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Second-order method for interface reconstruction in orthogonal coordinate systems

Description: We present a method in two-dimensions for reconstructing an interface from a distribution of volume fractions in a general orthogonal coordinate system. The method, in a cell by cell fashion, approximates the interface curve by a linear pro le. The approach requires only local volume fraction information for the reconstruction. An integral formulation is used that accounts for the orthogonal coordinate system in a natural way. We use nit different to approximate the slop of the required interface while retaining at worst second order accuracy for general interface orientations and an exact representation for coordinate system aligned o
Date: December 23, 1998
Creator: Colella, P.; Graves, D. T. & Greenough, J. G.
Partner: UNT Libraries Government Documents Department

A balancing domain decomposition method by constraints for advection-diffusion problems

Description: The balancing domain decomposition methods by constraints are extended to solving nonsymmetric, positive definite linear systems resulting from the finite element discretization of advection-diffusion equations. A pre-conditioned GMRES iteration is used to solve a Schur complement system of equations for the subdomain interface variables. In the preconditioning step of each iteration, a partially sub-assembled finite element problem is solved. A convergence rate estimate for the GMRES iteration is established, under the condition that the diameters of subdomains are small enough. It is independent of the number of subdomains and grows only slowly with the subdomain problem size. Numerical experiments for several two-dimensional advection-diffusion problems illustrate the fast convergence of the proposed algorithm.
Date: December 10, 2008
Creator: Tu, Xuemin & Li, Jing
Partner: UNT Libraries Government Documents Department

Multidimensional first and second order symmetric strang splitting for hyperbolic systems

Description: We propose an algebraic basis for symmetric Strang splitting for first and second order accurate schemes for hyperbolic systems in N dimensions. Examples are given for two and three dimensions. Optimal stability is shown for symmetric systems. Lack of strong stability is shown for a non-symmetric example. Some numerical examples are presented for some Euler-like constant coefficient problems.
Date: January 1, 2008
Creator: Kucharik, Milan & Wendroff, Burton
Partner: UNT Libraries Government Documents Department

Vector potential remap for 2d MHD

Description: This report describes an algorithm to remap (rezone) the magnetic vector potential in 2D MHD calculations. This extends a previously described Lagrangian scheme [1] for use with ALE grids, when combined with a suitable remap capability for the hydrodynamic variables. In this scheme, the magnetic field <b>B</b> is a zone quantity derived from the node based vector potential <b>A</b> (<i>B</i><sub>x</sub>, <i>B</i><sub>y</sub>, and <i>A</i><sub>z</sub> in Cartesian geometry, (<i>B</i><sub>z</sub>, <i>B</i><sub>r</sub>, and <i>A</i><sub>(small phi)</sub> in cylindrical geometry). The scheme outlined here is closely related to a flux conserving remap of the magnetic field. Because <b>B</b> is derived from the updated vector potential, however, flux conservation and vanishing divergence are guaranteed; only accuracy is a concern. This is in contrast to schemes based directly on <b>B</b>, which require the additional constraint of preserving zero divergence [2, 3]. Beginning with Cartesian geometry, a straight forward development of the algorithm is first presented; an alternative view is then considered which makes clear the relationship to a flux conservative remapping of the zonal magnetic field. Examples comparing first and second order algorithms are shown, and the issue of energy conservation is discussed. Finally, the generalization to cylindrical geometry is given.
Date: October 13, 1998
Creator: Rambo, P W
Partner: UNT Libraries Government Documents Department

Two-dimensional modeling of magnetically imploded liners

Description: Magnetically imploded massive cylindrical liner drivers have been studied in two-dimensions for low, intermediate and high energy pulsed power systems. The simulations have been carried out using a resistive Eulerian magnetohydrodynamics computational model which includes material strength, and models the interactions between the imploding liner and the electrode walls. The computations simulate the generation of perturbations and their subsequent growth during the implosion. At low energies a solid liner remains in the plastic regime, reaching an inner cylindrical target with velocities of a few mm per {mu}s. At higher energies (where one-dimensional models predict implosion velocities of order 1 cm/{mu}s or more) resistive heating of the liner results in melting, and the effects of magnetically driven instabilities become important. We discuss the two-dimensional issues which arise in these systems. These include: the onset of perturbations associated with the motion of the liner along the electrodes; the growth of instabilities in liquid layers; and the suppression of instability growth during the implosion by maintaining a solid inner layer. Studies have been made of liners designed for the Pegasus capacitor bank facility (currents in the 5 - 12 MA regime), and for the Procyon high explosive system (currents in the 20 MA regime). This work focus on the design and performance of the first Pegasus composite megabar liner experiment.
Date: November 1, 1996
Creator: Atchison, W.L.; Bowers, R.L.; Brownell, J.H. & Lee, H.
Partner: UNT Libraries Government Documents Department

