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A Finite-Difference Numerical Method for Onsager's Pancake Approximation for Fluid Flow in a Gas Centrifuge

Description: Gas centrifuges exhibit very complex flows. Within the centrifuge there is a rarefied region, a transition region, and a region with an extreme density gradient. The flow moves at hypersonic speeds and shock waves are present. However, the flow is subsonic in the axisymmetric plane. The analysis may be simplified by treating the flow as a perturbation of wheel flow. Wheel flow implies that the fluid is moving as a solid body. With the very large pressure gradient, the majority of the fluid is l… more
Date: November 12, 2007
Creator: de Stadler, M & Chand, K
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
open access

Multidimensional Conservation Laws and Low Regularity Solutions

Description: This is the concluding report for the project, a continuation of research by Keyfitz and co-workers on multidimensional conservation laws, and applications of nonhyperbolic conservation laws in the two-fluid model for multiphase flow. The multidimensional research project was started with Suncica Canic, at the University of Houston and with Eun Heui Kim, now at California State University Long Beach. Two postdoctoral researchers, Katarina Jegdic and Allen Tesdall, also worked on this research. … more
Date: June 16, 2007
Creator: Keyfitz, Barbara Lee
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Parallel Computation of Three-Dimensional Flows using Overlapping Grids with Adaptive Mesh Refinement

Description: This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid wit… more
Date: November 15, 2007
Creator: Henshaw, W & Schwendeman, D
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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The analysis of a sparse grid stochastic collocation method for partial differential equations with high-dimensional random input data.

Description: This work describes the convergence analysis of a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This… more
Date: December 1, 2007
Creator: Webster, Clayton; Tempone, Raul (Florida State University, Tallahassee, FL) & Nobile, Fabio (Politecnico di Milano, Italy)
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Performance and scaling of locally-structured grid methods forpartial differential equations

Description: In this paper, we discuss some of the issues in obtaining high performance for block-structured adaptive mesh refinement software for partial differential equations. We show examples in which AMR scales to thousands of processors. We also discuss a number of metrics for performance and scalability that can provide a basis for understanding the advantages and disadvantages of this approach.
Date: July 19, 2007
Creator: Colella, Phillip; Bell, John; Keen, Noel; Ligocki, Terry; Lijewski, Michael & Van Straalen, Brian
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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Dimensional reduction as a tool for mesh refinement and trackingsingularities of PDEs

Description: We present a collection of algorithms which utilizedimensional reduction to perform mesh refinement and study possiblysingular solutions of time-dependent partial differential equations. Thealgorithms are inspired by constructions used in statistical mechanics toevaluate the properties of a system near a critical point. The firstalgorithm allows the accurate determination of the time of occurrence ofa possible singularity. The second algorithm is an adaptive meshrefinement scheme which can be u… more
Date: June 10, 2007
Creator: Stinis, Panagiotis
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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Efficient parallel simulation of CO2 geologic sequestration insaline aquifers

Description: An efficient parallel simulator for large-scale, long-termCO2 geologic sequestration in saline aquifers has been developed. Theparallel simulator is a three-dimensional, fully implicit model thatsolves large, sparse linear systems arising from discretization of thepartial differential equations for mass and energy balance in porous andfractured media. The simulator is based on the ECO2N module of the TOUGH2code and inherits all the process capabilities of the single-CPU TOUGH2code, including a … more
Date: January 1, 2007
Creator: Zhang, Keni; Doughty, Christine; Wu, Yu-Shu & Pruess, Karsten
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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Nonequilibrium Gyrokinetic Fluctuation Theory and Sampling Noise in Gyrokinetic Particle-in-cell Simulations

Description: The present state of the theory of fluctuations in gyrokinetic GK plasmas and especially its application to sampling noise in GK particle-in-cell PIC simulations is reviewed. Topics addressed include the Δf method, the fluctuation-dissipation theorem for both classical and GK many-body plasmas, the Klimontovich formalism, sampling noise in PIC simulations, statistical closure for partial differential equations, the theoretical foundations of spectral balance in the presence of arbitrary noise s… more
Date: October 9, 2007
Creator: Krommes, John A.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Low-frequency dilatational wave propagation through unsaturated porous media containing two immiscible fluids

Description: An analytical theory is presented for the low-frequency behavior of dilatational waves propagating through a homogeneous elastic porous medium containing two immiscible fluids. The theory is based on the Berryman-Thigpen-Chin (BTC) model, in which capillary pressure effects are neglected. We show that the BTC model equations in the frequency domain can be transformed, at sufficiently low frequencies, into a dissipative wave equation (telegraph equation) and a propagating wave equation in the ti… more
Date: February 1, 2007
Creator: Lo, W.-C.; Sposito, G. & Majer, E.
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
open access

A data storage model for novel partial differential equation descretizations.

Description: The purpose of this report is to define a standard interface for storing and retrieving novel, non-traditional partial differential equation (PDE) discretizations. Although it focuses specifically on finite elements where state is associated with edges and faces of volumetric elements rather than nodes and the elements themselves (as implemented in ALEGRA), the proposed interface should be general enough to accommodate most discretizations, including hp-adaptive finite elements and even mimetic… more
Date: April 1, 2007
Creator: Doyle, Wendy S.K.; Thompson, David C. & Pebay, Philippe Pierre
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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Solving partial differential equations on irregular domains with moving interfaces, with applications to superconformal electrodeposition in semiconductor manufacturing

Description: We present a numerical algorithm for solving partial differential equations on irregular domains with moving interfaces. Instead of the typical approach of solving in a larger rectangular domain, our approach performs most calculations only in the desired domain. To do so efficiently, we have developed a one-sided multigrid method to solve the corresponding large sparse linear systems. Our focus is on the simulation of the electrodeposition process in semiconductor manufacturing in both two and… more
Date: December 10, 2007
Creator: Sethian, J. A. & Shan, Y.
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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Terascale Optimal PDE Simulations (TOPS) Center

Description: Our work has focused on the development and analysis of domain decomposition algorithms for a variety of problems arising in continuum mechanics modeling. In particular, we have extended and analyzed FETI-DP and BDDC algorithms; these iterative solvers were first introduced and studied by Charbel Farhat and his collaborators, see [11, 45, 12], and by Clark Dohrmann of SANDIA, Albuquerque, see [43, 2, 1], respectively. These two closely related families of methods are of particular interest sinc… more
Date: July 9, 2007
Creator: Widlund, Olof B.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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