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Sample records for ii numerical method

  1. Mie Light-Scattering Granulometer with an Adaptive Numerical Filtering Method. II. Experiments.

    PubMed

    Hespel, L; Delfour, A; Guillame, B

    2001-02-20

    A nephelometer is presented that theoretically requires no absolute calibration. This instrument is used for determining the particle-size distribution of various scattering media (aerosols, fogs, rocket exhausts, engine plumes, and the like) from angular static light-scattering measurements. An inverse procedure is used, which consists of a least-squares method and a regularization scheme based on numerical filtering. To retrieve the distribution function one matches the experimental data with theoretical patterns derived from Mie theory. The main principles of the inverse method are briefly presented, and the nephelometer is then described with the associated partial calibration procedure. Finally, the whole granulometer system (inverse method and nephelometer) is validated by comparison of measurements of scattering media with calibrated monodisperse or known size distribution functions. PMID:18357082

  2. The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models

    PubMed Central

    Noid, W. G.; Liu, Pu; Wang, Yanting; Chu, Jhih-Wei; Ayton, Gary S.; Izvekov, Sergei; Andersen, Hans C.; Voth, Gregory A.

    2008-01-01

    The multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005);J. Chem. Phys. 123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MS-CG variational principle determines the exact many-body potential of mean force (PMF) governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MS-CG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the many-body PMF. The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a one-site CG model of methanol and a molecular CG model of the EMIM+∕NO3− ionic liquid are provided to illustrate the method. PMID:18601325

  3. An instrumental and numerical method to determine the hydrogenic ratio in isotopic experiments in the TJ-II stellarator

    SciTech Connect

    Baciero, A. Zurro, B.; Martínez, M.

    2014-11-15

    The isotope effect is an important topic that is relevant for future D-T fusion reactors, where the use of deuterium, rather than hydrogen, may lean to improved plasma confinement. An evaluation of the ratio of hydrogen/deuterium is needed for isotope effect studies in current isotopic experiments. Here, the spectral range around H{sub α} and D{sub α} lines, obtained with an intensified multi-channel detector mounted to a 1-m focal length spectrometer, is analyzed using a fit function that includes several Gaussian components. The isotopic ratio evolution for a single operational day of the TJ-II stellarator is presented. The role of injected hydrogen by Neutral Beam Injection heating is also studied.

  4. An instrumental and numerical method to determine the hydrogenic ratio in isotopic experiments in the TJ-II stellarator

    NASA Astrophysics Data System (ADS)

    Baciero, A.; Zurro, B.; Martínez, M.

    2014-11-01

    The isotope effect is an important topic that is relevant for future D-T fusion reactors, where the use of deuterium, rather than hydrogen, may lean to improved plasma confinement. An evaluation of the ratio of hydrogen/deuterium is needed for isotope effect studies in current isotopic experiments. Here, the spectral range around Hα and Dα lines, obtained with an intensified multi-channel detector mounted to a 1-m focal length spectrometer, is analyzed using a fit function that includes several Gaussian components. The isotopic ratio evolution for a single operational day of the TJ-II stellarator is presented. The role of injected hydrogen by Neutral Beam Injection heating is also studied.

  5. An instrumental and numerical method to determine the hydrogenic ratio in isotopic experiments in the TJ-II stellarator.

    PubMed

    Baciero, A; Zurro, B; Martínez, M

    2014-11-01

    The isotope effect is an important topic that is relevant for future D-T fusion reactors, where the use of deuterium, rather than hydrogen, may lean to improved plasma confinement. An evaluation of the ratio of hydrogen/deuterium is needed for isotope effect studies in current isotopic experiments. Here, the spectral range around Hα and Dα lines, obtained with an intensified multi-channel detector mounted to a 1-m focal length spectrometer, is analyzed using a fit function that includes several Gaussian components. The isotopic ratio evolution for a single operational day of the TJ-II stellarator is presented. The role of injected hydrogen by Neutral Beam Injection heating is also studied. PMID:25430312

  6. Numerical methods in structural mechanics

    NASA Astrophysics Data System (ADS)

    Obraztsov, I. F.

    The papers contained in this volume focus on numerical, numerical-analytical, and theoretical methods for dealing with strength, stability, and dynamics problems in the design of the structural elements of flight vehicles. Topics discussed include the solution of homogeneous boundary value problems for systems of ordinary differential equations modified by a difference factorization method, a study of the rupture strength of a welded joint between plates, singular solutions in mixed problems for a wedge and a half-strip, and a thermoelasticity problem for an open-profile cylindrical shell with a localized temperature field.

  7. Numerical methods for turbulent flow

    NASA Astrophysics Data System (ADS)

    Turner, James C., Jr.

    1988-09-01

    It has generally become accepted that the Navier-Strokes equations predict the dynamic behavior of turbulent as well as laminar flows of a fluid at a point in space away form a discontinuity such as a shock wave. Turbulence is also closely related to the phenomena of non-uniqueness of solutions of the Navier-Strokes equations. These second order, nonlinear partial differential equations can be solved analytically for only a few simple flows. Turbulent flow fields are much to complex to lend themselves to these few analytical methods. Numerical methods, therefore, offer the only possibility of achieving a solution of turbulent flow equations. In spite of recent advances in computer technology, the direct solution, by discrete methods, of the Navier-Strokes equations for turbulent flow fields is today, and in the foreseeable future, impossible. Thus the only economically feasible way to solve practical turbulent flow problems numerically is to use statistically averaged equations governing mean-flow quantities. The objective is to study some recent developments relating to the use of numerical methods to study turbulent flow.

  8. Numerical methods for molecular dynamics

    SciTech Connect

    Skeel, R.D.

    1991-01-01

    This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.

  9. Numerical methods for multibody systems

    NASA Technical Reports Server (NTRS)

    Glowinski, Roland; Nasser, Mahmoud G.

    1994-01-01

    This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.

  10. Forebody and base region real gas flow in severe planetary entry by a factored implicit numerical method. II - Equilibrium reactive gas

    NASA Technical Reports Server (NTRS)

    Davy, W. C.; Green, M. J.; Lombard, C. K.

    1981-01-01

    The factored-implicit, gas-dynamic algorithm has been adapted to the numerical simulation of equilibrium reactive flows. Changes required in the perfect gas version of the algorithm are developed, and the method of coupling gas-dynamic and chemistry variables is discussed. A flow-field solution that approximates a Jovian entry case was obtained by this method and compared with the same solution obtained by HYVIS, a computer program much used for the study of planetary entry. Comparison of surface pressure distribution and stagnation line shock-layer profiles indicates that the two solutions agree well.

  11. Numerical methods used in fusion science numerical modeling

    NASA Astrophysics Data System (ADS)

    Yagi, M.

    2015-04-01

    The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.

  12. Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

    SciTech Connect

    Klein, R I; Stone, J M

    2007-11-20

    We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.

  13. On Numerical Methods For Hypersonic Turbulent Flows

    NASA Astrophysics Data System (ADS)

    Yee, H. C.; Sjogreen, B.; Shu, C. W.; Wang, W.; Magin, T.; Hadjadj, A.

    2011-05-01

    Proper control of numerical dissipation in numerical methods beyond the standard shock-capturing dissipation at discontinuities is an essential element for accurate and stable simulation of hypersonic turbulent flows, including combustion, and thermal and chemical nonequilibrium flows. Unlike rapidly developing shock interaction flows, turbulence computations involve long time integrations. Improper control of numerical dissipation from one time step to another would be compounded over time, resulting in the smearing of turbulent fluctuations to an unrecognizable form. Hypersonic turbulent flows around re- entry space vehicles involve mixed steady strong shocks and turbulence with unsteady shocklets that pose added computational challenges. Stiffness of the source terms and material mixing in combustion pose yet other types of numerical challenges. A low dissipative high order well- balanced scheme, which can preserve certain non-trivial steady solutions of the governing equations exactly, may help minimize some of these difficulties. For stiff reactions it is well known that the wrong propagation speed of discontinuities occurs due to the under-resolved numerical solutions in both space and time. Schemes to improve the wrong propagation speed of discontinuities for systems of stiff reacting flows remain a challenge for algorithm development. Some of the recent algorithm developments for direct numerical simulations (DNS) and large eddy simulations (LES) for the subject physics, including the aforementioned numerical challenges, will be discussed.