Fields and First Order Perturbation Effects in Two-DimensionalConductor Dominated Magnets

Description: General expressions are given for the field and its expansion coefficients produced by a two dimensional conductor structure surrounded by iron with a circular inside boundary. Saturation effects are described in terms of the tangential field at that boundary. The effects of the following types of perturbations are discussed: displacement, rotation and error excitation of a conductor, change of conductor shape, and modification of the inside contour of the iron. A design criterion is given to minimize the error fields associated with a displacement of the iron shell relative to the conductor structure. Expressions for the force and torque acting on a conductor are derived both for the unperturbed and perturbed magnet. Formulae are presented that allow convenient and fast evaluation of pertinent quantities with a computer when the structure is too complicated for hand computations.
Date: July 1, 1969
Creator: Halbach, K.
Partner: UNT Libraries Government Documents Department

Exact de Rham Sequences of Spaces Defined on Macro-elements in Two and Three Spatial Dimensions

Description: This paper proposes new finite element spaces that can be constructed for agglomerates of standard elements that have certain regular structure. The main requirement is that the agglomerates share faces that have closed boundaries composed of 1-d edges. The spaces resulting from the agglomerated elements are subspaces of the original de Rham sequence of H{sup 1}-conforming, H(curl) conforming, H(div) conforming and piecewise constant spaces associated with an unstructured 'fine' mesh. The procedure can be recursively applied so that a sequence of nested de Rham complexes can be constructed. As an illustration we generate coarser spaces from the sequence corresponding to the lowest order Nedelec spaces, lowest order Raviart-Thomas spaces, and for piecewise linear H{sup 1}-conforming spaces, all in three-dimensions. The resulting V-cycle multigrid methods used in preconditioned conjugate gradient iterations appear to perform similar to those of the geometrically refined case.
Date: July 23, 2007
Creator: Pasciak, J. & Vassilevski, P.
Partner: UNT Libraries Government Documents Department

Telluric and D.C. Resistivity Techniques Applied to the Geophysical Investigation of Basin and Range Geothermal Systems, Part II: A Numberical Model Study of the Dipole-Dipole and Schlumberger Resistivity Methods

Description: This paper is a two-dimensional numerical model study and comparison of the polar dipole-dipole and Schlumberger resistivity arrays. A catalog of dipole-dipole and Schlumberger apparent resistivity pseudo-sections is presented. It is concluded that: for the Schlumberger array, data can be accurately interpreted only if the resistivity structure is horizontally layered, and conductive bodies having a depth of burial greater than their width are not observed; for the dipole-dipole array, complex anomaly patterns unrelated in appearance to the causative structure result from simple models, hence, a familiarity with model results is essential to interpretation of these data.
Date: June 1, 1977
Creator: Beyer, J.H.
Partner: UNT Libraries Government Documents Department

2D Numerical Simulation of the Resistive Reconnection Layer

Description: In this paper we present a two-dimensional numerical simulation of a reconnection current layer in incompressible resistive magnetohydrodynamics with uniform resistivity in the limit of very large Lundquist numbers. We use realistic boundary conditions derived consistently from the outside magnetic field, and we also take into account the effect of the back pressure from flow into the separatrix region. We find that within a few Alfvén times the system reaches a steady state consistent with the Sweet-Parker model, even if the initial state is Petschek-like.
Date: March 1, 1999
Creator: Kulsrud, R. M. & Uzdensky, D. A.
Partner: UNT Libraries Government Documents Department

Maganom Software User's Guide

Description: Maganom is a computer program for modeling magnetic data over 2-D structures. The program computes the magnetic anomalies across 2-D structures (models) to allow you to compare observed and computed magnetic data across the model structure. If a match between the computed and the observed magnetic values is unsatisfactory, you construct a new model and rerun Maganom to recalculate new magnetic values. In this way, you can continue calculations until you obtain a satisfactory match between the observed and the calculated values.
Date: March 11, 1999
Creator: Sharma, B.
Partner: UNT Libraries Government Documents Department

Field simulation of axisymmetric plasma screw pinches by alternating-direction-implicit methods

