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in subjects: "Exact Solutions"

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Practical error estimates for Reynolds' lubrication approximation and its higher order corrections

Reynolds lubrication approximation is used extensively to study flows between moving machine parts, in narrow channels, and in thin films. The solution of Reynolds equation may be thought of as the zeroth order term in an expansion of the solution of the Stokes equations in powers of the aspect ratio {var_epsilon} of the domain. In this paper, we show how to compute the terms in this expansion to arbitrary order on a two-dimensional, x-periodic domain and derive rigorous, a-priori error bounds … more

Date: December 10, 2008

Creator: Wilkening, Jon

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Discretizing gravity in warped spacetime

We investigate the discretized version of the compact Randall-Sundrum model. By studying the mass eigenstates of the lattice theory, we demonstrate that for warped space, unlike for flat space, the strong coupling scale does not depend on the IR scale and lattice size. However, strong coupling does prevent us from taking the continuum limit of the lattice theory. Nonetheless, the lattice theory works in the manifestly holographic regime and successfully reproduces the most significant features … more

Date: July 11, 2005

Creator: Schwartz, Matthew; Randall, Lisa; Schwartz, Matthew D. & Thambyahpillai, Shiyamala

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

On prediction of wind-borne plumes with simple models of turbulenttransport

The dispersion of pollutants from the ground by turbulent winds is difficult to model in general. However, for flat homogeneous terrain and steady wind conditions, if the wind profile is modeled with a power-law dependence on height, the advection-dispersion equation has an exact solution. In this paper the analytical solution is compared to a numerical simulation of the coupled air-ground system for a leaking underground gas storage, with a power-law velocity profile that was fit to the logari… more

Date: June 21, 2006

Creator: Schwarz, Katherine; Patzek, Tad & Silin, Dmitriy

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Global paths of time-periodic solutions of the Benjamin-Ono equation connecting arbitrary traveling waves

We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accurate numerical continuation method to study several paths of non-trivial solutions beyond the realm of linear theory. These paths are found to either re-connect with a different traveling wave or to blow up. In the latter case, as the bifurcation parameter approaches a critical value, the amplitude of the initial condi… more

Date: December 11, 2008

Creator: Ambrose, David M. & Wilkening, Jon

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Chunking of Large Multidimensional Arrays

Data intensive scientific computations as well on-lineanalytical processing applications as are done on very large datasetsthat are modeled as k-dimensional arrays. The storage organization ofsuch arrays on disks is done by partitioning the large global array intofixed size hyper-rectangular sub-arrays called chunks or tiles that formthe units of data transfer between disk and memory. Typical queriesinvolve the retrieval of sub-arrays in a manner that accesses all chunksthat overlap the query r… more

Date: February 28, 2007

Creator: Rotem, Doron; Otoo, Ekow J. & Seshadri, Sridhar

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

On Sub-linear Convergence for Linearly Degenerate Waves in Capturing Schemes

A common attribute of capturing schemes used to find approximate solutions to the Euler equations is a sub-linear rate of convergence with respect to mesh resolution. Purely nonlinear jumps, such as shock waves produce a first-order convergence rate, but linearly degenerate discontinuous waves, where present, produce sub-linear convergence rates which eventually dominate the global rate of convergence. The classical explanation for this phenomenon investigates the behavior of the exact solution… more

Date: March 17, 2008

Creator: Banks, J W; Aslam, T & Rider, W J

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Parallel Computation of Three-Dimensional Flows using Overlapping Grids with Adaptive Mesh Refinement

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: Article

Partner: UNT Libraries Government Documents Department

open access

Post-processing V&V level II ASC milestone (2360) results.

The 9/30/2007 ASC Level 2 Post-Processing V&V Milestone (Milestone 2360) contains functionality required by the user community for certain verification and validation tasks. These capabilities include loading of edge and face data on an Exodus mesh, run-time computation of an exact solution to a verification problem, delivery of results data from the server to the client, computation of an integral-based error metric, simultaneous loading of simulation and test data, and comparison of that … more

Date: September 1, 2007

Creator: Chavez, Elmer; Karelitz, David B.; Brunner, Thomas A.; Trucano, Timothy Guy; Moreland, Kenneth D.; Weirs, V. Gregory et al.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Optimal Chunking of Large Multidimensional Arrays for Data Warehousing

