Hypersonic flow analysis is performed on an inflatable aerocapture device called a "Ballute" for Titan's Mission. An existing unstructured Cartesian grid methodology is used as a starting point by taking advantage of its ability to automatically generate grids over any deformed shape of the flexible ballute. The major effort for this thesis work is focused on advancing the existing unstructured Cartesian grid methodology. This includes implementing thermochemical nonequilibrium capability and porting it to a parallel computing environment using a Space-Filling-Curve (SFC) based domain decomposition technique. The implemented two temperature thermochemical nonequilibrium solver governs the finite rate chemical reactions and vibrational relaxation in the high temperature regimes of hypersonic flow. In order to avoid the stiffness problem in the explicit chemical solver, a point implicit method is adopted to calculate the chemical reaction source term. The AUSMPW+ scheme with MUSCL data reconstruction is adopted as the numerical scheme to avoid non-physical oscillations and the carbuncle phenomenon. The results for five species air model and for thirteen species N2-CH4-Ar model to simulate Titan entry are included for verification against DPLR (NASA Ames' structured grid hypersonic flow solver). The efficient parallel computation of any unstructured grid flow solver requires an adequate grid decomposition strategy because of its complex spatial data structure. The difficulties of even and block-contiguous partitioning in frequently adapting unstructured Cartesian grids are overcome by implementing the 3D Hilbert SFC. Grids constructed by the SFC for parallel environment promise short inter-CPU communication time while maintaining perfect load balancing between CPUs. The load imbalance due to the local solution adaption is simply apportioned by re-segmenting the curve into even pieces. The detailed structure of the 3D Hilbert SFC and parallel computing efficiency results based on this grid partition method are also presented. Finally, a structural dynamics tool (LS-DYNA) is loosely coupled with the present parallel thermochemical nonequilibrium flow solver to obtain the deformed surface definition of the ballute.

This research is mainly focused on the development of the adaptive Cartesian grid methods for compressibl  e flow. At first, the ghost cell method and its applications for inviscid compressible flow on adaptive tree Cartesian grid are developed. The proposed method is successfully used to evaluate various inviscid compressible flows around complex bodies. The mass conservation of the method is also studied by numerical analysis. The extension to three-dimensional flow is presented. Then, an h-adaptive Runge–Kutta discontinuous Galerkin (RKDG) method is presented in detail for the development of high accuracy numerical method under Cartesian grid. This method combined with the ghost cell immersed boundary method is also validated by well documented test problems involving both steady and unsteady compressible flows over complex bodies in a wide range of Mach numbers. In addition, in order to suppress the failure of preserving positivity of density or pressure, which may cause blow-ups of the high order numerical algorithms, a positivity-preserving limiter technique coupled with h-adaptive RKDG method is developed. Such a method has been successfully implemented to study flows with the large Mach number, strong shock/obstacle interactions and shock diffraction. The extension of the method to viscous flow under the adaptive Cartesian grid with hybrid overlapping bodyfitted grid is developed. The method is validated by benchmark problems and has been successfully implemented to study airfoil with ice accretion. Finally, based on an open source code, the detached eddy simulation (DES) is developed for massive separation flow, and it is used to perform the research on aerodynamic performance analysis over the wing with ice accretion.