Description: An axisymmetric plasma screw pinch is an axisymmetric column of ionized gaseous plasma radially confined by forces from axial and azimuthal currents driven in the plasma and its surroundings. This dissertation is a contribution to detailed, high resolution computer simulation of dynamic plasma screw pinches in 2-d {ital rz}-coordinates. The simulation algorithm combines electron fluid and particle-in-cell (PIC) ion models to represent the plasma in a hybrid fashion. The plasma is assumed to be quasineutral; along with the Darwin approximation to the Maxwell equations, this implies application of Ampere`s law without displacement current. Electron inertia is assumed negligible so that advective terms in the electron momentum equation are ignored. Electrons and ions have separate scalar temperatures, and a scalar plasma electrical resistivity is assumed. Altemating-direction-implicit (ADI) methods are used to advance the electron fluid drift velocity and the magnetic fields in the simulation. The ADI methods allow time steps larger than allowed by explicit methods. Spatial regions where vacuum field equations have validity are determined by a cutoff density that invokes the quasineutral vacuum Maxwell equations (Darwin approximation). In this dissertation, the algorithm was first checked against ideal MM stability theory, and agreement was nicely demonstrated. However, such agreement is not a new contribution to the research field. Contributions to the research field include new treatments of the fields in vacuum regions of the pinch simulation. The new treatments predict a level of magnetohydrodynamic turbulence near the bulk plasma surface that is higher than predicted by other methods.
Date: June 1, 1996
Creator: Lambert, M.A.
Partner: UNT Libraries Government Documents Department

An Investigation of Cross-Borehole Ground Penetrating Radar Measurements for Characterizing the 2D Moisture Content Distribution in the Vadose Zone

Description: The use of cross-borehole ground penetrating radar (GPR) imaging for determining g the two dimensional (2D) in situ moisture content distribution within the vadose zone is being investigated. The ultimate goal is to use the GPR images as input to a 2D hydrologic inversion scheme for recovering the van Genuchten parameters governing unsaturated ,hydraulic flow. Initial experiments conducted on synthetic data have shown that at least in theory, cross-borehole GPR measurements can provide realistic estimates of the spatial variation in moisture content that are needed for this type of hydrologic inversion scheme. However, the method can not recover exact values of moisture content due to the break down of the empirical expression often employed to convert GPR velocity images to moisture content, and to the smearing nature of the imaging algorithm. To test the applicability of this method in a real world environment cross- borehole GPR measurements were made at a hydrologic/geophysical vadose zone test site in Socorro, New Mexico. Results show that the GPR images compare well with the uncalibrated borehole neutron log data. GPR data acquisition will continue once an infiltration test has started, and the results from these measurements will be employed in a 2D hydrologic inverse scheme.
Date: January 25, 1999
Creator: Alumbaugh, D. & Paprocki, L.
Partner: UNT Libraries Government Documents Department

Anisotropic multi-resolution analysis in 2D, application to long-range correlations in cloud mm-radar fields

Description: Because of Earth`s gravitational field, its atmosphere is strongly anisotropic with respect to the vertical; the effect of the Earth`s rotation on synoptic wind patterns also causes a more subtle form of anisotropy in the horizontal plane. The authors survey various approaches to statistically robust anisotropy from a wavelet perspective and present a new one adapted to strongly non-isotropic fields that are sampled on a rectangular grid with a large aspect ratio. This novel technique uses an anisotropic version of Multi-Resolution Analysis (MRA) in image analysis; the authors form a tensor product of the standard dyadic Haar basis, where the dividing ratio is {lambda}{sub z} = 2, and a nonstandard triadic counterpart, where the dividing ratio is {lambda}{sub x} = 3. The natural support of the field is therefore 2{sup n} pixels (vertically) by 3{sup n} pixels (horizontally) where n is the number of levels in the MRA. The natural triadic basis includes the French top-hat wavelet which resonates with bumps in the field whereas the Haar wavelet responds to ramps or steps. The complete 2D basis has one scaling function and five wavelets. The resulting anisotropic MRA is designed for application to the liquid water content (LWC) field in boundary-layer clouds, as the prevailing wind advects them by a vertically pointing mm-radar system. Spatial correlations are notoriously long-range in cloud structure and the authors use the wavelet coefficients from the new MRA to characterize these correlations in a multifractal analysis scheme. In the present study, the MRA is used (in synthesis mode) to generate fields that mimic cloud structure quite realistically although only a few parameters are used to control the randomness of the LWC`s wavelet coefficients.
Date: March 1, 1999
Creator: Davis, A.B. & Clothiaux, E.
Partner: UNT Libraries Government Documents Department

