<p> This thesis presents a space-time extended finite element method (space-time XFEM) based on the Heaviside enrichment for transient problems with moving interfaces, and its applications to the fluid-structure interaction (FSI) analysis. The Heaviside-enriched XFEM is a promising method to discretize partial differential equations with discontinuities in space. However, significant approximation errors are introduced by time stepping schemes when the interface geometry changes in time. The proposed space-time XFEM applies the finite element discretization and the Heaviside enrichment in both space and time with elements forming a space-time slab. A simple space-time scheme is introduced to integrate the weak form of the governing equations. This scheme considers spatial intersection configuration at multiple temporal integration points. Standard spatial integration techniques can be applied for each spatial configuration. Nitsche's method and the face-oriented ghost-penalty method are extended to the proposed space-time XFEM formulation. The stability, accuracy and flexibility of the space-time XFEM for various interface conditions including moving interfaces are demonstrated with structural and fluid problems. Moreover, the space-time XFEM enables analyzing complex FSI problems using moving interfaces, such as FSI with contact. Two FSI methods using moving interfaces (full-Eulerian FSI and Lagrangian-immersed FSI) are studied. The Lagrangian-immersed FSI method is a mixed formulation of Lagrangian and Eulerian descriptions. As solid and fluid meshes are independently defined, the FSI is computed between non-matching interfaces based on Nitsche's method and projection techniques adopted from computational contact mechanics. The stabilized Lagrange multiplier method is used for contact. Numerical examples of FSI and FSI-contact problems provide insight into the characteristics of the combination of the space-time XFEM and the Lagrangian-immersed FSI method. The proposed combination is a promising method which has the versatility for various multi-physics simulations and the applicability such as optimization.</p><p>

<p> When an explosive detonates above ground, air is principally the only material involved in the transmission of shock waves that can result in damage. Hydrodynamic codes that simulate these explosions use equations of state (EOSs) for modeling the behavior of air at these high-pressure, high-velocity conditions. An investigation is made into the effect that the EOS selection for air has on the calculated overpressure-time waveforms of a blast event. Specifically, the ideal gas, Doan-Nickel, and SESAME EOSs in the SHAMRC code were used to reproduce experiments conducted at the Blast Load Simulator (BLS), a large-scale shock tube operated by the U.S. Army Engineer Research and Development Center, that consisted of subjecting an instrumented rigid box at three angles of orientation inside the BLS to a blast environment. Numerical comparisons were made against experimentally-derived confidence intervals using peak values and several error metrics, and an attempt was made to rank the EOS based on performance. Issues were noted with the duration of decay from maximum pressure to negative phase that resulted in a general underprediction of the integrated impulse regardless of EOS, while the largest errors were noted for gages on faces at 45 to 90 degrees from the initial flow direction. Although no significant differences were noticed in the pressure histories from different EOSs, the ideal gas consistently ranked last in terms of the error metrics considered and simultaneously required the least computing resources. Similarly, the Doan-Nickel EOS slightly performed better than SESAME while requiring additional wallclock time. The study showed that the Doan-Nickel and SESAME EOSs can produce blast signatures with less errors and more matches in peak pressure and impulse than the ideal gas EOS at the expense of more computational requirements. </p><p>

<p> In this dissertation, Large Eddy Simulations (LES) are used to model the coupled turbulence-reactive tracer dynamics within the upper mixed layer of the ocean. Prior work has shown that LES works well over the spatial and time scales relevant to both turbulence and reactive biogeochemistry. Additionally, the code intended for use is able to carry an arbitrary number of tracer equations, allowing for easy expansion of the species reactions. Research in this dissertation includes a study of 15 idealized non-reactive tracers within an evolving large-scale temperature front in order determine and understand the fundamental dynamics underlying turbulence-tracer interaction in the absence of reactions. The focus of this study, in particular, was on understanding the evolution of biogeochemically-relevant, non-reactive tracers in the presence of both large (~5 km) submesoscale eddies and smallscale (~100 m) wave-driven Langmuir turbulence. The 15 tracers studied have different initial, boundary, and source conditions and significant differences are seen in their distributions depending on these conditions. Differences are also seen between regions where submesoscale eddies and small-scale Langmuir turbulence are both present, and in regions with only Langmuir turbulence. A second study focuses on the examination of Langmuir turbulence effects on upper ocean carbonate chemistry. Langmuir mixing time scales are similar to those of chemical reactions, resulting in potentially strong tracer-flow coupling effects. The strength of the Langmuir turbulence is varied, from no wave-driven turbulence (i.e., only shear-driven turbulence), to Langmuir turbulence that is much stronger than that found in typical upper ocean conditions. Three different carbonate chemistry models are also used in this study: time-dependent chemistry, equilibrium chemistry, and no-chemistry (i.e., non-reactive tracers). The third and final study described in this dissertation details the development of a reduced-order biogeochemical model with 17 state equations that can accurately reproduce the Bermuda Atlantic Time-series Study (BATS) ecosystem behavior, but that can also be integrated within high-resolution LES.</p><p>

