Browsing by Subject "multiscale modeling"
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Item Computational upscaled modeling of heterogeneous porous media flow utilizing finite volume method(Texas A&M University, 2005-08-29) Ginting, Victor EralinggaIn this dissertation we develop and analyze numerical method to solve general elliptic boundary value problems with many scales. The numerical method presented is intended to capture the small scales effect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map. The multiscale method is more effective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a finite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coefficients. For linear coefficients, the multiscale finite volume element method is viewed as a perturbation of multiscale finite element method. The analysis uses substantially the existing finite element results and techniques. The multiscale method for nonlinear coefficients will be analyzed in the finite element sense. A class of correctors corresponding to the multiscale method will be discussed. In turn, the analysis will rely on approximation properties of this correctors. Several numerical experiments verifying the theoretical results will be given. Finally we will present several applications of the multiscale method in the flow in porous media. Problems that we will consider are multiphase immiscible flow, multicomponent miscible flow, and soil infiltration in saturated/unsaturated flow.Item Modeling Frameworks for Representing the Mechanical Behavior of Tissues with a Specific Look at Vasculature(2013-08-27) Andersohn, AlexanderMany mechanicstic models aimed at predicting tissue behavior attempt to connect constitutive factors (such as effects due to collagen or fibrin concentrations) with the overall tissue behavior. Such a link between constitutive and material behaviors would allow for a better understanding of the mechanobiology of diseased states and how one might return the tissue to a healthy state. Therefore, a literature search into present mechanistic models was performed and yielded a variety of models that were analyzed in order to determine their uniqueness, a requisite characteristic for this aim. It was found that many of these models did not make uniqueness a defining characteristic in their development and thus cannot be used for multiscale modeling (connecting constitutive behavior to material behavior).The literature search was then extended and narrowed to specifically analyze mechanical models describing vascular wall behavior. Once again, it was found that uniqueness was lacking in these models. To develop a unique model for inflation strains, an inflation experiment utilizing a bladder, syringe, and a pressure sensor was conducted to provide pressure vs. volume data for a sheep aorta. The data was then used to develop a unique model for inflation strains in an aorta utilizing a constitutive framework developed by Dr. John Criscione.