  14. A numerical method of detecting singularity

    NASA Technical Reports Server (NTRS)

    Laporte, M.; Vignes, J.

    1978-01-01

    A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.

  15. A numerical method for predicting hypersonic flowfields

    NASA Technical Reports Server (NTRS)

    Maccormack, Robert W.; Candler, Graham V.

    1989-01-01

    The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.

  16. Numerical Analysis of the Symmetric Methods

    NASA Astrophysics Data System (ADS)

    Xu, Ji-Hong; Zhang, A.-Li

    1995-03-01

    Aimed at the initial value problem of the particular second-order ordinary differential equations,y ″=f(x, y), the symmetric methods (Quinlan and Tremaine, 1990) and our methods (Xu and Zhang, 1994) have been compared in detail by integrating the artificial earth satellite orbits in this paper. In the end, we point out clearly that the integral accuracy of numerical integration of the satellite orbits by applying our methods is obviously higher than that by applying the same order formula of the symmetric methods when the integration time-interval is not greater than 12000 periods.

  17. EPACT II: project and methods.

    PubMed

    Juillerat, Pascal; Froehlich, Florian; Felley, Christian; Pittet, Valérie; Mottet, Christian; Gonvers, Jean-Jacques; Michetti, Pierre; Vader, John-Paul

    2007-01-01

    Building on the first European Panel on the Appropriateness of Crohn's Disease Treatment (EPACT I) which was held in Lausanne at the beginning of March 2004, a new panel will be convened in Switzerland (EPACT II, November to December 2007) to update this work. A combined evidence- and panel-based method (RAND) will be applied to assess the appropriateness of therapy for Crohn's disease (CD). In preparation for the meeting of experts, reviews of evidence-based literature were prepared for major clinical presentations of CD. During the meeting, an international multidis- ciplinary panel that includes gastroenterologists, surgeons and general practitioners weigh the strength of evidence and apply their clinical experience when assessing the appropriateness of therapy for 569 specific indications (clinical scenarios). This chapter describes in detail the process of updating the literature review and the systematic approach of the RAND Appropriateness Method used during the expert panel meeting. PMID:18239398

  18. Numerical Methods for Stochastic Partial Differential Equations

    SciTech Connect

    Sharp, D.H.; Habib, S.; Mineev, M.B.

    1999-07-08

    This is the final report of a Laboratory Directed Research and Development (LDRD) project at the Los Alamos National laboratory (LANL). The objectives of this proposal were (1) the development of methods for understanding and control of spacetime discretization errors in nonlinear stochastic partial differential equations, and (2) the development of new and improved practical numerical methods for the solutions of these equations. The authors have succeeded in establishing two methods for error control: the functional Fokker-Planck equation for calculating the time discretization error and the transfer integral method for calculating the spatial discretization error. In addition they have developed a new second-order stochastic algorithm for multiplicative noise applicable to the case of colored noises, and which requires only a single random sequence generation per time step. All of these results have been verified via high-resolution numerical simulations and have been successfully applied to physical test cases. They have also made substantial progress on a longstanding problem in the dynamics of unstable fluid interfaces in porous media. This work has lead to highly accurate quasi-analytic solutions of idealized versions of this problem. These may be of use in benchmarking numerical solutions of the full stochastic PDEs that govern real-world problems.

  19. Numerical methods for supersonic astrophysical jets

    NASA Astrophysics Data System (ADS)

    Ha, Youngsoo

    2003-09-01

    The Euler equations of gas dynamics are used for the simulation of general astrophysical fluid flows including high Mach number astrophysical jets with radiative cooling. To accurately compute supersonic jet solutions with sharp resolution of shock waves, three modern numerical methods for gas dynamics were used: (1)a second-order Godunov method in LeVeque's software package CLAWPACK, (2)the Nessyahu-Tadmor-Kurganov (NTK) central hyperbolic scheme, and (3)the WENO-LF (Weighted Essentially Non-Oscillatory Lax-Friedrichs) scheme. Then simulations of supersonic astrophysical jets were compared, first without and then with radiative cooling. CLAWPACK consists of routines for solving time-dependent nonlinear hyperbolic conservation laws based on higher order Godunov methods and approximate Riemann problem solutions; the NTK scheme solves conservation laws using a modified Lax-Friedrichs central difference method without appealing to Riemann problem solutions; and the WENO-LF finite difference scheme is based on the Essentially Non-Oscillatory (ENO) idea by using Lax- Friedrichs flux splitting. The ENO method constructs a solution using the smoothness of the interpolating polynomial on given stencils; on the other hand, the WENO scheme uses a convex combination of the interpolate functions on all candidate stencils. The third-order and fifth-order WENO-LF methods were used to simulate the high Mach number jets. Appropriate numerical methods for incorporating radiative cooling in these numerical methods are also discussed. Interactions of supersonic jets with their environments (jet-“blob” interactions) are shown after modifying the codes to handle high Mach numbers and radiative cooling.

  20. Hyperbolic conservation laws and numerical methods

    NASA Technical Reports Server (NTRS)

    Leveque, Randall J.

    1990-01-01

    The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.

  1. Numerical methods for molecular dynamics. Progress report

    SciTech Connect

    Skeel, R.D.

    1991-12-31

    This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.

  2. RELAP-7 Numerical Stabilization: Entropy Viscosity Method

    SciTech Connect

    R. A. Berry; M. O. Delchini; J. Ragusa

    2014-06-01

    The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.

  3. Numerical methods for engine-airframe integration

    SciTech Connect

    Murthy, S.N.B.; Paynter, G.C.

    1986-01-01

    Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison of full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment.

  4. Numerical methods for finding stationary gravitational solutions

    NASA Astrophysics Data System (ADS)

    Dias, Óscar J. C.; Santos, Jorge E.; Way, Benson

    2016-07-01

    The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory–Laflamme zero modes of small rotating black holes in AdS{}5× {S}5. We also include several tools and tricks that have been useful throughout the literature.

  5. Numerical analysis method for linear induction machines.

    NASA Technical Reports Server (NTRS)

    Elliott, D. G.

    1972-01-01

    A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.

  6. Application of numerical methods to elasticity imaging.

    PubMed

    Castaneda, Benjamin; Ormachea, Juvenal; Rodríguez, Paul; Parker, Kevin J

    2013-03-01

    Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity. PMID:24010245

  7. Mathematica with a Numerical Methods Course

    NASA Astrophysics Data System (ADS)

    Varley, Rodney

    2003-04-01

    An interdisciplinary "Numerical Methods" course has been shared between physics, mathematics and computer science since 1992 at Hunter C. Recently, the lectures and workshops for this course have become formalized and placed on the internet at http://www.ph.hunter.cuny.edu (follow the links "Course Listings and Websites" >> "PHYS385 (Numerical Methods)". Mathematica notebooks for the lectures are available for automatic download (by "double clicking" the lecture icon) for student use in the classroom or at home. AOL (or Netscape/Explorer) can be used provided Mathematica (or the "free" MathReader) has been made a "helper application". Using Mathematica has the virtue that mathematical equations (no LaTex required) can easily be included with the text and Mathematica's graphing is easy to use. Computational cells can be included within the notebook and students may easily modify the calculation to see the result of "what if..." questions. Homework is sent as Mathematica notebooks to the instructor via the internet and the corrected workshops are returned in the same manner. Most exam questions require computational solutions.

