based on a novel variant of immersed-boundary method (IBM). The solver takes into account full two-way fluid-solid interaction with 6 degrees-of-freedom (6DOF). The solid motion solver is seamlessly integrated into the Gerris flow solver hence called Gerris Immersed Solid Solver (GISS). The IBM developed treats both fluid and solid in the manner of “fluid fraction” such that any number of immersed solids of arbitrary geometry can be realised. Our IBM method also allows transient local mesh adaption in the fluid domain around the moving solid boundary, thereby avoiding problems caused by the mesh skewness (as seen in common mesh-adaption algorithms) and significantly improves the simulation efficiency. The solver is rigorously validated at levels of increasing complexity against theory and experiment at low to moderate flow Reynolds number. At low Reynolds numbers (Re 1) these include: the drag force and terminal settling velocities of spherical bodies (validating translational degrees of freedom), Jeffrey’s orbits tracked by elliptical solids under shear flow (validating rotational and translational degrees of freedom) and hydrodynamic interaction between a solid and wall. Studies are also carried out to understand hydrodynamic interaction between multiple solid bodies under shear flow. It is found that initial distance between bodies is crucial towards the nature of hydrodynamic interaction between them: at a distance smaller than a critical value the solid bodies cluster together (hydrodynamic attraction) and at a distance greater than this value the solid bodies travel away from each other (hydrodynamic repulsion). At moderately high flow rates (Re O(100)), the solver is validated against migratory motion of an eccentrically placed solid sphere in Poisuelle flow. Under inviscid conditions (at very high Reynolds number) the solver is validated against chaotic motion of an asymmetric solid body. These validations not only give us confidence but also demonstrate the versatility of the GISS towards tackling complex solid-fluid flows. This work demonstrates the first important step towards ultra-high resolution direct numerical simulations of solid-fluid flows. The GISS will be available as opensource code from February 2015.

This thesis presents a framework for simulating the fluid dynamical behavior of complex moving boundary problems in a high-performance computing environment. The framework is implemented in the pELAFINT3D software package. Moving boundaries are evolved in a seamless fashion through the use of distributed narrow band level set methods and the effect of moving boundaries is incorporated into the flow solution by a novel Cartesian grid method. The proposed Cartesian grid approach builds on the concept of a ghost fluid method where boundary conditions are applied through least-squares polynomial extrapolations. The method is hybridized such that computational cells adjacent to moving boundaries change discretization schemes smoothly in time to avoid the introduction of strong oscillations in the pressure field. The hybridization is shown to have minimal effect on accuracy while significantly suppressing pressure oscillations. The computational capability of the Cartesian grid approach is enhanced with a massively parallel adaptive meshing algorithm. Local mesh enrichment is effected through the use of octree refinement, and a scalable mesh pruning algorithm is used to reduce the memory footprint of the Cartesian grid for geometries which are not well bounded by a rectangular cuboid. The computational work is kept in a well-balanced state through the use of an adaptive repartitioning strategy. The numerical scheme is validated against many benchmark problems and the composite approach is demonstrated to work well on tens of thousands of computational cores. A simulation of the closure phase of a mechanical heart valve was carried out to demonstrate the ability of the pELAFINT3D package to compute high Reynolds number flows with complex moving boundaries and a wide disparity in length scales. Finally, a novel image-to-computation algorithm was implemented to demonstrate the flexibility the current method allows in designing new applications.

