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1-D closure models for slender 3-D viscoelastic free jets: von Karman flow geometry and elliptical cross section

Description: In this paper we derive one space dimensional, reduced systems of equations (1-D closure models) for viscoelastic free jets. We begin with the three-dimensional system of conservation laws and a Maxwell-Jeffreys constitutive law for an incompressible viscoelastic fluid. First, we exhibit exact truncations to a finite, closed system of 1-D equations based on classical velocity assumptions of von Karman. Next, we demonstrate that the 3-D free surface boundary conditions overconstrain these truncated systems, so that only a very limited class of solutions exist. We then proceed to derive approximate 1-D closure theories through a slender jet asymptotic scaling, combined with appropriate definitions of velocity, pressure and stress unknowns. Our nonaxisymmetric 1-D slender jet models incorporate the physical effects of inertia, viscoelasticity (viscosity, relaxation and retardation), gravity, surface tension, and properties of the ambient fluid, and include shear stresses and time dependence. Previous special 1-D slender jet models correspond to the lowest order equations in the present asymptotic theory by an a posteriori suppression to leading order of some of these effects, and a reduction to axisymmetry. Solutions of the lowest order system of equations in this asymptotic analysis are presented: For the special cases of elliptical inviscid and Newtonian free jets, subject to the effects of surface tension and gravity, our model predicts oscillation of the major axis of the free surface elliptical cross section between perpendicular directions with distance down the jet, and drawdown of the cross section, in agreement with observed behavior. 15 refs.
Date: January 1, 1988
Creator: Bechtel, S. E.; Forest, M. G.; Holm, D. D. & Lin, K. J.
Partner: UNT Libraries Government Documents Department

2-D and 3-D computations of curved accelerator magnets

Description: In order to save computer memory, a long accelerator magnet may be computed by treating the long central region and the end regions separately. The dipole magnets for the injector synchrotron of the Advanced Photon Source (APS), now under construction at Argonne National Laboratory (ANL), employ magnet iron consisting of parallel laminations, stacked with a uniform radius of curvature of 33.379 m. Laplace's equation for the magnetic scalar potential has a different form for a straight magnet (x-y coordinates), a magnet with surfaces curved about a common center (r-{theta} coordinates), and a magnet with parallel laminations like the APS injector dipole. Yet pseudo 2-D computations for the three geometries give basically identical results, even for a much more strongly curved magnet. Hence 2-D (x-y) computations of the central region and 3-D computations of the end regions can be combined to determine the overall magnetic behavior of the magnets. 1 ref., 6 figs.
Date: January 1, 1991
Creator: Turner, L.R.
Partner: UNT Libraries Government Documents Department

2-D Axisymmetric Line Transport

Description: The methods used in the ALTAIR code for computing the transfer of spectral line radiation in two-dimensional axially-symmetric geometry are described. ALTAIR uses a variable-Eddington-tensor approach, in which the transfer equation of non-coherent line scattering is written in moment form, and the moments are closed with an assumed tensor relating the monochromatic pressure tensor and energy density; this Eddington tensor is obtained self-consistently using an accurate angle-dependent solution of the transfer equation. The finite element method for solving the moment system, and the discontinuous finite element method for solving the S{sub n} equation of transfer are described. Two applications of the method are discussed: line formation in uniform cylinders with different length-diameter ratios, and monochromatic transfer on an irregular x-y mesh (the Mordant test problem). 13 refs., 2 figs.
Date: November 20, 1990
Creator: Castor, John I.; Dykema, Pieter G & Klein, Richard I.
Partner: UNT Libraries Government Documents Department