  8. Numerical methods for problems in computational aeroacoustics

    NASA Astrophysics Data System (ADS)

    Mead, Jodi Lorraine

    1998-12-01

    A goal of computational aeroacoustics is the accurate calculation of noise from a jet in the far field. This work concerns the numerical aspects of accurately calculating acoustic waves over large distances and long time. More specifically, the stability, efficiency, accuracy, dispersion and dissipation in spatial discretizations, time stepping schemes, and absorbing boundaries for the direct solution of wave propagation problems are determined. Efficient finite difference methods developed by Tam and Webb, which minimize dispersion and dissipation, are commonly used for the spatial and temporal discretization. Alternatively, high order pseudospectral methods can be made more efficient by using the grid transformation introduced by Kosloff and Tal-Ezer. Work in this dissertation confirms that the grid transformation introduced by Kosloff and Tal-Ezer is not spectrally accurate because, in the limit, the grid transformation forces zero derivatives at the boundaries. If a small number of grid points are used, it is shown that approximations with the Chebyshev pseudospectral method with the Kosloff and Tal-Ezer grid transformation are as accurate as with the Chebyshev pseudospectral method. This result is based on the analysis of the phase and amplitude errors of these methods, and their use for the solution of a benchmark problem in computational aeroacoustics. For the grid transformed Chebyshev method with a small number of grid points it is, however, more appropriate to compare its accuracy with that of high- order finite difference methods. This comparison, for an order of accuracy 10-3 for a benchmark problem in computational aeroacoustics, is performed for the grid transformed Chebyshev method and the fourth order finite difference method of Tam. Solutions with the finite difference method are as accurate. and the finite difference method is more efficient than, the Chebyshev pseudospectral method with the grid transformation. The efficiency of the Chebyshev

  9. An asymptotic homogenized neutron diffusion approximation. II. Numerical comparisons

    SciTech Connect

    Trahan, T. J.; Larsen, E. W.

    2012-07-01

    In a companion paper, a monoenergetic, homogenized, anisotropic diffusion equation is derived asymptotically for large, 3-D, multiplying systems with a periodic lattice structure [1]. In the present paper, this approximation is briefly compared to several other well known diffusion approximations. Although the derivation is different, the asymptotic diffusion approximation matches that proposed by Deniz and Gelbard, and is closely related to those proposed by Benoist. The focus of this paper, however, is a numerical comparison of the various methods for simple reactor analysis problems in 1-D. The comparisons show that the asymptotic diffusion approximation provides a more accurate estimate of the eigenvalue than the Benoist diffusion approximations. However, the Benoist diffusion approximations and the asymptotic diffusion approximation provide very similar estimates of the neutron flux. The asymptotic method and the Benoist methods both outperform the standard homogenized diffusion approximation, with flux weighted cross sections. (authors)

  10. Preliminary numerical study of Thailand Plasma Focus II (TPF-II) design

    NASA Astrophysics Data System (ADS)

    Tamman, Arlee; Nisoa, Mudtorlep; Onjun, Thawatchai

    2014-08-01

    In this work, we use the Lee model to predict the plasma parameters, such as plasma temperature and pinch duration, in the 3.37 kJ DPF device, called “Thailand Plasma Focus-II (TPF-II).” This numerical result is then used to optimize the electrode parameters for the maximum production rate of 18F. The crossing point of pinch duration and pinch temperature is considered to obtain the appropriate electrode length, anode radius and gas gap between anode and cathode. The gas gap between both electrodes is indicated in ratio between cathode radius and anode radius, c. The results show that the best values of c, anode radius and electrode length are 1.48, 1.2 cm and 26.1 cm, respectively, in which the plasma pinch temperature, peak current and pinch duration of 0.76 keV, 207 kA and 8.725 ns can be obtained.

  11. Numerical methods for analyzing electromagnetic scattering

    NASA Technical Reports Server (NTRS)

    Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.

    1985-01-01

    Numerical methods to analyze electromagnetic scattering are presented. The dispersions and attenuations of the normal modes in a circular waveguide coated with lossy material were completely analyzed. The radar cross section (RCS) from a circular waveguide coated with lossy material was calculated. The following is observed: (1) the interior irradiation contributes to the RCS much more than does the rim diffraction; (2) at low frequency, the RCS from the circular waveguide terminated by a perfect electric conductor (PEC) can be reduced more than 13 dB down with a coating thickness less than 1% of the radius using the best lossy material available in a 6 radius-long cylinder; (3) at high frequency, a modal separation between the highly attenuated and the lowly attenuated modes is evident if the coating material is too lossy, however, a large RCS reduction can be achieved for a small incident angle with a thin layer of coating. It is found that the waveguide coated with a lossy magnetic material can be used as a substitute for a corrugated waveguide to produce a circularly polarized radiation yield.

  12. A numerical method for cardiac mechanoelectric simulations.

    PubMed

    Pathmanathan, Pras; Whiteley, Jonathan P

    2009-05-01

    Much effort has been devoted to developing numerical techniques for solving the equations that describe cardiac electrophysiology, namely the monodomain equations and bidomain equations. Only a limited selection of publications, however, address the development of numerical techniques for mechanoelectric simulations where cardiac electrophysiology is coupled with deformation of cardiac tissue. One problem commonly encountered in mechanoelectric simulations is instability of the coupled numerical scheme. In this study, we develop a stable numerical scheme for mechanoelectric simulations. A number of convergence tests are carried out using this stable technique for simulations where deformations are of the magnitude typically observed in a beating heart. These convergence tests demonstrate that accurate computation of tissue deformation requires a nodal spacing of around 1 mm in the mesh used to calculate tissue deformation. This is a much finer computational grid than has previously been acknowledged, and has implications for the computational efficiency of the resulting numerical scheme. PMID:19263223

  13. Finite element methods in numerical relativity.

    NASA Astrophysics Data System (ADS)

    Mann, P. J.

    The finite element method is very successful in Newtonian fluid simulations, and can be extended to relativitstic fluid flows. This paper describes the general method, and then outlines some preliminary results for spherically symmetric geometries. The mixed finite element - finite difference scheme is introduced, and used for the description of spherically symmetric collapse. Baker's (Newtonian) shock modelling method and Miller's moving finite element method are also mentioned. Collapse in double-null coordinates requires non-constant time slicing, so the full finite element method in space and time is described.

  14. Numerical matrix method for quantum periodic potentials

    NASA Astrophysics Data System (ADS)

    Le Vot, Felipe; Meléndez, Juan J.; Yuste, Santos B.

    2016-06-01

    A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the wave functions as finite superpositions of eigenfunctions of the infinite well. A matrix eigenvalue equation then yields the energy levels of the periodic potential within an acceptable accuracy. The methodology has been successfully used to deal with problems based on the well-known Kronig-Penney (KP) model. Besides the original model, these problems are a dimerized KP solid, a KP solid containing a surface, and a KP solid under an external field. A short list of additional problems that can be solved with this procedure is presented.

  15. Method for numerical simulations of metastable states

    SciTech Connect

    Heller, U.M.; Seiberg, N.

    1983-06-15

    We present a numerical simulation of metastable states near a first-order phase transition in the example of a U(1) lattice gauge theory with a generalized action. In order to make measurements in these states possible their decay has to be prevented. We achieve this by using a microcanonical simulation for a finite system. We then obtain the coupling constant (inverse temperature) as a function of the action density. It turns out to be nonmonotonic and hence not uniquely invertible. From it we derive the effective potential for the action density. This effective potential is not always convex, a property that seems to be in contradiction with the standard lore about its convexity. This apparent ''paradox'' is resolved in a discussion about different definitions of the effective potential.

  16. Spectral multigrid methods for elliptic equations II

    NASA Technical Reports Server (NTRS)

    Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.

    1984-01-01

    A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

  17. Numerical methods in Markov chain modeling

    NASA Technical Reports Server (NTRS)

    Philippe, Bernard; Saad, Youcef; Stewart, William J.

    1989-01-01

    Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

  18. Interpolation Method Needed for Numerical Uncertainty

    NASA Technical Reports Server (NTRS)

    Groves, Curtis E.; Ilie, Marcel; Schallhorn, Paul A.

    2014-01-01

    Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.

  19. Numerical Relativity, Black Hole Mergers, and Gravitational Waves: Part II

    NASA Technical Reports Server (NTRS)

    Centrella, Joan

    2012-01-01

    This series of 3 lectures will present recent developments in numerical relativity, and their applications to simulating black hole mergers and computing the resulting gravitational waveforms. In this second lecture, we focus on simulations of black hole binary mergers. We hig hlight the instabilities that plagued the codes for many years, the r ecent breakthroughs that led to the first accurate simulations, and the current state of the art.

  20. Fish Pectoral Fin Hydrodynamics; Part II: Numerical Simulations and Analysis

    NASA Astrophysics Data System (ADS)

    Dong, H.; Madden, P. G.

