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A Numerical Method for Two-Dimensional Lagrangian Hydrodynamics

Description: Abstract: "A completely Lagrangian scheme for differencing hydrodynamical equations in two dimensions is described. The method conserves mass exactly. The advantages of Lagrangian over Eulerian schemes are briefly mentioned. An appendix gives the generalization to three dimensions."
Date: December 10, 1953
Creator: DeWitt, Bryce S.
Partner: UNT Libraries Government Documents Department

Bending of Rectangular Plates With Large Deflections

Description: Note presenting Von Kármán's equations for thin plates with large deflections are solved for the special cases of rectangular plates with ratios of length to width of 1.5 and 2 and loaded by uniform normal pressure. The boundary conditions are such to approximate panels with riveted edges under normal pressure greater than that of the surrounding panels.
Date: April 1948
Creator: Wang, Chi-Teh
Partner: UNT Libraries Government Documents Department

Automation of The Guiding Center Expansion

Description: We report on the use of the recently-developed Mathematica package VEST (Vector Einstein Summation Tools) to automatically derive the guiding center transformation. Our Mathematica code employs a recursive procedure to derive the transformation order-by-order. This procedure has several novel features. (1) It is designed to allow the user to easily explore the guiding center transformation's numerous nonunique forms or representations. (2) The procedure proceeds entirely in cartesian position and velocity coordinates, thereby producing manifestly gyrogauge invariant results; the commonly-used perpendicular unit vector fields e1, e2 are never even introduced. (3) It is easy to apply in the derivation of higher-order contributions to the guiding center transformation without fear of human error. Our code therefore stands as a useful tool for exploring subtle issues related to the physics of toroidal momentum conservation in tokamaks
Date: March 19, 2013
Creator: Burby, J. W.; Squire, J. & Qin, H.
Partner: UNT Libraries Government Documents Department

A Marker Method for the Solution of the Damped Burgers' Equatio

Description: A new method for the solution of the damped Burgers' equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations.
Date: November 1, 2005
Creator: Lewandowski, Jerome L.V.
Partner: UNT Libraries Government Documents Department

Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method

Description: A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.
Date: January 25, 2005
Creator: Lewandowski, Jerome L.V.
Partner: UNT Libraries Government Documents Department

Simulations of a stretching bar using a plasticity model from the shear transformation zone theory

Description: An Eulerian simulation is developed to study an elastoplastic model of amorphous materials that is based upon the shear transformation zone theory developed by Langer and coworkers. In this theory, plastic deformation is controlled by an effective temperature that measures the amount of configurational disorder in the material. The simulation is used to model ductile fracture in a stretching bar that initially contains a small notch, and the effects of many of the model parameters are examined. The simulation tracks the shape of the bar using the level set method. Within the bar, a finite difference discretization is employed that makes use of the essentially non-oscillatory (ENO) scheme. The system of equations is moderately stiff due to the presence of large elastic constants, and one of the key numerical challenges is to accurately track the level set and construct extrapolated field values for use in boundary conditions. A new approach to field extrapolation is discussed that is second order accurate and requires a constant amount of work per gridpoint.
Date: June 5, 2010
Creator: Rycroft, Chris H. & Gibou, Frederic
Partner: UNT Libraries Government Documents Department

Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model

Description: In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modi ed Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in ow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then a modelbased feedback controller is designed for the reduced order model using linear quadratic regulators (LQR). Finally, a linear quadratic gaussian (LQG) controller, which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.
Date: January 28, 2013
Creator: I.R. Goumiri, C.W. Rowley, Z. Ma, D.A. Gates, J.A. Krommes and J.B. Parker
Partner: UNT Libraries Government Documents Department

A Global, Multi-Resolution Approach to Regional Ocean Modeling

Description: In this collaborative research project between Pennsylvania State University, Colorado State University and Florida State University, we mainly focused on developing multi-resolution algorithms which are suitable to regional ocean modeling. We developed hybrid implicit and explicit adaptive multirate time integration method to solve systems of time-dependent equations that present two signi#12;cantly di#11;erent scales. We studied the e#11;ects of spatial simplicial meshes on the stability and the conditioning of fully discrete approximations. We also studies adaptive #12;nite element method (AFEM) based upon the Centroidal Voronoi Tessellation (CVT) and superconvergent gradient recovery. Some of these techniques are now being used by geoscientists(such as those at LANL).
Date: November 8, 2013
Creator: Du, Qiang
Partner: UNT Libraries Government Documents Department

Efficient Inversion of Multi-frequency and Multi-source Electromagnetic Data: Final report