[ES] La interacción de contacto entre sólidos deformables es uno de los fenómenos más complejos en el ámbito de la mecánica computacional. La resolución de este problema requiere de algoritmos robustos para el tratamiento de no linealidades geométricas. El Método de Elementos Finitos (MEF) es uno de los más utilizados para el diseño de componentes mecánicos, incluyendo la solución de problemas de contacto. En este método el coste asociado al proceso de discretización (generación de malla) está directamente vinculado a la definición del contorno a modelar, lo cual dificulta la introducción en la simulación de superficies complejas, como las superficies NURBS, cada vez más utilizadas en el diseño de componentes. Esta tesis está basada en el "Cartesian grid Finite Element Method" (cgFEM). En esta metodología, encuadrada en la categoría de métodos "Immersed Boundary", se extiende el problema a un dominio de aproximación (cuyo mallado es sencillo de generar) que contiene al dominio de análisis completamente en su interior. Al desvincular la discretización de la definición del contorno del problema se reduce drásticamente el coste de generación de malla. Es por ello que el método cgFEM es una herramienta adecuada para la resolución de problemas en los que es necesario modificar la geometría múltiples veces, como el problema de optimización de forma o la simulación de desgaste. El método cgFEM permite también crear de manera automática y eficiente modelos de Elementos Finitos a partir de imágenes médicas. La introducción de restricciones de contacto habilitaría la posibilidad de considerar los diferentes estados de integración implante-tejido en procesos de optimización personalizada de implantes. Así, en esta tesis se desarrolla una formulación para resolver problemas de contacto 3D con el método cgFEM, considerando tanto modelos de contacto sin fricción como problemas con rozamiento de Coulomb. La ausencia de nodos en el contorno en cgFEM impide la aplicación de métodos tradicionales para imponer las restricciones de contacto, por lo que se ha desarrollado una formulación estabilizada que hace uso de un campo de tensiones recuperado para asegurar la estabilidad del método. Para una mayor precisión de la solución, se ha introducido la definición analítica de las superficies en contacto en la formulación propuesta. Además, se propone la mejora de la robustez de la metodología cgFEM en dos aspectos: el control del mal condicionamiento del problema numérico mediante un método estabilizado, y la mejora del campo de tensiones recuperado, utilizado en el proceso de estimación de error. La metodología propuesta se ha validado a través de diversos ejemplos numéricos presentados en la tesis, mostrando el gran potencial de cgFEM en este tipo de problemas. / [CAT] La interacció de contacte entre sòlids deformables és un dels fenòmens més complexos en l'àmbit de la mecànica computacional. La resolució d'este problema requerix d'algoritmes robustos per al tractament de no linealitats geomètriques. El Mètode dels Elements Finits (MEF) és un dels més utilitzats per al disseny de components mecànics, incloent la solució de problemes de contacte. En este mètode el cost associat al procés de discretització (generació de malla) està directament vinculat a la definició del contorn a modelar, la qual cosa dificulta la introducció en la simulació de superfícies complexes, com les superfícies NURBS, cada vegada més utilitzades en el disseny de components. Esta tesi està basada en el "Cartesian grid Finite Element Method" (cgFEM). En esta metodologia, enquadrada en la categoria de mètodes "Immersed Boundary", s'estén el problema a un domini d'aproximació (el mallat del qual és senzill de generar) que conté al domini d'anàlisi completament en el seu interior. Al desvincular la discretització de la definició del contorn del problema es reduïx dràsticament el cost de generació de malla. És per això que el mètode cgFEM és una ferramenta adequada per a la resolució de problemes en què és necessari modificar la geometria múltiples vegades, com el problema d'optimització de forma o la simulació de desgast. El mètode cgFEM permet també crear de manera automàtica i eficient models d'Elements Finits a partir d'imatges mèdiques. La introducció de restriccions de contacte habilitaria la possibilitat de considerar els diferents estats d'integració implant-teixit en processos d'optimització personalitzada d'implants. Així, en esta tesi es desenvolupa una formulació per a resoldre problemes de contacte 3D amb el mètode cgFEM, considerant tant models de contacte sense fricció com a problemes amb fregament de Coulomb. L'absència de nodes en el contorn en cgFEM impedix l'aplicació de mètodes tradicionals per a imposar les restriccions de contacte, per la qual cosa s'ha desenvolupat una formulació estabilitzada que fa ús d'un camp de tensions recuperat per a assegurar l'estabilitat del mètode. Per a una millor precisió de la solució, s'ha introduït la definició analítica de les superfícies en contacte en la formulació proposada. A més, es proposa la millora de la robustesa de la metodologia cgFEM en dos aspectes: el