    2005-11-01

    High-fidelity numerical simulations are being used to examine the key hydrodynamic features and thrust performance of the pectoral fin of a bluegill sunfish which is moving at a constant forward velocity. The numerical modeling approach employs a parallelized immersed boundary solver which can perform direct (DNS) or large-eddy simulation (LES) of flow past highly deformable bodies such as fish pectoral fins. The three-dimensional, time-dependent fin kinematics is obtained via a stereo-videographic technique and experiments also provide PIV data which is used to validate the numerical simulations. The primary objectives of the CFD effort are to quantify the thrust performance of the bluegill sunfish pectoral fin as well as to establish the mechanisms responsible for thrust production. Simulations show that the pectoral fin produces a relatively large amount of thrust at all phases in the fin motion while limiting the magnitude of the transverse forces. The motion of the fin produces a distinct system of connected vortices which are examined in detail in order to gain insight into the thrust producing mechanisms.

  1. A numerical model of acoustic choking. II - Shocked solutions

    NASA Astrophysics Data System (ADS)

    Walkington, N. J.; Eversman, W.

    1986-01-01

    The one dimensional equations of gas dynamics are used to model subsonic acoustic choking. This model can accommodate non-linear distortion of waves and the eventual formation of shock waves. Several finite differencing schemes are adapted to obtain solutions. The results obtained with the various schemes are compared with the asymptotic results available. The results suggest that no one finite differencing scheme gives solutions significantly better than the others and that most of the difference solutions are close to the asymptotic results. If the acoustic shock wave is sufficiently strong it almost annihilates the acoustic wave; in this situation numerical errors may dominate the results. Such solutions involve very large acoustic attenuations.

  2. Modelling asteroid brightness variations. I - Numerical methods

    NASA Technical Reports Server (NTRS)

    Karttunen, H.

    1989-01-01

    A method for generating lightcurves of asteroid models is presented. The effects of the shape of the asteroid and the scattering law of a surface element are distinctly separable, being described by chosen functions that can easily be changed. The shape is specified by means of two functions that yield the length of the radius vector and the normal vector of the surface at a given point. The general shape must be convex, but spherical concavities producing macroscopic shadowing can also be modeled.

  3. A Numerical Treatment of the Rf SQUID: II. Noise Temperature

    SciTech Connect

    Kleiner, Reinhold; Koelle, Dieter; Clarke, John

    2007-01-15

    We investigate rf SQUIDs (Superconducting QUantum Interference Devices), coupled to a resonant input circuit, a readout tank circuit and a preamplifier, by numerically solving the corresponding Langevin equations and optimizing model parameters with respect to noise temperature. We also give approximate analytic solutions for the noise temperature, which we reduce to parameters of the SQUID and the tank circuit in the absence of the input circuit. The analytic solutions agree with numerical simulations of the full circuit to within 10%, and are similar to expressions used to calculate the noise temperature of dc SQUIDs. The best device performance is obtained when {beta}{sub L}{prime} {triple_bond} 2{pi}LI{sub 0}/{Phi}{sub 0} is 0.6-0.8; L is the SQUID inductance, I{sub 0} the junction critical current and F{sub 0} the flux quantum. For a tuned input circuit we find an optimal noise temperature T{sub N,opt} {approx} 3Tf/f{sub c}, where T, f and f{sub c} denote temperature, signal frequency and junction characteristic frequency, respectively. This value is only a factor of 2 larger than the optimal noise temperatures obtained by approximate analytic theories carried out previously in the limit {beta}{sub L}{prime} << 1. We study the dependence of the noise temperature on various model parameters, and give examples using realistic device parameters of the extent to which the intrinsic noise temperature can be realized experimentally.

  4. A numerical method for power plant simulations

    SciTech Connect

    Carcasci, C.; Facchini, B.

    1996-03-01

    This paper describes a highly flexible computerized method of calculating operating data in a power cycle. The computerized method presented here permits the study of steam, gas and combined plants. Its flexibility is not restricted by any defined cycle scheme. A power plant consists of simple elements (turbine, compressor, combustor chamber, pump, etc.). Each power plant component is represented by its typical equations relating to fundamental mechanical and thermodynamic laws, so a power plant system is represented by algebraic equations, which are the typical equations of components, continuity equations, and data concerning plant conditions. This equation system is not linear, but can be reduced to a linear equation system with variable coefficients. The solution is simultaneous for each component and it is determined by an iterative process. An example of a simple gas turbine cycle demonstrates the applied technique. This paper also presents the user interface based on MS-Windows. The input data, the results, and any characteristic parameters of a complex cycle scheme are also shown.

  5. Numerical methods for analyzing electromagnetic scattering

    NASA Technical Reports Server (NTRS)

    Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.

    1985-01-01

    Attenuation properties of the normal modes in an overmoded waveguide coated with a lossy material were analyzed. It is found that the low-order modes, can be significantly attenuated even with a thin layer of coating if the coating material is not too lossy. A thinner layer of coating is required for large attenuation of the low-order modes if the coating material is magnetic rather than dielectric. The Radar Cross Section (RCS) from an uncoated circular guide terminated by a perfect electric conductor was calculated and compared with available experimental data. It is confirmed that the interior irradiation contributes to the RCS. The equivalent-current method based on the geometrical theory of diffraction (GTD) was chosen for the calculation of the contribution from the rim diffraction. The RCS reduction from a coated circular guide terminated by a PEC are planned schemes for the experiments are included. The waveguide coated with a lossy magnetic material is suggested as a substitute for the corrugated waveguide.

  6. Methods for preparation of cyclopentadienyliron (II) arenes

    DOEpatents

    Keipert, Steven J.

    1991-01-01

    Two improved methods for preparation of compounds with the structure shown in equation X [(Cp)--Fe--(Ar)].sup.+.sub.b X.sup.b- (X) where Cp is an eta.sup.5 complexed, substituted or unsubstituted, cyclopentadienyl or indenyl anion, Ar is an eta.sup.6 complexed substituted or unsubstituted, pi-arene ligand anad X is a b-valent anion where b is an integer between 1 and 3. The two methods, which differ in the source of the cyclopentadienyl anion - Lewis acid complex, utilize a Lewis acid assisted ligand transfer reaction. The cyclopentadienyl anion ligand, assisted by a Lewis acid is transferred to ferrous ion in the presence of an arene. In the first method, the cyclopentadienyl anion is derived from ferrocene and ferrous chloride. In this reaction, the cyclopentadienyliron (II) arene product is derived partially from ferrocene and partially from the ferrous salt. In the second method, the cyclopentadienyl anion - Lewis acid complex is formed by direct reaction of the Lewis acid with an inorganic cyclopentadienide salt. The cyclopentadienyliron (II) arene product of this reaction is derived entirely from the ferrous salt. Cyclopentadienyliron (II) arene cations are of great interest due to their utility as photoactivatable catalysts for a variety of polymerization reactions.

  7. Numerical Weather Predictions Evaluation Using Spatial Verification Methods

    NASA Astrophysics Data System (ADS)

    Tegoulias, I.; Pytharoulis, I.; Kotsopoulos, S.; Kartsios, S.; Bampzelis, D.; Karacostas, T.

    2014-12-01

    During the last years high-resolution numerical weather prediction simulations have been used to examine meteorological events with increased convective activity. Traditional verification methods do not provide the desired level of information to evaluate those high-resolution simulations. To assess those limitations new spatial verification methods have been proposed. In the present study an attempt is made to estimate the ability of the WRF model (WRF -ARW ver3.5.1) to reproduce selected days with high convective activity during the year 2010 using those feature-based verification methods. Three model domains, covering Europe, the Mediterranean Sea and northern Africa (d01), the wider area of Greece (d02) and central Greece - Thessaly region (d03) are used at horizontal grid-spacings of 15km, 5km and 1km respectively. By alternating microphysics (Ferrier, WSM6, Goddard), boundary layer (YSU, MYJ) and cumulus convection (Kain-­-Fritsch, BMJ) schemes, a set of twelve model setups is obtained. The results of those simulations are evaluated against data obtained using a C-Band (5cm) radar located at the centre of the innermost domain. Spatial characteristics are well captured but with a variable time lag between simulation results and radar data. Acknowledgements: This research is co­financed by the European Union (European Regional Development Fund) and Greek national funds, through the action "COOPERATION 2011: Partnerships of Production and Research Institutions in Focused Research and Technology Sectors" (contract number 11SYN_8_1088 - DAPHNE) in the framework of the operational programme "Competitiveness and Entrepreneurship" and Regions in Transition (OPC II, NSRF 2007-­-2013).