We present a novel dimensionally split Cartesian cut cell method to compute inviscid, viscous and turbulent flows around rigid geometries. On a cut cell mesh, the existence of arbitrarily small boundary cells severely restricts the stable time step for an explicit numerical scheme. We solve this `small cell problem' when computing solutions for hyperbolic conservation laws by combining wave speed and geometric information to develop a novel stabilised cut cell flux. The convergence and stability of the developed technique are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. This work was recently published in the Journal of Computational Physics (Gokhale et al., 2018). Subsequently, we develop the method further to be able to compute solutions for the compressible Navier-Stokes equations. The method is globally second order accurate in the L1 norm, fully conservative, and allows the use of time steps determined by the regular grid spacing. We provide a full description of the three-dimensional implementation of the method and evaluate its numerical performance by computing solutions to a wide range of test problems ranging from the nearly incompressible to the highly compressible flow regimes. This work was recently published in the Journal of Computational Physics (Gokhale et al., 2018). It is the first presentation of a dimensionally split cut cell method for the compressible Navier-Stokes equations in the literature. Finally, we also present an extension of the cut cell method to solve high Reynolds number turbulent automotive flows using a wall-modelled Large Eddy Simulation (WMLES) approach. A full description is provided of the coupling between the (implicit) LES solution and an equilibrium wall function on the cut cell mesh. The combined methodology is used to compute results for the turbulent flow over a square cylinder, and for flow over the SAE Notchback and DrivAer reference automotive geometries. We intend to publish the promising results as part of a future publication, which would be the first assessment of a WMLES Cartesian cut cell approach for computing automotive flows to be presented in the literature.

Dynamic response of materials to high-speed and high-intensity loading conditions is important in several applications including high-speed flows with droplets, bubbles and particles, and hyper-velocity impact and penetration processes. In such high-pressure physics problems, simulations encounter challenges associated with the treatment of material interfaces, particularly when strong nonlinear waves like shock and detonation waves impinge upon them. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with levelset interface tracking is attractive. In this regard, a sharp interface Cartesian grid-based, Ghost Fluid Method (GFM) is developed for resolving embedded fluid, elasto-plastic solid and rigid (solid) objects in hyper-velocity impact and high-intensity shock loaded environment. The embedded boundaries are tracked and represented by virtue of the level set interface tracking technique. The evolving multi-material interface and the flow are coupled by meticulously enforcing the boundary conditions and jump relations at the interface. In addition, a tree-based Local Mesh Refinement scheme is employed to efficiently resolve the desired physics. The framework developed is generic and is applicable to interfaces separating a wide range of materials and for a broad spectrum of speeds of interaction (O(km/s)). The wide repertoire of problems solved in this work demonstrates the flexibility, stability and robustness of the method in accurately capturing the dynamics of the embedded interface. Shocks interacting with large ensembles of particles are also computed.

Cardiovascular modeling has the capability to provide valuable information allowing clinicians to better classify patients and aid in surgical planning. Modeling is advantageous for being non-invasive, and also allows for quantification of values not easily obtained from physical measurements. Hemodynamics are heavily dependent on vessel geometry, which varies greatly from patient to patient. For this reason, clinically relevant approaches must perform these simulations on patient-specific geometry. Geometry is acquired from various imaging modalities, including magnetic resonance imaging, computed tomography, and ultrasound. The typical approach for generating a computational model requires construction of a triangulated surface mesh for use with finite volume or finite element solvers. Surface mesh construction can result in a loss of anatomical features and often requires a skilled user to execute manual steps in 3rd party software. An alternative to this method is to use a Cartesian grid solver to conduct the fluid simulation. Cartesian grid solvers do not require a surface mesh. They can use the implicit geometry representation created during the image segmentation process, but they are constrained to a cuboidal domain. Since patient-specific geometry usually deviate from the orthogonal directions of a cuboidal domain, flow extensions are often implemented. Flow extensions are created via a skilled user and 3rd party software, rendering the Cartesian grid solver approach no more clinically useful than the triangulated surface mesh approach. This work presents an alternative to flow extensions by developing a method of applying vessel inlet and outlet boundary conditions to regions inside the Cartesian domain.