<p> Low-order numerical methods are widespread in academic solvers and ubiquitous in industrial solvers due to their robustness and usability. High-order methods are less robust and more complicated to implement; however, they exhibit low numerical dissipation and have the potential to improve the accuracy of flow simulations at a lower computational cost when compared to low-order methods. This motivates our development of a high-order compact method using Huynh's flux reconstruction scheme for solving unsteady incompressible flow on unstructured grids. We use Chorin's classic artificial compressibility formulation with dual time stepping to solve unsteady flow problems. In 2D, an implicit non-linear lower-upper symmetric Gauss-Seidel scheme with backward Euler discretization is used to efficiently march the solution in pseudo time, while a second-order backward Euler discretization is used to march in physical time. We verify and validate implementation of the high-order method coupled with our implicit time stepping scheme using both steady and unsteady incompressible flow problems. The current implicit time stepping scheme is proven effective in satisfying the divergence-free constraint on the velocity field in the artificial compressibility formulation. The high-order solver is extended to 3D and parallelized using MPI. Due to its simplicity, time marching for 3D problems is done explicitly. The feasibility of using the current implicit time stepping scheme for large scale three-dimensional problems with high-order polynomial basis still remains to be seen. </p><p> We directly use the aforementioned numerical solver to simulate pulsatile flow of a Newtonian blood-analog fluid through a rigid 180-degree curved artery model. One of the most physiologically relevant forces within the cardiovascular system is the wall shear stress. This force is important because atherosclerotic regions are strongly correlated with curvature and branching in the human vasculature, where the shear stress is both oscillatory and multidirectional. Also, the combined effect of curvature and pulsatility in cardiovascular flows produces unsteady vortices. The aim of this research as it relates to cardiovascular fluid dynamics is to predict the spatial and temporal evolution of vortical structures generated by secondary flows, as well as to assess the correlation between multiple vortex pairs and wall shear stress. We use a physiologically (pulsatile) relevant flow rate and generate results using both fully developed and uniform entrance conditions, the latter being motivated by the fact that flow upstream of a curved artery may not have sufficient straight entrance length to become fully developed. Under the two pulsatile inflow conditions, we characterize the morphology and evolution of various vortex pairs and their subsequent effect on relevant haemodynamic wall shear stress metrics.</p><p>

<p> Computational fluid dynamic (CFD) simulations were conducted on a known low aspect ratio wing design as well as four variant designs incorporating Coanda effect circulation control (CC) for lift generation. The U.S. Navy&rsquo;s Kestrel code was employed to explore the relation of slot height and lip thickness to maximize lift augmentation. Reynolds Averaged Navier-Stokes calculations were performed at a Reynolds number of 2.1 million over wing configurations with a 1 ft span and chord with top slot flow blowing coefficients of 0, 0.005, 0.05, 0.1, and 0.15 over the angles of attack of 0&deg;, 4&deg;, 8&deg;, 14&deg;, and 18&deg;. The computational results were compared to experimental measurements of slot unblown and blown configurations. General findings include higher lift augmentation ratios of modified designs with similar lip thickness and larger slot gap. Greater lift coefficients were found with larger lip thicknesses and smaller slot heights.</p><p>

Complex interactions between solid, liquid and gas occur in many practical engineering applications, and are often difficult to quantify experimentally. A few examples include boiling over solid heaters, solidification melt-dynamics in metal casting, and convective cooling of electronic components. With the availability of scalable computational tools, high-fidelity simulations can provide new insight into these phenomena and answer open questions. In the present work, a multiphase solver is presented which can simulate problems involving phase transition over complex geometries. The dynamics of liquid-gas interface are modeled using a level-set technique, which utilizes Ghost Fluid Method (GFM) to account for sharp jump in pressure, velocity, and temperature across the multiphase boundary. The fluid-solid interactions are modeled using an Immersed Boundary Method (IBM) which uses a Moving Least Squared (MLS) reconstruction to calculate fluid-flow around the solid, along with an additional GFM forcing to model its effect on pressure, temperature and Conjugate Heat Transfer (CHT). The resulting three dimensional solver is fully explicit in time and uses a fractional step method for Navier-Stokes, energy, and mass transfer equations. Validation and verification cases are presented to demonstrate the accuracy of the solver in comparison to experimental and analytical problems, and results of high fidelity pool boiling simulations in varying gravity environments are discussed in detail.