Description: BES grant DE-FG02-06ER15819 supported efforts at Oregon State University (OSU) to develop improved inversion methods for 3D subsurface electromagnetic (EM) imaging. Three interrelated activities have been supported by this grant, and its predecessor (DE-FG02-06ER15818): (1) collaboration with a former student of the PI, Dr. Weerachai Siripunvaraporn (now Professor at Mahidol University in Bangkok, Thailand) on developing and refining inversion methods for 3D Magnetotelluric (MT) data . (2) Development at Oregon State University of a new modular system of computer codes for EM inversion, and initial testing and application of this inversion on several large field data sets. (3) Research on more efficient approaches to multi-transmitter EM inverse problems, to optimize use of expensive data sensitivity calculations needed for gradient based inversion schemes. The last of these activities was the main motivation for this research project, but the first two activities were important enabling steps that produced useful products and results in their own right, including freely avaialable software for 3D inversion of EM geophysical data.
Date: April 10, 2013
Creator: Egbert, Gary D.
Partner: UNT Libraries Government Documents Department

The Hamiltonian Structure and Euler-Poincare Formulation of the Valsov-Maxwell and Gyrokinetic System

Description: We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with the Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. __________________________________________________
Date: September 25, 2012
Creator: Squire, J.; Qin, H. & Tang, W. M.
Partner: UNT Libraries Government Documents Department

Comment on "Wall Forces Produced During ITER Disruptions" by H. R. Strauss, R. Paccagnella, and J. Breslau (PHYSICS OF PLASMAS 17, 082505 (2010)

Description: The paper by H.R. Strauss presents numerical simulations, which pretend to describe the disruption instability in ITER device. The simulations were performed with numerical code M3D, described in Ref.[7] of the paper.
Date: October 20, 2010
Creator: Zakharov, Leonid E.
Partner: UNT Libraries Government Documents Department

Edge Plasma Boundary Layer Generated By Kink Modes in Tokamaks

Description: This paper describes the structure of the electric current generated by external kink modes at the plasma edge using the ideally conducting plasma model. It is found that the edge current layer is created by both wall touching and free boundary kink modes. Near marginal stability, the total edge current has a universal expression as a result of partial compensation of the δ-functional surface current by the bulk current at the edge. The resolution of an apparent paradox with the pressure balance across the plasma boundary in the presence of the surface currents is provided.
Date: November 22, 2010
Creator: Zakharov, L.E.
Partner: UNT Libraries Government Documents Department

The Theory of Variances in Equilibrium Reconstruction

Description: The theory of variances of equilibrium reconstruction is presented. It complements existing practices with information regarding what kind of plasma profiles can be reconstructed, how accurately, and what remains beyond the abilities of diagnostic systems. The #27;σ-curves, introduced by the present theory, give a quantitative assessment of quality of effectiveness of diagnostic systems in constraining equilibrium reconstructions. The theory also suggests a method for aligning the accuracy of measurements of different physical nature.
Date: January 14, 2008
Creator: Leonid E. Zakharov, Jerome Lewandowski, Elizabeth L. Foley, Fred M. Levinton, Howard Y. Yuh, Vladimir Drozdov, and Darren McDonald
Partner: UNT Libraries Government Documents Department

Self-correcting Multigrid Solver

Description: A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work.
Date: June 29, 2004
Creator: Lewandowski, Jerome L.V.
Partner: UNT Libraries Government Documents Department

Gabor Wave Packet Method to Solve Plasma Wave Equations

Description: A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach.
Date: June 18, 2003
Creator: Pletzer, A.; Phillips, C.K. & Smithe, D.N.
Partner: UNT Libraries Government Documents Department

Low-noise Collision Operators for Particle-in-cell Simulations

Description: A new method to implement low-noise collision operators in particle-in-cell simulations is presented. The method is based on the fact that relevant collision operators can be included naturally in the Lagrangian formulation that exemplifies the particle-in-cell simulation method. Numerical simulations show that the momentum and energy conservation properties of the simulated plasma associated with the low-noise collision operator are improved as compared with standard collision algorithms based on random numbers.
Date: March 8, 2005
Creator: Lewandowski, J.L.V.
Partner: UNT Libraries Government Documents Department

Implicit Solution of the Four-field Extended-magnetohydroynamic Equations using High-order High-continuity Finite Elements

Description: Here we describe a technique for solving the four-field extended-magnetohydrodynamic (MHD) equations in two dimensions. The introduction of triangular high-order finite elements with continuous first derivatives (C{sup 1} continuity) leads to a compact representation compatible with direct inversion of the associated sparse matrices. The split semi-implicit method is introduced and used to integrate the equations in time, yielding unconditional stability for arbitrary time step. The method is applied to the cylindrical tilt mode problem with the result that a non-zero value of the collisionless ion skin depth will increase the growth rate of that mode. The effect of this parameter on the reconnection rate and geometry of a Harris equilibrium and on the Taylor reconnection problem is also demonstrated. This method forms the basis for a generalization to a full extended-MHD description of the plasma with six, eight, or more scalar fields.
Date: December 17, 2004
Creator: Jardin, S.C. & Breslau, J.A.
Partner: UNT Libraries Government Documents Department