2, Pulse-mode expansions and refractive indices in plane-wave propagation

Description: This memo presents basic background theory for treating simultaneous propagation of electromagnetic pulses of various colors, directed along a common ray, through a molecular vapor. The memo discusses some techniques for expanding the positive frequency part of the transverse electric field into pulse modes, characterized by carrier frequencies within a modulated envelope. We discuss, in the approximation of plane waves with slowly varying envelopes, a set of uncoupled envelope equations in which a polarization mode-envelope acts as a source for an electric-field envelope. These equations, when taken with a prescription for the polarization field, are the basic equations of plane-wave pulse propagation through a molecular medium. We discuss two ways of treating dispersive media, one based upon expansions in the frequency domain and the other based in the time domain. In both cases we find envelope equations that involve group velocities. This memo represents a portion of a more extensive treatment of propagation to be presented separately. Many of the equations presented here have been described in various books and articles. They are collected and described here as a summary and review of contemporary theory.
Date: June 20, 1987
Creator: Shore, B.W.; Sacks, R.; Karr, T.; Morris, J. & Paisner, J.A.
Partner: UNT Libraries Government Documents Department

3-D magnetic field calculations for wiggglers using MAGNUS-3D

Description: The recent but steady trend toward increased magnetic and geometric complexity in the design of wigglers and undulators, of which tapered wigglers, hybrid structures, laced electromagnetic wigglers, magnetic cladding, twisters and magic structures are examples, has caused a need for reliable 3-D computer models and a better understanding of the behavior of magnetic systems in three dimensions. The capabilities of the MAGNUS-3D Group of Programs are ideally suited to solve this class of problems and provide insight into 3-D effects. MAGNUS-3D can solve any problem of Magnetostatics involving permanent magnets, linear or nonlinear ferromagnetic materials and electric conductors of any shape in space. The magnetic properties of permanent magnets are described by the complete nonlinear demagnetization curve as provided by the manufacturer, or, at the user's choice, by a simpler approximation involving the coercive force, the residual induction and the direction of magnetization. The ferromagnetic materials are described by a magnetization table and an accurate interpolation relation. An internal library with properties of common industrial steels is available. The conductors are independent of the mesh and are described in terms of conductor elements from an internal library.
Date: January 1, 1988
Creator: Pissanetzky, S. & Tompkins, P.
Partner: UNT Libraries Government Documents Department

A 3-D model of superfluid helium suitable for numerical analysis

Description: The two-fluid description is a very successful phenomenological representation of the properties of Helium II. A 3-D model suitable for numerical analysis based on the Landau-Khalatnikov description of Helium II is proposed. In this paper we introduce a system of partial differential equations that is both complete and consistent as well as practical, to be used for a 3-D solution of the flow of Helium II. The development of a 3-D numerical model for Helium II is motivated by the need to validate experimental results obtained by observing the normal component velocity distribution in a Helium II thermal counter-flow using the Particle Image Velocimetry (PIV) technique.
Date: January 1, 2008
Creator: Darve, C.; U., /Fermilab /Northwestern; Patankar, N.A.; U., /Northwestern; Van Sciver, S.W. & Lab., /Natl. High Mag. Field
Partner: UNT Libraries Government Documents Department

3-D numerical analysis of a high-gain free-electron laser

Description: We present a novel approach to the 3-dimensional high-gain free- electron laser amplifier problem. The method allows us to write the laser field as an integral equation which can be efficiently and accurately evaluated on a small computer. The model is general enough to allow the inclusion of various initial electron beam distributions to study the gain reduction mechanism and its dependence on the physical parameters. 16 refs., 8 figs., 1 tab.
Date: October 19, 1988
Creator: Gallardo, J.C.
Partner: UNT Libraries Government Documents Department

3-D treatment of convective flow in the earth's mantle

Description: A three-dimensional finite-element method is used to investigate thermal convection in the earth's mantle. The equations of motion are solved implicitly by means of a fast multigrid technique. The computational mesh for the spherical problem is derived from the regular icosahedron. The calculation described use a mesh with 43,554 nodes and 81,920 elements and were run on a Cray X. The earth's mantle is modeled as a thick spherical shell with isothermal, free-slip boundaries. The infinite Prandtl number problem is formulated in terms of pressure, density, absolute temperature, and velocity and assumes an isotropic Newtonian rheology. Solutions are obtained for Rayleigh numbers up to approximately 10/sup 6/ for a variety of modes of heating. Cases initialized with a temperature distribution with warmer temperatures beneath speading ridges and cooler temperatures beneath present subduction zones yield whole-mantle convection solutions with surface velocities that correlate well with currently observed plate velocities. 8 references, 6 figures.
Date: May 1, 1984
Creator: Baumgardner, J.R.
Partner: UNT Libraries Government Documents Department