Very large multidimensional arrays are commonly used in data intensive scientific computations as well as on-line analytical processingapplications referred to as MOLAP. The storage organization of such arrays on disks is done by partitioning the large global array into fixed size sub-arrays called chunks or tiles that form the units of data transfer between disk and memory. Typical queries involve the retrieval of sub-arrays in a manner that access all chunks that overlap the query results. An… more

Date: February 15, 2008

Creator: Otoo, Ekow J.; Otoo, Ekow J.; Rotem, Doron & Seshadri, Sridhar

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Assessing the RELAPS-3D Heat Conduction Enclosure Model

Three heat conduction problems that have exact solutions are modeled with RELAP5-3D using the conduction enclosure model. These comparisons are designed to be used in the RELAP5-3D development assessment scheduled to be completed in 2009. It is shown that with proper input choices and adequate model detail the exact solutions can be matched. In addition, this analysis identified an error and the required correction in the cylindrical and spherical heat conductor models in RELAP5-3D which will b… more

Date: September 30, 2008

Creator: McCann, Larry D.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Decomposition of Large Scale Semantic Graphsvia an Efficient Communities Algorithm

Semantic graphs have become key components in analyzing complex systems such as the Internet, or biological and social networks. These types of graphs generally consist of sparsely connected clusters or 'communities' whose nodes are more densely connected to each other than to other nodes in the graph. The identification of these communities is invaluable in facilitating the visualization, understanding, and analysis of large graphs by producing subgraphs of related data whose interrelationship… more

Date: February 8, 2008

Creator: Yao, Y

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Exact solution of the envelope equations for a matched quadrupole-focused beam in the low space-charged limit

The Kapchinskij-Vladimirskij equations are widely used to study the evolution of the beam envelopes in a periodic system of quadrupole focusing cells. In this paper, we analyze the case of a matched beam. Our model is analogous to that used by Courant and Snyder [E.D. Courant and H.S. Snyder, Ann. Phys. 3, 1 (1958)]in obtaining a first-order approximate solution for a synchrotron. Here, we treat a linear machine and obtain an exact solution. The model uses a full occupancy, piecewise-constant f… more

Date: September 23, 2008

Creator: Anderson, O. A. & LoDestro, L. L.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Exact solution of the envelope equations for a matchedquadrupole-focused beam in the zero space-charge limit

The Kapchinskij-Vladimirskij equations are widely used to study the evolution of the beam envelopes in a periodic system of quadrupole focusing cells. In this paper, we analyze the case of a matched beam. Our model is analogous to that used by Courant and Snyder [E.D. Courant and H.S. Snyder, Ann. Phys. 3, 1 (1958)] in obtaining a first-order approximate solution for a synchrotron. Here, we treat a linear machine and obtain an exact solution. The model uses a full occupancy, piecewise-constant … more

Date: November 7, 2008

Creator: Anderson, Oscar A. & LoDestro, L. L.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

An Exact Solution of Transport in Porous Media with Equilibrium and Kinetic Reactions

This paper presents an analytical solution of reactive transport with equilibrium and kinetic reactions. A benchmark model of A {leftrightarrow} B {leftrightarrow} C {yields} chain reactions is developed for the purpose of verifying numerical computer codes and qualifying mathematical models. A reaction matrix is derived for both the equilibrium and first-order kinetic reactions and further decoupled as a diagonal matrix. Therefore, the partial differential equations (PDEs) coupled by the react… more

Date: April 12, 2006

Creator: Lu, X. & Sun, Y.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Deciphering the genetic regulatory code using an inverse error control coding framework.

We have found that developing a computational framework for reconstructing error control codes for engineered data and ultimately for deciphering genetic regulatory coding sequences is a challenging and uncharted area that will require advances in computational technology for exact solutions. Although exact solutions are desired, computational approaches that yield plausible solutions would be considered sufficient as a proof of concept to the feasibility of reverse engineering error control co… more

Date: March 1, 2005

Creator: Rintoul, Mark Daniel; May, Elebeoba Eni; Brown, William Michael; Johnston, Anna Marie & Watson, Jean-Paul

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Exact solutions in a model of vertical gas migration

