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Comparison of equations for the EDTD solution in anisotropic and dispersive media

Description: The recursive-convolution solution for anisotropic and dispersive media was seen to yield accurate results for reflection from ferrite slabs up to a frequency limit set by the sampling interval. Depending on the application, the results shown might be considered usable up to about 300 GHz, which corresponds to about 13 cells per wavelength. Results at still higher frequencies might be usable when a time delay or frequency shift due to dispersion can be tolerated. Several different forms of the update equations were considered which can result from different approximations in reducing the continuous equations to discrete form.
Date: January 1, 1997
Creator: Burke, G.J. & Steich, D.J.
Partner: UNT Libraries Government Documents Department

An Investigation of Wavelet Bases for Grid-Based Multi-Scale Simulations Final Report

Description: The research summarized in this report is the result of a two-year effort that has focused on evaluating the viability of wavelet bases for the solution of partial differential equations. The primary objective for this work has been to establish a foundation for hierarchical/wavelet simulation methods based upon numerical performance, computational efficiency, and the ability to exploit the hierarchical adaptive nature of wavelets. This work has demonstrated that hierarchical bases can be effective for problems with a dominant elliptic character. However, the strict enforcement of orthogonality was found to be less desirable than weaker semi-orthogonality or bi-orthogonality for solving partial differential equations. This conclusion has led to the development of a multi-scale linear finite element based on a hierarchical change of basis. The reproducing kernel particle method has been found to yield extremely accurate phase characteristics for hyperbolic problems while providing a convenient framework for multi-scale analyses.
Date: November 1, 1998
Creator: Baty, R.S.; Burns, S.P.; Christon, M.A.; Roach, D.W.; Trucano, T.G.; Voth, T.E. et al.
Partner: UNT Libraries Government Documents Department

Mathematical and numerical studies of nonstandard difference equation models of differential equations. Final technical report, September 1995--September 1997

Description: The major thrust of this proposal was to continue our investigations of so-called non-standard finite-difference schemes as formulated by other authors. These schemes do not follow the standard rules used to model continuous differential equations by discrete difference equations. The two major aspects of this procedure consist of generalizing the definition of the discrete derivative and using a nonlocal model (on the computational grid or lattice) for nonlinear terms that may occur in the differential equations. Our aim was to investigate the construction of nonstandard finite-difference schemes for several classes of ordinary and partial differential equations. These equations are simple enough to be tractable, yet, have enough complexity to be both mathematically and scientifically interesting. It should be noted that all of these equations differential equations model some physical phenomena under an appropriate set of experimental conditions. The major goal of the project was to better understand the process of constructing finite-difference models for differential equations. In particular, it demonstrates the value of using nonstandard finite-difference procedures. A secondary goal was to construct and study a variety of analytical techniques that can be used to investigate the mathematical properties of the obtained difference equations. These mathematical procedures are of interest in their own right and should be a valuable contribution to the mathematics research literature in difference equations. All of the results obtained from the research done under this project have been published in the relevant research/technical journals or submitted for publication. Our expectation is that these results will lead to improved finite difference schemes for the numerical integration of both ordinary and partial differential equations. Section G of the Appendix gives a concise summary of the major results obtained under funding by the grant.
Date: December 12, 1997
Creator: Mickens, R.E.
Partner: UNT Libraries Government Documents Department

Saturated flow in a single fracture: Evaluation of the Reynolds equation in measured aperture fields

Description: Fracture transmissivity and detailed aperture fields are measured in analog fractures specially designed to evaluate the utility of the Reynolds equation. The authors employ a light transmission technique with well-defined accuracy ({approximately}1% error) to measure aperture fields at high spatial resolution ({approximately}0.015 cm). A Hele-Shaw cell is used to confirm the approach by demonstrating agreement between experimental transmissivity, simulated transmissivity on the measured aperture field, and the parallel plate law. In the two rough-walled analog fractures considered, the discrepancy between the experimental and numerical estimates of fracture transmissivity was sufficiently large ({approximately} 22--47%) to exclude numerical and experimental errors (< 2%)as a source. They conclude that the three-dimensional character of the flow field is important for fully describing fluid flow in the two rough-walled fractures considered, and that the approach of depth averaging inherent in the formulation of the Reynolds equation is inadequate. They also explore the effects of spatial resolution, aperture measurement technique, and alternative definitions for link transmissivities in the finite-difference formulation, including some that contain corrections for tortuosity perpendicular to the mean fracture plane and Stokes flow. Various formulations for link transmissivity are shown to converge at high resolution ({approximately} 1/5 the spatial correlation length) in the smoothly varying fracture. At coarser resolutions, the solution becomes increasingly sensitive to definition of link transmissivity and measurement technique. Aperture measurements that integrate over individual grid blocks were less sensitive to measurement scale and definition of link transmissivity than point sampling techniques.
Date: January 28, 2000
Partner: UNT Libraries Government Documents Department