A major drawback in the operation of mechanical heart valve prostheses is thrombus formation in the near valve region potentially due to the high shear stresses present in the leakage jet flows through small gaps between leaflets and the valve housing. Detailed flow analysis in this region during the valve closure phase is of interest in understanding the relationship between shear stress and platelet activation. An efficient Cartesian grid method is developed for the simulation of incompressible flows around stationary and moving three-dimensional immersed solid bodies as well as fluid-fluid interfaces. The embedded boundaries are represented using Levelsets and treated in a sharp manner without the use of source terms to represent boundary effects. The resulting algorithm is implemented in a straightforward manner in three dimensions and retains global second-order accuracy. When dealing with problems of disparate length scales encountered in many applications, it is necessary to resolve the physically important length scales adequately to ensure accuracy of the solution. Fixed grid methods often have the disadvantage of heavy mesh requirement for well resolved calculations. A quadtree based adaptive local mesh refinement scheme is developed to complement the sharp interface Cartesian grid method scheme for efficient and optimized calculations. Detailed timing and accuracy data is presented for a variety of benchmark problems involving moving boundaries. The above method is then applied to modeling heart valve closure and predicting thrombus formation. Leaflet motion is calculated dynamically based on the fluid forces acting on it employing a fluid-structure interaction algorithm. Platelets are modeled and tracked as point particles by a Lagrangian particle tracking method which incorporates the hemodynamic forces on the particles. Leaflet closure dynamics including rebound is analyzed and validated against previous studies. Vortex shedding and formation of recirculation regions are observed downstream of the valve, particularly in the gap between the valve and the housing. Particle exposure to high shear and entrapment in recirculation regions with high residence time in the vicinity of the valve are observed corresponding to regions prone to thrombus formation.

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity. / Singapore-MIT Alliance (SMA)

Viscoelastic fluid flow with immersed boundaries of complex geometry is widely found both in nature and engineering processes. Examples include haemocytes moving in human blood flow, self-propulsion of microscopic organisms in complex liquids, hydraulic fracturing with sand in oil flow, and suspension flow with viscoelastic medium. Computational modelling of such systems is important for understanding complex biological processes and assisting engineering designs. Conventional simulation methods use conformed meshes to resolve the boundaries of complex geometry. Dynamically updating the conformed mesh is computationally expensive and makes parallelization difficult. In comparison, Cartesian grid methods are more promising for large scale parallel simulation. Using Cartesian grid methods to simulate viscoelastic fluid flow with complex boundaries is a relatively unexplored area. In this thesis, a sharp interface Cartesian grid method (SICG) and a smoothed interface immersed boundary method (SIIB) are developed in order to simulate viscoelastic fluids in complex geometries. The SICG method shows a better prediction of the stress on stationary boundaries while the SIIB method shows reduced non-physical oscillations in the computation of drag and lift forces on moving boundaries. Parallel implementations of both solvers are developed. Convergence of the numerical schemes is shown and the implementations are validated with a few benchmark problems with both stationary and moving boundaries. This study also focuses on the simulation of flows past 2D cylindrical or 3D spherical particles. Lateral migration of particles induced by inertial and viscoelastic effects are investigated with different flow types. Equilibrium positions of inertia-induced migration are reported as a function of the particle Reynolds number and the blockage ratio. The migration in the viscoelastic fluid is simulated from zero elastic number to a finite elastic number. The inclusion of both inertial and viscoelastic effects on the lateral migration of a particle is the first of its kind. New findings are reported for the equilibrium positions of a spherical particle in square duct flow, which suggest the need for future experimental and computational work.