3 Dimensional radiation transport in dispersive media

Description: In plasmas the collective motion of free electrons affects the propagation of radiation by bending the light ray trajectory. The closer the light wave frequency is to the electron plasma frequency in value, the more pronounced the effect. We will present the results of radiation transport calculations in 3 spatial dimensions in the refractive plasma environment and compare the calculation to one done where the ray bending has been neglected (straight line ray paths). We also present the numerical method used for the refractive transport. 4 refs., 5 figs.
Date: November 1, 1990
Creator: Mayle, R.W.
Partner: UNT Libraries Government Documents Department

2D accelerator design for SITEX negative ion source

Description: Solving the Poisson-Vlasov equations where the magnetic field, B, is assumed constant, we optimize the optical system of a SITEX negative ion source in infinite slot geometry. Algorithms designed to solve the above equations were modified to include the curved emitter boundary data appropriate to a negative ion source. Other configurations relevant to negative ion sources are examined.
Date: January 1, 1983
Creator: Whealton, J.H.; Raridon, R.J.; McGaffey, R.W.; McCollough, D.H.; Stirling, W.L. & Dagenhart, W.K.
Partner: UNT Libraries Government Documents Department

2D full-wave modeling of ICRH with finite E/parallel/

Description: In this paper, the Oak Ridge ion cyclotron wave propagation code ORION has been extended to include nonzero E/parallel/ in both axisymmetric tokamak and helically symmetric stellarator geometries. Flux surfaces, conducting boundaries, and antennas can be of arbitrary shape, and antenna current is assumed to be divergence free (not a necessary assumption). Cartesian coordinates eliminate the singularity that occurs at the origin of cylindrical coordinate systems. In this paper we consider two alternative numerical approaches to this problem. One solves Maxwell's equations directly in terms of the electric field /rvec E/. The second approach introduces the electromagnetic potentials /rvec A/ and /phi/ with the Coulomb gauge /triangledown/ /center dot/ /rvec A/ = 0. 7 refs., 4 figs.
Date: January 1, 1988
Creator: Batchelor, D.B.; Jaeger, E.F. & Weitzner, H.
Partner: UNT Libraries Government Documents Department

3D electromagnetic modeling using staggered finite differences

Description: The method of finite differences has been employed to solve a variety of 3D electromagnetic (EM) forward problems arising in geophysical applications. Specific sources considered include dipolar and magnetotelluric (MT) field excitation in the frequency domain. In the forward problem, the EM fields are simulated using a vector Helmholtz equation for the electric field, which are approximated using finite differences on a staggered grid. To obtain the fields, a complex-symmetric matrix system of equations is assembled and iteratively solved using the quasi minimum method (QMR) method. Perfectly matched layer (PML) absorbing boundary conditions are included in the solution and are necessary to accurately simulate fields in propagation regime (frequencies > 10 MHZ). For frequencies approaching the static limit (< 10 KHz), the solution also includes a static-divergence correction, which is necessary to accurately simulate MT source fields and can be used to accelerate convergence for the dipolar source problem.
Date: June 1, 1997
Creator: Newman, G.A. & Alumbaugh, D.L.
Partner: UNT Libraries Government Documents Department

Ab initio methods for electron-molecule collisions

Description: This review concentrates on the recent advances in treating the electronic aspect of the electron-molecule interaction and leaves to other articles the description of the rotational and vibrational motions. Those methods which give the most complete treatment of the direct, exchange, and correlation effects are focused on. Such full treatments are generally necessary at energies below a few Rydbergs (approx. = 60 eV). This choice unfortunately necessitates omission of those active and vital areas devoted to the development of model potentials and approximate scattering formulations. The ab initio and model approaches complement each other and are both extremely important to the full explication of the electron-scattering process. Due to the rapid developments of recent years, the approaches that provide the fullest treatment are concentrated on. 81 refs.
Date: January 1, 1987
Creator: Collins, L.A. & Schneider, B.I.
Partner: UNT Libraries Government Documents Department