Modeling the conversion of hydroacoustic to seismic energy at island and continental margins: preliminary analysis of Ascension Island data

Description: Seismic stations at islands and continental margins will be an essential component of the International Monitoring System (IMS) for event location and identification in support of Comprehensive Nuclear-Test-Ban Treaty (CTBT) monitoring. Particularly important will be the detection and analysis of hydroacoustic-to-seismic converted waves (T-phases) at island or continental margins. Acoustic waves generated by sources in or near the ocean propagate for long distances very efficiently due to the ocean sound speed channel (SOFAR) and low attenuation. When ocean propagating acoustic waves strike an island or continental margin they are converted to seismic (elastic) waves. We are using a finite difference code to model the conversion of hydroacoustic T-waves at an island or continental margin. Although ray-based methods are far more efficient for modeling long-range (> 1000 km) high-frequency hydroacoustic propagation, the finite difference method has the advantage of being able to model both acoustic and elastic wave propagation for a broad range of frequencies. The method allows us to perform simulations of T-phases to relatively high frequencies ({>=}10 Hz). Of particular interest is to identify factors that affect the efficiency of T-phase conversion, such as the topographic slope and roughness at the conversion point and elastic velocity structure within the island or continent. Previous studies have shown that efficient T-phase conversion occurs when the topographic slope at the conversion point is steep (Cansi and Bethoux, 1985; Talandier and Okal, 1998). Another factor impacting T-phase conversion may be the near-shore structure of the sound channel. It is well known that the depth to the sound channel axis decreases in shallow waters. This can weaken the channeled hydroacoustic wave. Elastic velocity structure within the island or continent will impact how the converted seismic wave is refracted to recording stations at the surface and thus impact the T-phase amplitudes. For this paper we ...
Date: July 26, 1999
Creator: Harben, P. & Rodgers, A.
Partner: UNT Libraries Government Documents Department

Fast Solutions of Maxwell's Equation for High Resolution Electromagnetic Imaging of Transport Pathways

Description: A fast precondition technique has been developed which accelerates the finite difference solutions of the 3D Maxwell's equations for geophysical modeling. The technique splits the electric field into its curl free and divergence free projections, and allows for the construction of an inverse operator. Test examples show an order of magnitude speed up compared with a simple Jacobi preconditioner. Using this preconditioner a low frequency Neumann series expansion is developed and used to compute responses at multiple frequencies very efficiently. Simulations requiring responses at multiple frequencies, show that the Neumann series is faster than the preconditioned solution, which must compute solutions at each discrete frequency. A Neumann series expansion has also been developed in the high frequency limit along with spectral Lanczos methods in both the high and low frequency cases for simulating multiple frequency responses with maximum efficiency. The research described in this report was to have been carried out over a two-year period. Because of communication difficulties, the project was funded for first year only. Thus the contents of this report are incomplete with respect to the original project objectives.
Date: October 1, 1999
Partner: UNT Libraries Government Documents Department

Finite difference micromagnetic simulation with self-consistent currents and smooth surfaces

Description: A micromagnetic algorithm has been developed using the finite difference method (FDM). Elliptic field equations are solved on the mesh using the efficient Dynamic Alternating Direction Implicit method. Smooth surfaces have been included in the FDM formulation so structures of irregular shape can be modeled. The current distribution and temperature of devices are also calculated. Keywords: Micromagnetic simulation, Magnetic dots, Read heads, Thermal Effects
Date: May 27, 1999
Creator: Cerjan, C.; Gibbons, M. R.; Hewett, D. W. & Parker, G.
Partner: UNT Libraries Government Documents Department

Hydrogen Isotope Exchange Tests in Support of HT-TCAP (U)