  8. Coordinated Optimization of Visual Cortical Maps (II) Numerical Studies

    PubMed Central

    Reichl, Lars; Heide, Dominik; Löwel, Siegrid; Crowley, Justin C.; Kaschube, Matthias; Wolf, Fred

    2012-01-01

    In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological

  9. Numerical modelling of mesoscale atmospheric dispersion. (Volumes I and II)

    SciTech Connect

    Moran, M.D.

    1992-01-01

    Mesoscale atmospheric dispersion is more complicated than smaller-scale dispersion because the mean wind field can no longer be considered steady or horizontally homogeneous over mesoscale time and space scales. Wind shear also plays an important role on the mesoscale, and horizontal dispersion can be enhanced and even dominated by vertical wind shear through either the simultaneous or delayed interaction of horizontal differential advection and vertical mixing. The CSU mesoscale atmospheric dispersion modelling system has been used in this study to simulate the transport and diffusion of a perfluorocarbon gas for episodic releases made during two mesoscale dispersion field experiments. The physiography of the two experimental domains was quite different, permitting isolation and examination of the roles of terrain forcing and differential advection in mesoscale atmospheric dispersion. Suites of numerical experiments of increasing complexity were carried out for both case studies. The experiments differed in the realism of their representation of both the synoptic-scale flow and the underlying terrain. The contributions of differential advection and mesoscale deformation to mesoscale dispersion dominated those of small-scale turbulent diffusion for both cases, and Pasquill's (1962) delayed-shear-enhancement mechanism for lateral dispersion was found to be particularly important. This study was also the first quantitative evaluation of the CSU mesoscale dispersion modelling system with episodic mesoscale dispersion field data. The modelling system showed considerable skill in predicting quantitative tracer-cloud characteristics such as peak concentration, maximum cloud width, arrival time, transit time, and crosswind integrated exposure. Model predictions also compared favorably with predictions made by a number of other mesoscale dispersion models for the same two case studies.

  10. Pillars and globules at the edges of H ii regions. Confronting Herschel observations and numerical simulations

    NASA Astrophysics Data System (ADS)

    Tremblin, P.; Minier, V.; Schneider, N.; Audit, E.; Hill, T.; Didelon, P.; Peretto, N.; Arzoumanian, D.; Motte, F.; Zavagno, A.; Bontemps, S.; Anderson, L. D.; André, Ph.; Bernard, J. P.; Csengeri, T.; Di Francesco, J.; Elia, D.; Hennemann, M.; Könyves, V.; Marston, A. P.; Nguyen Luong, Q.; Rivera-Ingraham, A.; Roussel, H.; Sousbie, T.; Spinoglio, L.; White, G. J.; Williams, J.

    2013-12-01

    Context. Herschel far-infrared imaging observations have revealed the density structure of the interface between H ii regions and molecular clouds in great detail. In particular, pillars and globules are present in many high-mass star-forming regions, such as the Eagle nebula (M 16) and the Rosette molecular cloud, and understanding their origin will help characterize triggered star formation. Aims: The formation mechanisms of these structures are still being debated. The initial morphology of the molecular cloud and its turbulent state are key parameters since they generate deformations and curvatures of the shell during the expansion of the H ii region. Recent numerical simulations have shown how pillars can arise from the collapse of the shell in on itself and how globules can be formed from the interplay of the turbulent molecular cloud and the ionization from massive stars. The goal here is to test this scenario through recent observations of two massive star-forming regions, M 16 and the Rosette molecular cloud. Methods: First, the column density structure of the interface between molecular clouds and associated H ii regions was characterized using column density maps obtained from far-infrared imaging of the Herschel HOBYS key programme. Then, the DisPerSe algorithm was used on these maps to detect the compressed layers around the ionized gas and pillars in different evolutionary states. Column density profiles were constructed. Finally, their velocity structure was investigated using CO data, and all observational signatures were tested against some distinct diagnostics established from simulations. Results: The column density profiles have revealed the importance of compression at the edge of the ionized gas. The velocity properties of the structures, i.e. pillars and globules, are very close to what we predict from the numerical simulations. We have identified a good candidate of a nascent pillar in the Rosette molecular cloud that presents the velocity

  11. A Novel Numerical Method for Fuzzy Boundary Value Problems

    NASA Astrophysics Data System (ADS)

    Can, E.; Bayrak, M. A.; Hicdurmaz

    2016-05-01

    In the present paper, a new numerical method is proposed for solving fuzzy differential equations which are utilized for the modeling problems in science and engineering. Fuzzy approach is selected due to its important applications on processing uncertainty or subjective information for mathematical models of physical problems. A second-order fuzzy linear boundary value problem is considered in particular due to its important applications in physics. Moreover, numerical experiments are presented to show the effectiveness of the proposed numerical method on specific physical problems such as heat conduction in an infinite plate and a fin.

  12. Improvements of the KIVA-II computer program for numerical combustion

    NASA Astrophysics Data System (ADS)

    O'Rourke, P. J.; Amsden, A. A.; Butler, T. D.; McKinley, T. L.

    This paper describes and illustrates the principal differences between the newly-released KIVA-II and the KIVA computer programs. Both programs are for the numerical calculation of two- and three-dimensional fluid flows with chemical reactions and sprays. Because of improvements to KIVA-II, it is faster, more accurate, and applicable to a wider variety of problems involving combustion and two-phase flow.

  13. Asymptotic-induced numerical methods for conservation laws

    NASA Technical Reports Server (NTRS)

    Garbey, Marc; Scroggs, Jeffrey S.

    1990-01-01

    Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.

  14. Parallel processing numerical method for confined vortex dynamics and applications

    NASA Astrophysics Data System (ADS)

    Bistrian, Diana Alina

    2013-10-01

    This paper explores a combined analytical and numerical technique to investigate the hydrodynamic instability of confined swirling flows, with application to vortex rope dynamics in a Francis turbine diffuser, in condition of sophisticated boundary constraints. We present a new approach based on the method of orthogonal decomposition in the Hilbert space, implemented with a spectral descriptor scheme in discrete space. A parallel implementation of the numerical scheme is conducted reducing the computational time compared to other techniques.

  15. Investigating Convergence Patterns for Numerical Methods Using Data Analysis

    ERIC Educational Resources Information Center

    Gordon, Sheldon P.

    2013-01-01

    The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…

  16. Collocation Method for Numerical Solution of Coupled Nonlinear Schroedinger Equation

    SciTech Connect

    Ismail, M. S.

    2010-09-30

    The coupled nonlinear Schroedinger equation models several interesting physical phenomena presents a model equation for optical fiber with linear birefringence. In this paper we use collocation method to solve this equation, we test this method for stability and accuracy. Numerical tests using single soliton and interaction of three solitons are used to test the resulting scheme.

  17. A numerical method for solving singular De`s

    SciTech Connect

    Mahaver, W.T.

    1996-12-31

    A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

  18. A new numerical method of total solar eclipse photography processing

    NASA Astrophysics Data System (ADS)

    Druckmüller, M.; Rušin, V.; Minarovjech, M.

    2006-10-01

    A new numerical method of image processing suitable for visualization of corona images taken during total solar eclipses is presented. This method allows us to study both small- and large-scale coronal structures that remain invisible on original images because of their very high dynamic range of the coronal brightness. The method is based on the use of adaptive filters inspired by human vision and the sensitivity of resulting images is thus very close to that of the human eye during an eclipse. A high precision alignment method for white-light corona images is also discussed. The proposed method highly improves a widely used unsharp masking method employing a radially blurred mask. The results of these numerical image processing techniques are illustrated by a series of images taken during eclipses of the last decade. The method minimizes the risk of processing artifacts.

  19. 25 Years of Self-organized Criticality: Numerical Detection Methods

    NASA Astrophysics Data System (ADS)

    McAteer, R. T. James; Aschwanden, Markus J.; Dimitropoulou, Michaila; Georgoulis, Manolis K.; Pruessner, Gunnar; Morales, Laura; Ireland, Jack; Abramenko, Valentyna

    2016-01-01

    The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.

  20. Comparison of methods for numerical calculation of continuum damping

    SciTech Connect

    Bowden, G. W.; Hole, M. J.; Dennis, G. R.; Könies, A.; Gorelenkov, N. N.