control del mal condicionament del problema numèric per mitjà d'un mètode estabilitzat, i la millora del camp de tensions recuperat, utilitzat en el procés d'estimació d'error. La metodologia proposada s'ha validat a través de diversos exemples numèrics presentats en la tesi, mostrant el gran potencial de cgFEM en este tipus de problemes. / [EN] The contact interaction between elastic solids is one of the most complex phenomena in the computational mechanics research field. The solution of such problem requires robust algorithms to treat the geometrical non-linearities characteristic of the contact constrains. The Finite Element Method (FE) has become one of the most popular options for the mechanical components design, including the solution of contact problems. In this method the computational cost of the generation of the discretization (mesh generation) is directly related to the complexity of the analysis domain, namely its boundary. This complicates the introduction in the numerical simulations of complex surfaces (for example NURBS), which are being increasingly used in the CAD industry. This thesis is grounded on the Cartesian grid Finite Element Method (cgFEM). In this methodology, which belongs to the family of Immersed Boundary methods, the problem at hand is extended to an approximation domain which completely embeds the analysis domain, and its meshing is straightforward. The decoupling of the boundary definition and the discretization mesh results in a great reduction of the mesh generation's computational cost. Is for this reason that the cgFEM is a suitable tool for the solution of problems that require multiple geometry modifications, such as shape optimization problems or wear simulations. The cgFEM is also capable of automatically generating FE models from medical images without the intermediate step of generating CAD entities. The introduction of the contact interaction would open the possibility to consider different states of the union between implant and living tissue for the design of optimized implants, even in a patient-specific process. Hence, in this thesis a formulation for solving 3D contact problems with the cgFEM is presented, considering both frictionless and Coulomb's friction problems. The absence of nodes along the boundary in cgFEM prevents the enforcement of the contact constrains using the standard procedures. Thus, we develop a stabilized formulation that makes use of a recovered stress field, which ensures the stability of the method. The analytical definition of the contact surfaces (by means of NURBS) has been included in the proposed formulation in order to increase the accuracy of the solution. In addition, the robustness of the cgFEM methodology is increased in this thesis in two different aspects: the control of the numerical problem's ill-conditioning by means of a stabilized method, and the enhancement of the stress recovered field, which is used in the error estimation procedure. The proposed methodology has been validated through several numerical examples, showing the great potential of the cgFEM in these type of problems. / Navarro Jiménez, JM. (2019). Contact problem modelling using the Cartesian grid Finite Element Method [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/124348 / TESIS

In this dissertation, Immersed Boundary Method (IBM) is evaluated in ribbed duct geometries to show the potential of simulating complex geometry with a simple structured grid. IBM is first investigated in well-accepted benchmark cases: channel flow and pipe flow with circular cross-section. IBM captures all the flow features with very good accuracy in these two cases. Then a two side ribbed duct geometry is test using IBM at Reynolds number of 20,000 under fully developed assumption. The IBM results agrees well with body conforming grid predictions. A one side ribbed duct geometry is also tested at a bulk Reynolds number of 1.5⨉10⁴. Three cases have been examined for this geometry: a stationary case; a case of positive rotation at a rotation number (Ro=ΩDₕ/U) of 0.3 (destabilizing); and a case of negative rotation at Ro= -0.3 (stabilizing). Time averaged mean, turbulent quantities are presented, together with heat transfer. The overall good agreement between IBM, BCG and experimental results suggests that IBM is a promising method to apply to complex blade geometries. Due to the disadvantage of IBM that it requires large amount of cells to resolve the boundary near the immersed surface, wall modeled LES (WMLES) is evaluated in the final part of this thesis. WMLES is used for simulating turbulent flow in a developing staggered ribbed U-bend duct. Three cases have been tested at a bulk Reynolds number of 10⁵: a stationary case; a positive rotation case at a rotation number Ro=0.2; and a negative rotation case at Ro=-0.2. Coriolis force effects are included in the calculation to evaluate the wall model under the influence of these effects which are known to affect shear layer turbulence production on the leading and trailing sides of the duct. Wall model LES prediction shows good agreement with experimental data. / Master of Science