Description: Hydrogen isotope exchange kinetics of Pd/k was tested in laboratory scale columns to help troubleshoot the HT-TCAP performance problem. The main objective was to evaluate the effects of old and new Pd/k, column diameter, and metal foam on hydrogen isotope exchange efficiency. This efficiency affects the separation performance of the TCAP column. Three kinds of columns were used in the tests: (1) 3/4 inch pipe, 6 inch long, U-shape column. This column was used because it was readily available due to a completed PDRD project. This group of tests compared new Pd/k and old Pd/k, and produced a bake-out recipe for new Pd/k. (2) 3-ft long columns of various diameters: 3/4 inch, 1.25 inch and 2 inch with and without foam (aluminum and copper). This group of tests compared the effect of diameter, foam and Pd/k on staging performance. (3) The Jacobs coil, an existing 20-ft coil filled with Al foam identical to HT-TCAP. This group of tests was to see how a plant-type column performed. The following methods and computer programs were developed to help evaluate the test data: (1) An equation and a visual basic program for calculating response curves to step changes in inert feed concentration. (2) A finite difference method and a visual basic program for calculating response curves to step changes in hydrogen isotope concentration. (3) A finite difference method and a visual basic program for calculating response curves to pulse changes in hydrogen isotope concentration. The pulse response test and calculation were found most useful for comparing the isotope exchange performance of Pd/k packed columns. Increasing column diameter from 1.25 inch to 2 inch reduced the number of equilibrium stages by about 40 percent. Aluminum foam and copper foam did not reduce the number of stages. The new Pd/k required much more bake-out and ...
Date: July 15, 2004
Partner: UNT Libraries Government Documents Department

A finite-difference frequency-domain code for electromagnetic induction tomography

Description: We are developing a new 3D code for application to electromagnetic induction tomography and applications to environmental imaging problems. We have used the finite-difference frequency- domain formulation of Beilenhoff et al. (1992) and the anisotropic PML (perfectly matched layer) approach (Berenger, 1994) to specify boundary conditions following Wu et al. (1997). PML deals with the fact that the computations must be done in a finite domain even though the real problem is effectively of infinite extent. The resulting formulas for the forward solver reduce to a problem of the form Ax = y, where A is a non-Hermitian matrix with real values off the diagonal and complex values along its diagonal. The matrix A may be either symmetric or nonsymmetric depending on details of the boundary conditions chosen (i.e., the particular PML used in the application). The basic equation must be solved for the vector x (which represents field quantities such as electric and magnetic fields) with the vector y determined by the boundary conditions and transmitter location. Of the many forward solvers that could be used for this system, relatively few have been thoroughly tested for the type of matrix encountered in our problem. Our studies of the stability characteristics of the Bi-CG algorithm raised questions about its reliability and uniform accuracy for this application. We have found the stability characteristics of Bi-CGSTAB [an alternative developed by van der Vorst (1992) for such problems] to be entirely adequate for our application, whereas the standard Bi-CG was quite inadequate. We have also done extensive validation of our code using semianalytical results as well as other codes. The new code is written in Fortran and is designed to be easily parallelized, but we have not yet tested this feature of the code. An adjoint method is being developed for solving the ...
Date: December 17, 1998
Creator: Sharpe, R M; Berryman, J G; Buettner, H M; Champagne, N J.,II & Grant, J B
Partner: UNT Libraries Government Documents Department

A stable and convergent scheme for viscoelastic flow in contraction channels

Description: We present a new algorithm to simulate unsteady viscoelastic flows in abrupt contraction channels. In our approach we split the viscoelastic terms of the Oldroyd-B constitutive equation using Duhamel's formula and discretize the resulting PDEs using a semi-implicit finite difference method based on a Lax-Wendroff method for hyperbolic terms. In particular, we leave a small residual elastic term in the viscous limit by design to make the hyperbolic piece well-posed. A projection method is used to impose the incompressibility constraint. We are able to compute the full range of elastic flows in an abrupt contraction channel--from the viscous limit to the elastic limit--in a stable and convergent manner for elastic Mach numbers less than one. We demonstrate the method for unsteady Oldroyd-B and Maxwell fluids in planar contraction channels.
Date: February 15, 2004
Creator: Trebotich, David; Colella, Phillip & Miller, Gregory
Partner: UNT Libraries Government Documents Department