Ab initio quantum chemistry in parallel-portable tools and applications

Description: In common with many of the computational sciences, ab initio chemistry faces computational constraints to which a partial solution is offered by the prospect of highly parallel computers. Ab initio codes are large and complex (O(10{sup 5}) lines of FORTRAN), representing a significant investment of communal effort. The often conflicting requirements of portability and efficiency have been successfully resolved on vector computers by reliance on matrix oriented kernels. This proves inadequate even upon closely-coupled shared-memory parallel machines. We examine the algorithms employed during a typical sequence of calculations. Then we investigate how efficient portable parallel implementations may be derived, including the complex multi-reference singles and doubles configuration interaction algorithm. A portable toolkit, modeled after the Intel iPSC and the ANL-ACRF PARMACS, is developed, using shared memory and TCP/IP sockets. The toolkit is used as an initial platform for programs portable between LANS, Crays and true distributed-memory MIMD machines. Timings are presented. 53 refs., 4 tabs.
Date: January 1, 1991
Creator: Harrison, R.J.; Shepard, R. (Argonne National Lab., IL (United States)) & Kendall, R.A. (Battelle Pacific Northwest Lab., Richland, WA (United States))
Partner: UNT Libraries Government Documents Department

Ablation gas dynamics of low-Z materials illuminated by soft x-rays

Description: Though many of our results will have much greater generality, the main purpose of this paper is to provide a simple, accurate, physical theory of what happens when a Planckian spectrum of soft x-rays is incident on one side of the slab of initially cold, dense material, of small nuclear charge Z. Our approach will be to consider in some detail the idealized situation. A semi-infinite (x {le} 0) slab of initially cold (T < 300 K), dense ({rho} {approximately} 1 {minus} 10 g/cc), low-Z (Z < 5) material is suddenly subjected at time t = 0 and thereafter to radiation incoming from x = +{infinity} with a specific intensity in directions toward the slab that is Planckian, characterized by a black-body temperature, T{sub R} in the soft x-ray region.
Date: September 6, 1991
Creator: Hatchett, S.P.
Partner: UNT Libraries Government Documents Department

Acceleration to hypervelocities using minimum energy concepts

Description: Experiments have begun at Los Alamos to assess the potential of using spheromaks to transfer energy from large, slow moving metal walls to much smaller, faster moving less massive walls so as to achieve hypervelocities in the 20 to 60 km/s range. A large plate transfers energy to the spheromak during a slow compression. The spheromak then releases this energy in a much shorter time to the small plate, accelerating it to much higher velocity. It has been estimated that velocity gains in excess of 4 (V/sub final/ ..-->.. 20 km/s) can be achieved in a practical single stage experiment.
Date: June 1, 1987
Creator: Marklin, G.
Partner: UNT Libraries Government Documents Department

Acoustic-structure interaction problems. Final report

Description: The purpose of this report is to compare and evaluate different numerical methods for solving problems of interaction between elastic solids and acoustic fluids. In particular, we concentrate our efforts on solution techniques involving the finite element method. To that end, in Chapter 2 we discuss different options for analysis of infinite fluids. In particular, the method of mesh trunction and the use of radiation elements and the use of infinite elements are discussed. Also discussed is the analysis of scattering from rigid boundaries. Chapter 3 is a brief discussion of finite element formulations for elastic solids. We review the development, of two dimensional plane strain elements and one dimensional plate and shell elements. In Chapter 4, there is a discussion of the method used to couple the solid and the fluid. We give examples for solution of scattering of pressure waves from thin elastic shell structures. Chapter 5 is a brief conclusion of results and includes recommendations for the best methods of solution and additional research.
Date: December 1, 1993
Creator: Love, E. & Taylor, R.L.
Partner: UNT Libraries Government Documents Department