This work is motivated by the growing interest in injectingcarbon dioxide into deep geological formations as a means of avoidingatmospheric emissions of carbon dioxide and consequent global warming.One of the key questions regarding the feasibility of this technology isthe potential rate of leakage out of the primary storage formation. Weseek exact solutions in a model of gas flow driven by a combination ofbuoyancy, viscous and capillary forces. Different combinations of theseforces and charact… more

Date: June 27, 2006

Creator: Silin, Dmitriy B.; Patzek, Tad W. & Benson, Sally M.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

A Quantitative Comparison of Numerical Methods for the Compressible Euler Equations: Fifth-order WENO and Piecewise-Linear Godunov

A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler Equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube probl… more

Date: November 5, 2003

Creator: Greenough, J A & Rider, W J

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Low-frequency fluid waves in fractures and pipes

Low-frequency analytical solutions have been obtained for phase velocities of symmetrical fluid waves within both an infinite fracture and a pipe filled with a viscous fluid. Three different fluid wave regimes can exist in such objects, depending on the various combinations of parameters, such as fluid density, fluid viscosity, walls shear modulus, channel thickness, and frequency. Equations for velocities of all these regimes have explicit forms and are verified by comparisons with the exact s… more

Date: September 1, 2010

Creator: Korneev, Valeri

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Generalized Courant-Snyder Theory and Kapchinskij-Vladimirskij Distribution For High-intensity Beams In A Coupled Transverse Focusing Lattice

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in a uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are non-commutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear V… more

Date: July 18, 2011

Creator: QIn, Hong & Davidson, Ronald

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

A TWO-DIMENSIONAL METHOD OF MANUFACTURED SOLUTIONS BENCHMARK SUITE BASED ON VARIATIONS OF LARSEN'S BENCHMARK WITH ESCALATING ORDER OF SMOOTHNESS OF THE EXACT SOLUTION

The quantification of the discretization error associated with the spatial discretization of the Discrete Ordinate(DO) equations in multidimensional Cartesian geometries is the central problem in error estimation of spatial discretization schemes for transport theory as well as computer code verification. Traditionally fine mesh solutions are employed as reference, because analytical solutions only exist in the absence of scattering. This approach, however, is inadequate when the discretization… more

Date: May 1, 2011

Creator: Schunert, Sebastian & Azmy, Yousry Y.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

ALFVEN-WAVE OSCILLATIONS IN A SPHERE, WITH APPLICATIONS TO ELECTRON-HOLE DROPS IN Ge

The problem of Alfven-wave oscillations in an anisotropic sphere is studied, and two solutions are presented. One solution is exact, involving an expansion of the current inside the sphere in a series of orthonormal modes. The second is approximate, based on a perturbation expansion of the induced fields and currents in powers of the sphere radius. The approximate solution can be applied to a material having a completely general conductivity tensor, while the exact solution is restricted to sit… more

Date: January 1, 1978

Creator: Markiewicz, R. S.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

COMPARISON OF THE ACCURACY OF VARIOUS SPATIAL DISCRETIZATION SCHEMES OF THE DISCRETE ORDINATES EQUATIONS IN 2D CARTESIAN GEOMETRY

We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the d… more

Date: May 1, 2011

Creator: Schunert, Sebastian; Azmy, Yousry Y. & Fournier, Damien

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Exact Magnetic Diffusion Solutions for Magnetohydrodynamic Code Verification

In this paper, the authors present several new exact analytic space and time dependent solutions to the problem of magnetic diffusion in R-Z geometry. These problems serve to verify several different elements of an MHD implementation: magnetic diffusion, external circuit time integration, current and voltage energy sources, spatially dependent conductivities, and ohmic heating. The exact solutions are shown in comparison with 2D simulation results from the Ares code.

Date: December 3, 2010

Creator: Miller, D. S.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Development of a thermal equilibrium prediction algorithm.

A thermal equilibrium prediction algorithm is developed and tested using a heat conduction model and data sets from calorimetric measurements. The physical model used in this study is the exact solution of a system of two partial differential equations that govern the heat conduction in the calorimeter. A multi-parameter estimation technique is developed and implemented to estimate the effective volumetric heat generation and thermal diffusivity in the calorimeter measurement chamber, and the e… more

Date: January 1, 2001

Creator: Aviles-Ramos, C. (Cuauhtemoc)

Item Type: Article

Partner: UNT Libraries Government Documents Department