    2014-05-15

    Continuum resonance damping is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this damping, particularly, in the case of the toroidicity-induced shear Alfvén eigenmode. This paper compares results obtained using an analytical perturbative approach with those found using resistive and complex contour numerical approaches. It is found that the perturbative method does not provide accurate agreement with reliable numerical methods for the range of parameters examined. This discrepancy exists even in the limit where damping approaches zero. When the perturbative technique is implemented using a standard finite element method, the damping estimate fails to converge with radial grid resolution. The finite elements used cannot accurately represent the eigenmode in the region of the continuum resonance, regardless of the number of radial grid points used.

  1. Numerical Methods in Quantum Mechanics: Analysis of Numerical Schemes on One-Dimensional Schrodinger Wave Problems

    NASA Astrophysics Data System (ADS)

    Jones, Marvin Quenten, Jr.

    The motion and behavior of quantum processes can be described by the Schrodinger equation using the wave function, Psi(x,t). The use of the Schrodinger equation to study quantum phenomena is known as Quantum Mechanics, akin to classical mechanics being the tool to study classical physics. This research focuses on the emphasis of numerical techniques: Finite-Difference, Fast Fourier Transform (spectral method), finite difference schemes such as the Leapfrog method and the Crank-Nicolson scheme and second quantization to solve and analyze the Schrodinger equation for the infinite square well problem, the free particle with periodic boundary conditions, the barrier problem, tight-binding hamiltonians and a potential wall problem. We discuss these techniques and the problems created to test how these different techniques draw both physical and numerical conclusions in a tabular summary. We observed both numerical stability and quantum stability (conservation of energy, probability, momentum, etc.). We found in our results that the Crank-Nicolson scheme is an unconditionally stable scheme and conserves probability (unitary), and momentum, though dissipative with energy. The time-independent problems conserved energy, momentum and were unitary, which is of interest, but we found when time-dependence was introduced, quantum stability (i.e. conservation of mass, momentum, etc.) was not implied by numerical stability. Hence, we observed schemes that were numerically stable, but not quantum stable as well as schemes that were quantum stable, but not numerically stable for all of time, t. We also observed that second quantization removed the issues with stability as the problem was transformed into a discrete problem. Moreover, all quantum information is conserved in second quantization. This method, however, does not work universally for all problems.

  2. Numerical modeling of magnetic induction tomography using the impedance method.

    PubMed

    Ramos, Airton; Wolff, Julia G B

    2011-02-01

    This article discusses the impedance method in the forward calculation in magnetic induction tomography (MIT). Magnetic field and eddy current distributions were obtained numerically for a sphere in the field of a coil and were compared with an analytical model. Additionally, numerical and experimental results for phase sensitivity in MIT were obtained and compared for a cylindrical object in a planar array of sensors. The results showed that the impedance method provides results that agree very well with reality in the frequency range from 100 kHz to 20 MHz and for low conductivity objects (10 S/m or less). This opens the possibility of using this numerical approach in image reconstruction in MIT. PMID:21229327

  3. Numerical Predictions of Wind Turbine Power and Aerodynamic Loads for the NREL Phase II and IV Combined Experiment Rotor

    NASA Technical Reports Server (NTRS)

    Duque, Earl P. N.; Johnson, Wayne; vanDam, C. P.; Chao, David D.; Cortes, Regina; Yee, Karen

    1999-01-01

    Accurate, reliable and robust numerical predictions of wind turbine rotor power remain a challenge to the wind energy industry. The literature reports various methods that compare predictions to experiments. The methods vary from Blade Element Momentum Theory (BEM), Vortex Lattice (VL), to variants of Reynolds-averaged Navier-Stokes (RaNS). The BEM and VL methods consistently show discrepancies in predicting rotor power at higher wind speeds mainly due to inadequacies with inboard stall and stall delay models. The RaNS methodologies show promise in predicting blade stall. However, inaccurate rotor vortex wake convection, boundary layer turbulence modeling and grid resolution has limited their accuracy. In addition, the inherently unsteady stalled flow conditions become computationally expensive for even the best endowed research labs. Although numerical power predictions have been compared to experiment. The availability of good wind turbine data sufficient for code validation experimental data that has been extracted from the IEA Annex XIV download site for the NREL Combined Experiment phase II and phase IV rotor. In addition, the comparisons will show data that has been further reduced into steady wind and zero yaw conditions suitable for comparisons to "steady wind" rotor power predictions. In summary, the paper will present and discuss the capabilities and limitations of the three numerical methods and make available a database of experimental data suitable to help other numerical methods practitioners validate their own work.

  4. Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems

    SciTech Connect

    Cai, Wei

    2014-05-15

    Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equations such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.

  5. COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE

    SciTech Connect

    Kritsuk, Alexei G.; Collins, David; Norman, Michael L.; Xu Hao E-mail: dccollins@lanl.gov

    2011-08-10

    Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the

  6. A novel gas-droplet numerical method for spray combustion

    NASA Technical Reports Server (NTRS)

    Chen, C. P.; Shang, H. M.; Jiang, Y.

    1991-01-01

    This paper presents a non-iterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully-interacting combination of Eulerian fluid and Lagrangian particle calculation. The interaction calculations between the two phases are formulated on a pressure-velocity coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell (PSIC) procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data, as well as efficiency assessments are given for some sprays typical of spray combustion applications.

  7. Simple numerical method for predicting steady compressible flows

    NASA Technical Reports Server (NTRS)

    Vonlavante, Ernst; Nelson, N. Duane

    1986-01-01

    A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.

  8. Singularity Preserving Numerical Methods for Boundary Integral Equations

    NASA Technical Reports Server (NTRS)

    Kaneko, Hideaki (Principal Investigator)

    1996-01-01

    In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

  9. The development of accurate and efficient methods of numerical quadrature

    NASA Technical Reports Server (NTRS)

    Feagin, T.

    1973-01-01

    Some new methods for performing numerical quadrature of an integrable function over a finite interval are described. Each method provides a sequence of approximations of increasing order to the value of the integral. Each approximation makes use of all previously computed values of the integrand. The points at which new values of the integrand are computed are selected in such a way that the order of the approximation is maximized. The methods are compared with the quadrature methods of Clenshaw and Curtis, Gauss, Patterson, and Romberg using several examples.

  10. The TAB method for numerical calculation of spray droplet breakup

    NASA Astrophysics Data System (ADS)

    Orourke, P. J.; Amsden, A. A.

    A short history is given of the major milestones in the development of the stochastic particle method for calculating liquid fuel sprays. The most recent advance has been the discovery of the importance of drop breakup in engine sprays. A new method, called TAB, for calculating drop breakup is presented. Some theoretical properties of the method are derived; its numerical implementation in the computer program KIVA is described; and comparisons are presented between TAB-method calculations and experiments and calculations using another breakup model.

  11. A numerical method for interface problems in elastodynamics

    NASA Technical Reports Server (NTRS)

    Mcghee, D. S.

    1984-01-01

    The numerical implementation of a formulation for a class of interface problems in elastodynamics is discussed. This formulation combines the use of the finite element and boundary integral methods to represent the interior and the exteriro regions, respectively. In particular, the response of a semicylindrical alluvial valley in a homogeneous halfspace to incident antiplane SH waves is considered to determine the accuracy and convergence of the numerical procedure. Numerical results are obtained from several combinations of the incidence angle, frequency of excitation, and relative stiffness between the inclusion and the surrounding halfspace. The results tend to confirm the theoretical estimates that the convergence is of the order H(2) for the piecewise linear elements used. It was also observed that the accuracy descreases as the frequency of excitation increases or as the relative stiffness of the inclusion decreases.

  12. 2D/1D approximations to the 3D neutron transport equation. II: Numerical comparisons

    SciTech Connect

    Kelley, B. W.; Collins, B.; Larsen, E. W.

    2013-07-01

    In a companion paper [1], (i) several new '2D/1D equations' are introduced as accurate approximations to the 3D Boltzmann transport equation, (ii) the simplest of these approximate equations is systematically discretized, and (iii) a theoretically stable iteration scheme is developed to solve the discrete equations. In this paper, numerical results are presented that confirm the theoretical predictions made in [1]. (authors)

  13. Numerical simulation methods for the Rouse model in flow

    NASA Astrophysics Data System (ADS)

    Howard, Michael P.; Milner, Scott T.