Acoustic Wave Equations for a Linear Viscous Fluid and An Ideal Fluid

Description: The mathematical description of acoustic wave propagation within a time- and space-varying, and moving, linear viscous fluid is formulated as a system of coupled linear equations. This system is rigorously developed from fundamental principles of continuum mechanics (conservation of mass, balance of linear and angular momentum, balance of entropy) and various constitutive relations (for stress, entropy production, and entropy conduction) by linearizing all expressions with respect to the small-amplitude acoustic wavefield variables. A significant simplification arises if the fluid medium is neither viscous nor heat conducting (i.e., an ideal fluid). In this case the mathematical system can be reduced to a set of five, coupled, first-order partial differential equations. Coefficients in the systems depend on various mechanical and thermodynamic properties of the ambient medium that supports acoustic wave propagation. These material properties cannot all be arbitrarily specified, but must satisfy another system of nonlinear expressions characterizing the dynamic behavior of the background medium. Dramatic simplifications in both systems occur if the ambient medium is simultaneously adiabatic and stationary.
Date: July 1, 2002
Partner: UNT Libraries Government Documents Department

Acoustic wave scattering from a circular crack: comparison of different computational methods

Description: The work reported was motivated by disagreement between the results obtained from two computations of scattering of an axially incident elastic p-wave on a circular crack. One calculation involves the direct solution of the Helmholtz integral equation, showing an oscillating total cross section. The other uses a program called MOOT, in which the elastic displacement near the crack is expanded in regular spherical eigenfunctions of the elastic wave equation. This calculation shows that the oscillations in total cross section disappear rapidly at high wave numbers. The conjecture that the basis for the MOOT expansion was inappropriate is examined by application to a test problem. Results indicate that there is no inadequacy in the spherical basis set. (LEW)
Date: January 1, 1986
Creator: Visscher, W.M.
Partner: UNT Libraries Government Documents Department

Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients

Description: This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close ...
Date: April 2, 2012
Creator: Kalchev, D
Partner: UNT Libraries Government Documents Department

Adaptive-grid methods for time-dependent partial differential equations

Description: This paper contains a survey of recent developments of adaptive-grid algorithms for time-dependent partial differential equations. Two lines of research are discussed. One involves the automatic selection of moving grids to follow propagating waves. The other is based on stationary grids but uses local mesh refinement in both space and time. Advantages and disadvantages of both approaches are discussed. The development of adaptive-grid schemes shows promise of greatly increasing our ability to solve problems in several spatial dimensions.
Date: January 1, 1981
Creator: Hedstrom, G.W. & Rodrique, G.H.
Partner: UNT Libraries Government Documents Department

Adaptive grids and implicit differencing applied to plasma simulation

Description: To understand the kinetic processes that determine energy confinement and impurity production in magnetic confinement experiments, we are developing methods to model kinetic effects on magnetohydrodynamic time scales in realistic geometries. We are using implicit methods and adaptive grids to achieve this goal. 9 refs., 2 figs.
Date: January 1, 1990
Creator: Brackbill, J.U.; Forslund, D.W. & Vu, Hoanh.
Partner: UNT Libraries Government Documents Department

An adaptive level set method

Description: This thesis describes a new method for the numerical solution of partial differential equations of the parabolic type on an adaptively refined mesh in two or more spatial dimensions. The method is motivated and developed in the context of the level set formulation for the curvature dependent propagation of surfaces in three dimensions. In that setting, it realizes the multiple advantages of decreased computational effort, localized accuracy enhancement, and compatibility with problems containing a range of length scales.
Date: December 1, 1995
Creator: Milne, R. B.
Partner: UNT Libraries Government Documents Department

Adaptive mesh refinement algorithm development and dissemination

Description: This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project objective was to develop and disseminate adaptive mesh refinement (AMR) algorithms for structured and unstructured meshes. Development of ARM algorithms will continue along several directions. These directions include algorithms for parallel architectures, techniques for the solution of partial differential equations on adaptive meshes, mesh generation, and algorithms for nontraditional or generic applications of AMR. Dissemination of AMR algorithms is also a goal of the project. AMR algorithms are perceived as difficult to meld to current algorithms. The authors are developing tools that diminish this perception and allow more computational scientists to use AMR within their own work.
Date: August 1, 1997
Creator: Saltzman, J.S.; Brown, D.L.; Brislawn, K.D.; Chesshire, G.S.; Quinlan, D.J. & Berger, M.
Partner: UNT Libraries Government Documents Department