Numerical anomalies mimicking physical effects

Description: Numerical simulations of flows with shock waves typically use finite-difference shock-capturing algorithms. These algorithms give a shock a numerical width in order to generate the entropy increase that must occur across a shock wave. For algorithms in conservation form, steady-state shock waves are insensitive to the numerical dissipation because of the Hugoniot jump conditions. However, localized numerical errors occur when shock waves interact. Examples are the ``excess wall heating`` in the Noh problem (shock reflected from rigid wall), errors when a shock impacts a material interface or an abrupt change in mesh spacing, and the start-up error from initializing a shock as a discontinuity. This class of anomalies can be explained by the entropy generation that occurs in the transient flow when a shock profile is formed or changed. The entropy error is localized spatially but under mesh refinement does not decrease in magnitude. Similar effects have been observed in shock tube experiments with partly dispersed shock waves. In this case, the shock has a physical width due to a relaxation process. An entropy anomaly from a transient shock interaction is inherent in the structure of the conservation equations for fluid flow. The anomaly can be expected to occur whenever heat conduction can be neglected and a shock wave has a non-zero width, whether the width is physical or numerical. Thus, the numerical anomaly from an artificial shock width mimics a real physical effect.
Date: September 1, 1995
Creator: Menikoff, R.
Partner: UNT Libraries Government Documents Department

A reduced grid model for shallow flows on the sphere

Description: The authors describe a numerical model for simulating shallow water flows on a rotating sphere. The model is augmented by a reduced grid capability that increases the allowable time step based on stability requirements, and leads to significant improvements in computational efficiency. The model is based on finite difference techniques, and in particular on the nonoscillatory forward-in-time advection scheme MPDATA. They have implemented the model on the massively parallel CM-5, and have used it to simulate shallow water flows representative of global atmospheric motions. Here they present simulations of two flows, the Rossby-Haurwitz wave of period four, a nearly steady pattern with a complex balance of large and small scale motions, and also a zonal flow perturbed by an obstacle. They compare the accuracy and efficiency of using the reduced grid option with that of the original model. The authors also present simulations at several levels of resolution to show how the efficiency of the model scales with problem size.
Date: September 1, 1995
Creator: Reisner, J.M.; Margolin, L.G. & Smolarkiewicz, P.K.
Partner: UNT Libraries Government Documents Department

AMESH A mesh creating program for the integral finite differencemethod: A User's Manual

Description: Amesh program generates discrete grids for numerical modeling of flow and transport problems in which the formulation is based on integral finite difference method (IFDM). For example, the output of Amesh can be used directly as (part of) the input to TOUGH2 or TOUGH numerical Simulator (Pruess, 1987, 1990, Pruess, et al., 1996). The code Amesh can generate 1D, 2D or 3D numerical grids for a given set of locations, i.e. the centers of each discrete sub-domain. In the 2D aerial plane the Voronoi tessellation method is used (Voronoi, 1908; Ahuja, 1982; Aurehammer, 1991; Fortune, 1987, 1988, 1993). In this method we can create a mesh of elements, within model domain, where the interfaces between neighbor elements are the perpendicular bisectors of the line connecting the element centers. The interface distances are simply the medians of the line connecting the centers. To create the 3D grid, the vertical direction interface areas are always treated as horizontal projections of the 2D areal plane. In the lateral direction the interface areas are always vertical projections. In both cases the direction of gravity vector is given by the cosine of angle formed by the line joining the element centers and the vertical. From the list of element locations (center points), the program determines element volumes, and the connection information, i.e. areas, connection distances and the angle. The default input file is ''in''. The output files are ''eleme'' are ''conne'' and ''segmt''. The files ''eleme'' and ''come'' contain all the data required to describe a TOUGH2 input and together they describe the input TOUGH2 input file called ''MESH'', for the specified domain. The file ''segmt'' can be used to plot the geometrical shape of each element in each layer of the input domain. The input data into Amesh does not have to be ordered. ...
Date: August 31, 1998
Creator: Haukwa, Charles
Partner: UNT Libraries Government Documents Department