Dispersive water waves in one and two dimensions

Description: This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). We derived and analyzed new shallow water equations for one-dimensional flows near the critical Froude number as well as related integrable systems of evolutionary nonlinear partial differential equations in one spatial dimension, while developing new directions for the mathematics underlying the integrability of these systems. In particular, we applied the spectrum generating equation method to create and study new integrable systems of nonlinear partial differential equations related to our integrable shallow water equations. We also investigated the solutions of these systems of equations on a periodic spatial domain by using methods from the complex algebraic geometry of Riemann surfaces. We developed certain aspects of the required mathematical tools in the course of this investigation, such as inverse scattering with degenerate potentials, asymptotic reduction of the angle representations, geometric singular perturbation theory, modulation theory and singularity tracking for completely integrable equations. We also studied equations that admit weak solutions, i.e., solutions with discontinuous derivatives in the form of comers or cusps, even though they are solutions of integrable models, a property that is often incorrectly assumed to imply smooth solution behavior. In related work, we derived new shallow water equations in two dimensions for an incompressible fluid with a free surface that is moving under the force of gravity. These equations provide an estimate of the long-time asymptotic effects of slowly varying bottom topography and weak hydrostatic imbalance on the vertically averaged horizontal velocity, and they describe the flow regime in which the Froude number is small -- much smaller even than the small aspect ratio of the shallow domain.
Date: August 1, 1997
Creator: Holm, D.D. & Camassa, R.A.
Partner: UNT Libraries Government Documents Department

Beam charge and current neutralization of high-charge-state heavy ions

Description: High-charge-state heavy-ions may reduce the accelerator voltage and cost of heavy-ion inertial fusion drivers, if ways can be found to neutralize the space charge of the highly charged beam ions as they are focused to a target in a fusion chamber. Using 2-D Particle-In- Cell simulations, we have evaluated the effectiveness of two different methods of beam neutralization: (1) by redistribution of beam charge in a larger diameter, preformed plasma in the chamber, and (2), by introducing a cold-electron-emitting source within the beam channel at the beam entrance into the chamber. We find the latter method to be much more effective for high-charge-state ions.
Date: October 29, 1997
Creator: Logan, B.G. & Callahan, D.A.
Partner: UNT Libraries Government Documents Department

Two dimensional simulation of high power laser-surface interaction

Description: For laser intensities in the range of 10{sup 8}--10{sup 9} W/cm{sup 2}, and pulse lengths of order 10 {micro}sec or longer, the authors have modified the inertial confinement fusion code Lasnex to simulate gaseous and some dense material aspects of the laser-matter interaction. The unique aspect of their treatment consists of an ablation model which defines a dense material-vapor interface and then calculates the mass flow across this interface. The model treats the dense material as a rigid two-dimensional mass and heat reservoir suppressing all hydrodynamic motion in the dense material. The computer simulations and additional post-processors provide predictions for measurements including impulse given to the target, pressures at the target interface, electron temperatures and densities in the vapor-plasma plume region, and emission of radiation from the target. The authors will present an analysis of some relatively well diagnosed experiments which have been useful in developing their modeling. The simulations match experimentally obtained target impulses, pressures at the target surface inside the laser spot, and radiation emission from the target to within about 20%. Hence their simulational technique appears to form a useful basis for further investigation of laser-surface interaction in this intensity, pulse-width range. This work is useful in many technical areas such as materials processing.
Date: August 1, 1998
Creator: Goldman, S.R.; Wilke, M.D.; Green, R.E.L.; Johnson, R.P. & Busch, G.E.
Partner: UNT Libraries Government Documents Department

Angular quadratures for improved transport computations

Description: This paper introduces new octant-range, composite-type Gauss and mid-point rule angular quadrature formulas for neutron and photon transport computations. A generalization to octant-range quadratures is also introduced in order to allow for discontinuities at material interfaces for two- and three-dimensional transport problems which can be modeled with 60-degree triangular or hexagonal mesh subdivisions in the x-y plane.
Date: July 22, 1999
Creator: Abu-Shumays, I.K.
Partner: UNT Libraries Government Documents Department

Application of 2-D Simulations to Z-Pinch Experiment Design and Analysis

Description: The successful 2-D simulations of z-pinch experiments (reproducing such features as the measured experimental current drive, radiation pulse shape, peak power and total radiated energy) can lead to a better understanding of the underlying physics in z-pinch implosions and to the opportunity to use such simulations in the analysis of experimental data and in the design of new experiments. Such use has been made with LANL simulations of experiments on the Sandia Saturn and Z accelerators. Applications have included ''vacuum'' and ''dynamic'' hohlraum experiments; variations in mass, radius and length; and ''nested'' array configurations. Notable examples include the explanation of the power/length results in reduced length pinches and the prediction of the current best power and pulsewidth nested array experiment. Examples of circumstances where the simulation results do not match the experiments will be given along with a discussion of opportunities for improved simulation results.
Date: October 19, 1998
Creator: Peterson, D.L.; Bowers, R.L.; Matuska, W.; Chandler, G.A.; Deeney, C.; Derzon, M.S. et al.
Partner: UNT Libraries Government Documents Department