Browsing by Subject "Numerical"
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Item Bridging scales in modeling and simulation of thermal transport processes(2014-08) Wheeler, Vincent MichaelThe vastly disparate length and time scales existing in new devices and materials born out of nanotechnology have made thermal modeling and simulation more important and more difficult. The experimental thermal characterization of such systems, e.g. modern computer processors, can be prohibitively difficult or expensive making numerical simulation the only route to effective technology design. However, obtaining solutions that account for small scales, but are still computationally feasible, requires innovative modeling approaches. The research contained herein represents three independent contributions to the understanding of the modeling of thermal transport processes in systems with nano-sized features. At their common core, all contributions in this thesis are rooted in transport theory--the solution or approximation of the Boltzmann equation (BE)--to statistically describe a system made up of a great many energy-carrying particles. The work roughly divides into the three modes of heat transfer--convection, conduction, and radiation. First, a framework for the discretization of the BE (in its many forms) based on lattices is presented. The widely-used lattice Boltzmann method for the simulation of fluid flow is shown to be a sub-case. The framework gives a new rigorous foundation to the use of lattice methods which have emerged in recent years with applications ranging from Brownian motion to astrophysical radiation. Second, we give a thorough presentation of recently proposed models of heat conduction derived from the phonon BE which provides rigor and insight into the different approaches. Most notably, the "new heat equation" is derived directly from the phonon BE for the first time along with a novel boundary condition. The result is shown to give excellent agreement with the more detailed description provided by the equation of phonon radiative transport. Last, we provide the radiative characterization of a nano-porous material using Maxwell's equations in order to recover coefficients to the linear BE governing thermal radiative transfer.Item Establishing Quantitative Understanding of Energy Transfer to High Frequency in Nonlinear Dispersive Equations(2017-05-01) Callis, Keagan GWe present a family of particular solutions to a Hamiltonian system which was derived to study energy transfer to higher Fourier modes in solutions to the cubic defocusing nonlinear Schrödinger equation. The solutions in this family are not direct solutions to this nonlinear Schrödinger equation, but instead approximate solutions which transfer energy to higher Fourier modes. Our numerical work follows and expands upon work done in [4] and [8], where the existence of solutions exhibiting these properties was proven non-constructively. The solutions presented here depend heavily upon phase interactions in the Hamiltonian system, which has previously been poorly understood.Item Modeling of blade cutting of viscoelastic biomaterials(2013-06) Peng, YunThe work in this thesis focuses on the modeling of blade cutting of viscoelastic materials. The blade cutting procedure is modeled in two stages. The first stage is the contact of the blade with the cutting material and the second stage is the fracture during continuous cutting. The modeling of the first stage is used to predict the initiation of the cutting fracture and the modeling of the second stage is use to characterize the cutting force during continuous fracture. Experiments that are used to determine the material parameters for the simulations and calculations of the cutting process are also carried out.The first stage is modeled as the area contact between the edge of the blade and cutting materials. It is modeled by applying the elastic-viscoelastic correspondence principle to the solutions for point load and then by performing a numerical integration scheme to extend the solutions to distributed pressure cases. The stress tensor was analytically obtained at any given point inside the viscoelastic material. The effect of slicing angles on the stress distribution is then evaluated. Using the principal stresses, the location of damage is predicted using Tresca's failure criterion. In the continuous damage stage, FEM simulation using ABAQUS is used as the modeling method. A bi-layered structure is applied to represent the tissue-bone structure which could be widely seen in a deboning process. In the simulation, the cutting force is monitored during the blade cuts through the interface. The dynamic change of the force pattern when the blade approaches the interface is analyzed in order to propose a control algorithm that prevents the blade cutting into bones. In order to provide realistic data for the simulation, several relaxation tests are designed to obtain the tensile relaxation modulus for biomaterials. Ligaments obtained from chicken wings and legs are used as specimens. The experimental data was theoretically fitted into a Burgers Model for the simulation and calculation. The model developed in this research can serve as a guideline for many applications such as the design of a surgical simulator to facilitate the training of new doctors and the intelligent control of a robot for deboning process to improve cutting yield and meat harvesting quality.Item Simulations and synthetic observations of active galactic nuclei jets in galaxy clusters: numerical tools and experiments.(2011-07) Mendygral, Peter JohnWe present the results and analysis of three-dimensional magnetohydrodynamic (MHD) simulations of jets from active galactic nuclei (AGN) in galaxy cluster environments. The purpose of these simulations was to investigate the interaction of AGN outflows with their environments and to understand the observational consequences that interaction produces. Synthetic X-ray observations of a set of simulations with AGN jets embedded in an analytically defined galaxy cluster were used to examine the reliability of common observational techniques. We explored the accuracy of measuring the enthalpy of X-ray cavities produced by AGN jets and found that observational techniques are accurate to within a factor of 2. We also tested observational methods for estimating the cavity age and mechanical power of AGN. Despite the simplified nature of the models these techniques are based on, estimates of cavity ages and jet powers were also accurate to within a factor of two. To expand our ability to produce more realistic simulations of AGN outflows we developed a new MHD code for numerical astrophysics called WOMBAT. This code was specifically designed and optimized for high performance and scaling on modern supercomputers. It has several additional physics modules for including optically thin radiative cooling, the effects of gravity and the transport and evolution of cosmic rays. We also present a new total energy conserving method for including the effects of gravity that was implemented into WOMBAT. We demonstrate that a non-conservative gravity scheme negatively impacts the accuracy and convergence of numerical Riemann solvers. Finally, we present WOMBAT simulations of AGN outflows in a galaxy cluster extracted from a cosmological simulation. We explore the effects of cluster "weather" on AGN jets and lobes. Although we chose a relatively relaxed cluster for these simulations, we find that bulk flows in the intra-cluster medium (ICM) were sufficient to significantly deflect the jets and lobes. We present synthetic X-ray observations that show highly asymmetric X-ray cavity structures. Synthetic radio images reveal similarities between "double-double" radio galaxies and our intermittent jets as well as morphologies similar to wide-angle tail galaxies. We show that variations in ram pressure in the ICM dominated both magnetic stresses and pressure variations on large scales. On smaller scales, however, magnetic stresses were dominant in localized regions around the jets and lobes. Through this work we find that observational methods used to estimate critical characteristics of AGN outflows, such as the energy released by the central engine, are reliable to within a factor of a few. We also found that AGN outflows can be significantly influenced ICM "weather". These findings reenforce the reliability of our understanding of these systems, and demonstrate how AGN outflows might be used to probe many of the properties of their environments.