Fluid-structure interaction (FSI) is an important physical phenomenon in many applications and across various disciplines including aerospace, civil and bio-engineering. In civil engineering, applications include the design of wind turbines, pipelines, suspension bridges and offshore platforms. Ocean structures such as drilling risers, mooring lines, cables, undersea piping and tension-leg platforms can be subject to strong ocean currents, and such structures may suffer from Vortex-Induced Vibrations (VIV's), where vortex shedding of the flow interacts with the structural properties, leading to large amplitude vibrations in both in-line and cross-flow directions. Over the past years, many experimental and numerical studies have been conducted to comprehend the underlying physical mechanisms. However, to date there is still limited understanding of the effect of oscillatory interactions between fluid flow and structural behavior though such interactions can cause large deformations. This research proposes a mathematical framework to accurately predict FSI for elastically supported rigid structures. The numerical method developed solves the Navier-Stokes (NS) equations for the fluid and the Equation of Motion (EOM) for the structure. The proposed method employs Finite Differences (FD) on Cartesian grids together with an improved, efficient and oscillation-free Immersed Boundary Method (IBM), the accuracy of which is verified for several test cases of increasing complexity. A variety of two and three dimensional FSI simulations are performed to demonstrate the accuracy and applicability of the method. In particular, forced and a free vibration of a rigid cylinder including Vortex-Induced Vibration (VIV) of an elastically supported cylinder are presented and compared with reference simulations and experiments. Then, the interference between two cylinders in tandem arrangement at two different spacing is investigated. In terms of VIV, three different scenarios were studied for each cylinder arrangement to compare resonance regime to a single cylinder. Finally, the IBM is implemented into a three-dimensional Large-Eddy Simulation (LES) method and two high Reynolds number (Re) flows are studied for a stationary and transversely oscillating cylinder. The robustness, accuracy and applicability of the method for high Re number flow is demonstrated by comparing the turbulence statistics of the two cases and discussing differences in the mean and instantaneous flows.

La perméabilisation des cellules à l’aide d’impulsions électriques intenses, appelée électroperméabilisation, est un phénomène biologique impliqué dans des thérapies anticancéreuses récentes. Elle permet, par exemple, d’améliorer l’efficacité d’une chimiothérapie en diminuant les effets secondaires, d’effectuer des transferts de gènes, ou encore de procéder à l’ablation de tumeurs. Les mécanismes de l’électroperméabilisation restent cependant encore méconnus, et l’hypothèse majoritairement admise par la communauté de formation de pores à la surface des membranes cellulaires est en contradiction avec certains résultats expérimentaux.Le travail de modélisation proposé dans cette thèse est basé sur une approche différente des modèles d’électroporation existants. Au lieu de proposer des lois sur les propriétés des membranes à partir d’hypothèses à l’échelle moléculaire, nous établissons des lois ad hoc pour les décrire, en se basant uniquement sur les informations expérimentales disponibles. Aussi, afin de rester au plus prèsde ces dernières et faciliter la phase de calibration à venir, nous avons ajouté un modèle de transport et de diffusion de molécules dans la cellule. Une autre spécificité de notre modèle est que nous faisons la distinction entre l’état conducteur et l’état perméable des membranes.Des méthodes numériques spécifiques ainsi qu’un code en 3D et parallèle en C++ ont été écrits et validés pour résoudre les équations aux dérivées partielles de ces différents modèles. Nous validons le travail de modélisation en montrant que les simulations reproduisent qualitativement les comportements observés in vitro. / Cell permeabilization by intense electric pulses, called electropermeabilization, is a biological phenomenon involved in recent anticancer therapies. It allows, for example, to increase the efficacy of chemotherapies still reducing their side effects, to improve gene transfer, or to proceed tumor ablation. However, mechanisms of electropermeabilization are not clearly explained yet, and the mostly adopted hypothesis of the formation of pores at the membrane surface is in contradiction with several experimental results.This thesis modeling work is based on a different approach than existing electroporation models. Instead of deriving equations on membranes properties from hypothesis at the molecular scale, we prefer to write ad hoc laws to describe them, based on available experimental data only. Moreover, to be as close as possible to these data, and to ease the forthcoming work of parameter calibration, we added to our model equations of transport and diffusion of molecules in the cell. Another important feature of our model is that we differentiate the conductive state of membranes from their permeable state.Numerical methods, as well as a 3D parallel C++ code were written and validated in order to solve the partial differential equations of our models. The modeling work was validated by showing qualitative match between our simulations and the behaviours that are observed in vitro