    2011-11-01

    Simulation of the Rouse model in flow underlies a great variety of numerical investigations of polymer dynamics, in both entangled melts and solutions and in dilute solution. Typically a simple explicit stochastic Euler method is used to evolve the Rouse model. Here we compare this approach to an operator splitting method, which splits the evolution operator into stochastic linear and deterministic nonlinear parts and takes advantage of an analytical solution for the linear Rouse model in terms of the noise history. We show that this splitting method has second-order weak convergence, whereas the Euler method has only first-order weak convergence. Furthermore, the splitting method is unconditionally stable, in contrast to the limited stability range of the Euler method. Similar splitting methods are applicable to a broad class of problems in stochastic dynamics in which noise competes with ordering and flow to determine steady-state order parameter structures.

  14. Numerical Polynomial Homotopy Continuation Method and String Vacua

    DOE PAGESBeta

    Mehta, Dhagash

    2011-01-01

    Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less

  15. Numerical methods for characterization of synchrotron radiation based on the Wigner function method

    NASA Astrophysics Data System (ADS)

    Tanaka, Takashi

    2014-06-01

    Numerical characterization of synchrotron radiation based on the Wigner function method is explored in order to accurately evaluate the light source performance. A number of numerical methods to compute the Wigner functions for typical synchrotron radiation sources such as bending magnets, undulators and wigglers, are presented, which significantly improve the computation efficiency and reduce the total computation time. As a practical example of the numerical characterization, optimization of betatron functions to maximize the brilliance of undulator radiation is discussed.

  16. Projected discrete ordinates methods for numerical transport problems

    SciTech Connect

    Larsen, E.W.

    1985-01-01

    A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.

  17. Computational methods for aerodynamic design using numerical optimization

    NASA Technical Reports Server (NTRS)

    Peeters, M. F.

    1983-01-01

    Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.

  18. Fast and stable numerical method for neuronal modelling

    NASA Astrophysics Data System (ADS)

    Hashemi, Soheil; Abdolali, Ali

    2016-11-01

    Excitable cell modelling is of a prime interest in predicting and targeting neural activity. Two main limits in solving related equations are speed and stability of numerical method. Since there is a tradeoff between accuracy and speed, most previously presented methods for solving partial differential equations (PDE) are focused on one side. More speed means more accurate simulations and therefore better device designing. By considering the variables in finite differenced equation in proper time and calculating the unknowns in the specific sequence, a fast, stable and accurate method is introduced in this paper for solving neural partial differential equations. Propagation of action potential in giant axon is studied by proposed method and traditional methods. Speed, consistency and stability of the methods are compared and discussed. The proposed method is as fast as forward methods and as stable as backward methods. Forward methods are known as fastest methods and backward methods are stable in any circumstances. Complex structures can be simulated by proposed method due to speed and stability of the method.

  19. Automatic numerical integration methods for Feynman integrals through 3-loop

    NASA Astrophysics Data System (ADS)

    de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.

    2015-05-01

    We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.

  20. Numerical method for shear bands in ductile metal with inclusions

    SciTech Connect

    Plohr, Jee Yeon N; Plohr, Bradley J

    2010-01-01

    A numerical method for mesoscale simulation of high strain-rate loading of ductile metal containing inclusions is described. Because of small-scale inhomogeneities, such a composite material is prone to localized shear deformation (adiabatic shear bands). The modeling framework is the Generalized Method of Cells of Paley and Aboudi [Mech. Materials, vol. 14, pp. /27-139, 1992], which ensures that the micromechanical response of the material is reflected in the behavior of the composite at the mesoscale. To calculate the effective plastic strain rate when shear bands are present, the analytic and numerical analysis of shear bands by Glimm, Plohr, and Sharp [Mech. Materials, vol. 24, pp. 31-41, 1996] is adapted and extended.

  1. Numerical Method for the Astronomical Almanac and Orbit Calculations

    NASA Astrophysics Data System (ADS)

    Kim, Kap-Sung

    1993-12-01

    We have calculated the astronomical almanac 1994 and simulated the trajectory of a satellite orbit considering all perturbative forces with various initial conditions. In this work, Gauss Jackson multistep integration method has been used to calculate our basic equation of motion with high numerical accuracy. It has been found that our results agree well with the Astronomical Almanac Data distributed by JPL of NASA and the orbit simulations have been carried out with fast speed, stability and excellent round-off error accumulation, comparing with other numerical methods. In order to be carried out our works on almanac and orbit calculations easily by anyone who uses a personal computer, we have made a computer program on graphical user interface to provide various menus for detail works selected by a mouse.

  2. Asymptotic and Numerical Methods for Rapidly Rotating Buoyant Flow

    NASA Astrophysics Data System (ADS)

    Grooms, Ian G.

    This thesis documents three investigations carried out in pursuance of a doctoral degree in applied mathematics at the University of Colorado (Boulder). The first investigation concerns the properties of rotating Rayleigh-Benard convection -- thermal convection in a rotating infinite plane layer between two constant-temperature boundaries. It is noted that in certain parameter regimes convective Taylor columns appear which dominate the dynamics, and a semi-analytical model of these is presented. Investigation of the columns and of various other properties of the flow is ongoing. The second investigation concerns the interactions between planetary-scale and mesoscale dynamics in the oceans. Using multiple-scale asymptotics the possible connections between planetary geostrophic and quasigeostrophic dynamics are investigated, and three different systems of coupled equations are derived. Possible use of these equations in conjunction with the method of superparameterization, and extension of the asymptotic methods to the interactions between mesoscale and submesoscale dynamics is ongoing. The third investigation concerns the linear stability properties of semi-implicit methods for the numerical integration of ordinary differential equations, focusing in particular on the linear stability of IMEX (Implicit-Explicit) methods and exponential integrators applied to systems of ordinary differential equations arising in the numerical solution of spatially discretized nonlinear partial differential equations containing both dispersive and dissipative linear terms. While these investigations may seem unrelated at first glance, some reflection shows that they are in fact closely linked. The investigation of rotating convection makes use of single-space, multiple-time-scale asymptotics to deal with dynamics strongly constrained by rotation. Although the context of thermal convection in an infinite layer seems somewhat removed from large-scale ocean dynamics, the asymptotic

  3. Efficient and accurate numerical methods for the Klein-Gordon-Schroedinger equations

    SciTech Connect

    Bao, Weizhu . E-mail: bao@math.nus.edu.sg; Yang, Li . E-mail: yangli@nus.edu.sg

    2007-08-10

    In this paper, we present efficient, unconditionally stable and accurate numerical methods for approximations of the Klein-Gordon-Schroedinger (KGS) equations with/without damping terms. The key features of our methods are based on: (i) the application of a time-splitting spectral discretization for a Schroedinger-type equation in KGS (ii) the utilization of Fourier pseudospectral discretization for spatial derivatives in the Klein-Gordon equation in KGS (iii) the adoption of solving the ordinary differential equations (ODEs) in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying Crank-Nicolson/leap-frog for linear/nonlinear terms for time derivatives. The numerical methods are either explicit or implicit but can be solved explicitly, unconditionally stable, and of spectral accuracy in space and second-order accuracy in time. Moreover, they are time reversible and time transverse invariant when there is no damping terms in KGS, conserve (or keep the same decay rate of) the wave energy as that in KGS without (or with a linear) damping term, keep the same dynamics of the mean value of the meson field, and give exact results for the plane-wave solution. Extensive numerical tests are presented to confirm the above properties of our numerical methods for KGS. Finally, the methods are applied to study solitary-wave collisions in one dimension (1D), as well as dynamics of a 2D problem in KGS.

  4. An alternative numerical method for the stationary pulsar magnetosphere

    NASA Astrophysics Data System (ADS)

    Takamori, Yohsuke; Okawa, Hirotada; Takamoto, Makoto; Suwa, Yudai

    2014-02-01

    Stationary pulsar magnetospheres in the force-free system are governed by the pulsar equation. In 1999, Contopoulos, Kazanas, and Fendt (hereafter CKF) numerically solved the pulsar equation and obtained a pulsar magnetosphere model called the CKF solution that has both closed and open magnetic field lines. The CKF solution is a successful solution, but it contains a poloidal current sheet that flows along the last open field line. This current sheet is artificially added to make the current system closed. In this paper, we suggest an alternative method to solve the pulsar equation and construct pulsar magnetosphere models without a current sheet. In our method, the pulsar equation is decomposed into Ampère's law and the force-free condition. We numerically solve these equations simultaneously with a fixed poloidal current. As a result, we obtain a pulsar magnetosphere model without a current sheet, which is similar to the CKF solution near the neutron star and has a jet-like structure at a distance along the pole. In addition, we discuss physical properties of the model and find that the force-free condition breaks down in a vicinity of the light cylinder due to dissipation that is included implicitly in the numerical method.