New advances in three-dimensional controlled-sourceelectromagnetic inversion

Description: New techniques for improving both the computational andimaging performance of the three dimensional (3D) electromagnetic inverseproblem are presented. A non-linear conjugate gradient algorithm is theframework of the inversion scheme. Full wave equation modelling forcontrolled sources is utilized for data simulation along with anefficient gradient computation approach for the model update. Improvingthe modelling efficiency of the 3D finite difference method involves theseparation of the potentially large modelling mesh, defining the set ofmodel parameters, from the computational finite difference meshes usedfor field simulation. Grid spacings and thus overall grid sizes can bereduced and optimized according to source frequencies and source-receiveroffsets of a given input data set. Further computational efficiency isobtained by combining different levels of parallelization. While theparallel scheme allows for an arbitrarily large number of parallel tasks,the relative amount of message passing is kept constant. Imageenhancement is achieved by model parameter transformation functions,which enforce bounded conductivity parameters and thus prevent parameterovershoots. Further, a remedy for treating distorted data within theinversion process is presented. Data distortions simulated here includepositioning errors and a highly conductive overburden, hiding the desiredtarget signal. The methods are demonstrated using both synthetic andfield data.
Date: May 19, 2007
Creator: Commer, Michael & Newman, Gregory A.
Partner: UNT Libraries Government Documents Department

FDTD simulation tools for UWB antenna analysis.

Description: This paper describes the development of a set of software tools useful for analyzing ultra-wideband (UWB) antennas and structures. These tools are used to perform finite difference time domain (FDTD) simulation of a conical antenna with continuous wave (CW) and UWB pulsed excitations. The antenna is analyzed using spherical coordinate-based FDTD equations that are derived from first principles. The simulation results for CW excitation are compared to simulation and measured results from published sources; the results for UWB excitation are new.
Date: December 1, 2004
Creator: Brocato, Robert Wesley
Partner: UNT Libraries Government Documents Department

DCPT: A dual-continua random walk particle tracker fortransport

Description: Accurate and efficient simulation of chemical transport processes in the unsaturated zone of Yucca Mountain is important to evaluate the performance of the potential repository. The scale of the unsaturated zone model domain for Yucca Mountain (50 km{sup 2} area with a 600 meter depth to the water table) requires a large gridblock approach to efficiently analyze complex flow & transport processes. The conventional schemes based on finite element or finite difference methods perform well for dispersion-dominated transport, but are subject to considerable numerical dilution/dispersion for advection-dominated transport, especially when a large gridblock size is used. Numerical dispersion is an artificial, grid-dependent chemical spreading, especially for otherwise steep concentration fronts. One effective scheme to deal with numerical dispersion is the random walk particle method (RWPM). While significant progress has been made in developing RWPM algorithms and codes for single continuum systems, a random walk particle tracker, which can handle chemical transport in dual-continua (fractured porous media) associated with irregular grid systems, is still absent (to our knowledge) in the public domain. This is largely due to the lacking of rigorous schemes to deal with particle transfer between the continua, and efficient schemes to track particles in irregular grid systems. The main objectives of this study are (1) to develop approaches to extend RWPM from a single continuum to a dual-continua system; (2) to develop an efficient algorithm for tracking particles in 3D irregular grids; and (3) to integrate these approaches into an efficient and user-friendly software, DCPT, for simulating chemical transport in fractured porous media.
Date: April 11, 2000
Creator: Pan, L.; Liu, H.H.; Cushey, M. & Bodvarsson, G.S.
Partner: UNT Libraries Government Documents Department

Mimetic finite difference method for the stokes problem on polygonal meshes

Description: Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.
Date: January 1, 2009
Creator: Lipnikov, K; Beirao Da Veiga, L; Gyrya, V & Manzini, G
Partner: UNT Libraries Government Documents Department

An algorithm for ``rezoning`` particle-in-cell calculations

Description: To give particle-in-cell methods (PIC) the same flexibility as finite-difference methods, one must be able to add and delete particles as needed. This flexibility is needed to model flows with large variations in density, to use variable grid spacing to resolve multiple length scale structures, and to use PIC in cylindrical geometry. The PIC method is applied to both kinetic and fluid problems. In kinetic calculations, the information and the interest lies in the distribution in velocity. In fluid calculations, moments of the velocity distribution, e.g., mass, momentum, and energy, are conserved. Thus, different kinds of information must be preserved in fluid and kinetic calculations when particles are added and deleted. We describe two algorithms for controlling the number of particles in PIC calculations, one for kinetic md one for fluid calculations. These algorithms, which we call ``particle rezoners ,`` are designed to preserve essential information in each case and to be simple and inexpensive to apply.
Date: August 1, 1994
Creator: Lapenta, G. & Brackbill, J. U.
Partner: UNT Libraries Government Documents Department