A Numerical Instability in an ADI Algorithm for Gyrokinetics

Description: We explore the implementation of an Alternating Direction Implicit (ADI) algorithm for a gyrokinetic plasma problem and its resulting numerical stability properties. This algorithm, which uses a standard ADI scheme to divide the field solve from the particle distribution function advance, has previously been found to work well for certain plasma kinetic problems involving one spatial and two velocity dimensions, including collisions and an electric field. However, for the gyrokinetic problem we find a severe stability restriction on the time step. Furthermore, we find that this numerical instability limitation also affects some other algorithms, such as a partially implicit Adams-Bashforth algorithm, where the parallel motion operator v{sub {parallel}} {partial_derivative}/{partial_derivative}z is treated implicitly and the field terms are treated with an Adams-Bashforth explicit scheme. Fully explicit algorithms applied to all terms can be better at long wavelengths than these ADI or partially implicit algorithms.
Date: December 17, 2004
Creator: Belli, E.A. & Hammett, G.W.
Partner: UNT Libraries Government Documents Department

3-D Force-balanced Magnetospheric Configurations

Description: The knowledge of plasma pressure is essential for many physics applications in the magnetosphere, such as computing magnetospheric currents and deriving magnetosphere-ionosphere coupling. A thorough knowledge of the 3-D pressure distribution has however eluded the community, as most in-situ pressure observations are either in the ionosphere or the equatorial region of the magnetosphere. With the assumption of pressure isotropy there have been attempts to obtain the pressure at different locations by either (a) mapping observed data (e.g., in the ionosphere) along the field lines of an empirical magnetospheric field model or (b) computing a pressure profile in the equatorial plane (in 2-D) or along the Sun-Earth axis (in 1-D) that is in force balance with the magnetic stresses of an empirical model. However, the pressure distributions obtained through these methods are not in force balance with the empirical magnetic field at all locations. In order to find a global 3-D plasma pressure distribution in force balance with the magnetospheric magnetic field, we have developed the MAG-3D code, that solves the 3-D force balance equation J x B = (upside-down delta) P computationally. Our calculation is performed in a flux coordinate system in which the magnetic field is expressed in terms of Euler potentials as B = (upside-down delta) psi x (upside-down delta) alpha. The pressure distribution, P = P(psi,alpha), is prescribed in the equatorial plane and is based on satellite measurements. In addition, computational boundary conditions for y surfaces are imposed using empirical field models. Our results provide 3-D distributions of magnetic field and plasma pressure as well as parallel and transverse currents for both quiet-time and disturbed magnetospheric conditions.
Date: February 10, 2003
Creator: Zaharia, Sorin; Cheng, C. Z. & Maezawa, K.
Partner: UNT Libraries Government Documents Department

Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer

Description: A graduate level course for Thermal Hydraulics (T/H) was taught through Idaho State University in the spring of 2004. A numerical approach was taken for the content of this course since the students were employed at the Idaho National Laboratory and had been users of T/H codes. The majority of the students had expressed an interest in learning about the Courant Limit, mass error, semi-implicit and implicit numerical integration schemes in the context of a computer code. Since no introductory text was found the author developed notes taught from his own research and courses taught for Westinghouse on the subject. The course started with a primer on control volume methods and the construction of a Homogeneous Equilibrium Model (HEM) (T/H) code. The primer was valuable for giving the students the basics behind such codes and their evolution to more complex codes for Thermal Hydraulics and Computational Fluid Dynamics (CFD). The course covered additional material including the Finite Element Method and non-equilibrium (T/H). The control volume primer and the construction of a three-equation (mass, momentum and energy) HEM code are the subject of this paper . The Fortran version of the code covered in this paper is elementary compared to its descendants. The steam tables used are less accurate than the available commercial version written in C Coupled to a Graphical User Interface (GUI). The Fortran version and input files can be downloaded at www.microfusionlab.com.
Date: October 1, 2004
Creator: Lucas, D. S.
Partner: UNT Libraries Government Documents Department

Variational Symplectic Integrator for Long-Time Simulations of the Guiding-Center Motion of Charged Particles in General Magnetic Fields

Description: A variational symplectic integrator for the guiding-center motion of charged particles in general magnetic fields is developed for long-time simulation studies of magnetized plasmas. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing the dynamics. The variational symplectic integrator conserves exactly a discrete Lagrangian symplectic structure, and has better numerical properties over long integration time, compared with standard integrators, such as the standard and variable time-step fourth order Runge-Kutta methods.
Date: February 11, 2008
Creator: Qin, H. & Guan, X.
Partner: UNT Libraries Government Documents Department

Simulating Photons and Plasmons in a Three-dimensional Lattice

Description: Three-dimensional metallic photonic structures are studied using a newly developed mixed finite element-finite difference (FE-FD) code, Curly3d. The code solves the vector Helmholtz equation as an eigenvalue problem in the unit cell of a triply periodic lattice composed of conductors and/or dielectrics. The mixed FE-FD discretization scheme ensures rapid numerical convergence of the eigenvalue and allows the code to run at low resolution. Plasmon and photonic band structure calculations are presented.
Date: September 3, 2002
Creator: Pletzer, A. & Shvets, G.
Partner: UNT Libraries Government Documents Department