  5. [Numerical methods for multi-fluid flows]. Final progress report

    SciTech Connect

    Pozrikidis, C.

    1998-07-21

    The central objective of this research has been to develop efficient numerical methods for computing multi-fluid flows with large interfacial deformations, and apply these methods to study the rheology of suspensions of deformable particles with viscous and non-Newtonian interfacial behavior. The mathematical formulation employs boundary-integral, immersed-boundary, and related numerical methods. Particles of interest include liquid drops with constant surface tension and capsules whose interfaces exhibit viscoelastic and incompressible characteristics. In one family of problems, the author has considered the shear-driven and pressure-driven flow of a suspension of two-dimensional liquid drops with ordered and random structure. In a second series of investigations, the author carried out dynamic simulations of two-dimensional, unbounded, doubly-periodic shear flows with random structure. Another family of problems addresses the deformation of three-dimensional capsules whose interfaces exhibit isotropic surface tension, viscous, elastic, or incompressible behavior, in simple shear flow. The numerical results extend previous asymptotic theories for small deformations and illuminate the mechanism of membrane rupture.

  6. Numerical method for wave forces acting on partially perforated caisson

    NASA Astrophysics Data System (ADS)

    Jiang, Feng; Tang, Xiao-cheng; Jin, Zhao; Zhang, Li; Chen, Hong-zhou

    2015-04-01

    The perforated caisson is widely applied to practical engineering because of its great advantages in effectively wave energy consumption and cost reduction. The attentions of many scientists were paid to the fluid-structure interaction between wave and perforated caisson studies, but until now, most concerns have been put on theoretical analysis and experimental model set up. In this paper, interaction between the wave and the partial perforated caisson in a 2D numerical wave flume is investigated by means of the renewed SPH algorithm, and the mathematical equations are in the form of SPH numerical approximation based on Navier-Stokes equations. The validity of the SPH mathematical method is examined and the simulated results are compared with the results of theoretical models, meanwhile the complex hydrodynamic characteristics when the water particles flow in or out of a wave absorbing chamber are analyzed and the wave pressure distribution of the perforated caisson is also addressed here. The relationship between the ratio of total horizontal force acting on caisson under regular waves and its influence factors is examined. The data show that the numerical calculation of the ratio of total horizontal force meets the empirical regression equation very well. The simulations of SPH about the wave nonlinearity and breaking are briefly depicted in the paper, suggesting that the advantages and great potentiality of the SPH method is significant compared with traditional methods.

  7. The instanton method and its numerical implementation in fluid mechanics

    NASA Astrophysics Data System (ADS)

    Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

    2015-08-01

    A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.

  8. Dielectric Boundary Forces in Numerical Poisson-Boltzmann Methods: Theory and Numerical Strategies.

    PubMed

    Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

    2011-10-01

    Continuum modeling of electrostatic interactions based upon the numerical solutions of the Poisson-Boltzmann equation has been widely adopted in biomolecular applications. To extend their applications to molecular dynamics and energy minimization, robust and efficient methodologies to compute solvation forces must be developed. In this study, we have first reviewed the theory for the computation of dielectric boundary forces based on the definition of the Maxwell stress tensor. This is followed by a new formulation of the dielectric boundary force suitable for the finite-difference Poisson-Boltzmann methods. We have validated the new formulation with idealized analytical systems and realistic molecular systems. PMID:22125339

  9. Dielectric boundary force in numerical Poisson-Boltzmann methods: Theory and numerical strategies

    NASA Astrophysics Data System (ADS)

    Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

    2011-10-01

    Continuum modeling of electrostatic interactions based upon the numerical solutions of the Poisson-Boltzmann equation has been widely adopted in biomolecular applications. To extend their applications to molecular dynamics and energy minimization, robust and efficient methodologies to compute solvation forces must be developed. In this study, we have first reviewed the theory for the computation of dielectric boundary force based on the definition of the Maxwell stress tensor. This is followed by a new formulation of the dielectric boundary force suitable for the finite-difference Poisson-Boltzmann methods. We have validated the new formulation with idealized analytical systems and realistic molecular systems.

  10. Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

    NASA Astrophysics Data System (ADS)

    Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

    2015-05-01

    We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

  11. Numerical methods for scattering from electrically large objects

    NASA Astrophysics Data System (ADS)

    Enguist, Bjorn; Murphy, W. D.; Rokhlin, Vladimir; Vassiliou, Marius S.

    1991-05-01

    A new and computationally very efficient integral equation numerical method for computing electromagnetic scattering and radar cross section (RCS) was developed. A theory of higher order impedance boundary conditions was derived to handle single and multiple dielectric coatings around conductors. The method was tested in two dimensions using a 14,000-line FORTRAN program and was found to be very promising for electrically large objects. Initial ideas for extensions to three dimensions were explored. Treatments of trailing edge and corner singularities were developed.

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

    SciTech Connect

    Lucas, D.S.

    2004-10-03

    This paper covers the basics of the implementation of the control volume method in the context of the Homogeneous Equilibrium Model (HEM)(T/H) code using the conservation equations of mass, momentum, and energy. This primer uses the advection equation as a template. The discussion will cover the basic equations of the control volume portion of the course in the primer, which includes the advection equation, numerical methods, along with the implementation of the various equations via FORTRAN into computer programs and the final result for a three equation HEM code and its validation.

  13. Integrated numerical methods for hypersonic aircraft cooling systems analysis

    NASA Technical Reports Server (NTRS)

    Petley, Dennis H.; Jones, Stuart C.; Dziedzic, William M.

    1992-01-01

    Numerical methods have been developed for the analysis of hypersonic aircraft cooling systems. A general purpose finite difference thermal analysis code is used to determine areas which must be cooled. Complex cooling networks of series and parallel flow can be analyzed using a finite difference computer program. Both internal fluid flow and heat transfer are analyzed, because increased heat flow causes a decrease in the flow of the coolant. The steady state solution is a successive point iterative method. The transient analysis uses implicit forward-backward differencing. Several examples of the use of the program in studies of hypersonic aircraft and rockets are provided.

  14. Optimization methods and silicon solar cell numerical models

    NASA Technical Reports Server (NTRS)

    Girardini, K.; Jacobsen, S. E.

    1986-01-01

    An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.

  15. Numerical methods for the Poisson-Fermi equation in electrolytes

    NASA Astrophysics Data System (ADS)

    Liu, Jinn-Liang

    2013-08-01

    The Poisson-Fermi equation proposed by Bazant, Storey, and Kornyshev [Phys. Rev. Lett. 106 (2011) 046102] for ionic liquids is applied to and numerically studied for electrolytes and biological ion channels in three-dimensional space. This is a fourth-order nonlinear PDE that deals with both steric and correlation effects of all ions and solvent molecules involved in a model system. The Fermi distribution follows from classical lattice models of configurational entropy of finite size ions and solvent molecules and hence prevents the long and outstanding problem of unphysical divergence predicted by the Gouy-Chapman model at large potentials due to the Boltzmann distribution of point charges. The equation reduces to Poisson-Boltzmann if the correlation length vanishes. A simplified matched interface and boundary method exhibiting optimal convergence is first developed for this equation by using a gramicidin A channel model that illustrates challenging issues associated with the geometric singularities of molecular surfaces of channel proteins in realistic 3D simulations. Various numerical methods then follow to tackle a range of numerical problems concerning the fourth-order term, nonlinearity, stability, efficiency, and effectiveness. The most significant feature of the Poisson-Fermi equation, namely, its inclusion of steric and correlation effects, is demonstrated by showing good agreement with Monte Carlo simulation data for a charged wall model and an L type calcium channel model.

  16. Comparative analysis of numerical estimation methods of epithelial nerve fibers using tissue sections.

    PubMed

    Hilliges, M; Johansson, O

    1999-01-01

    The proper assessment of neuron numbers in the nervous system during physiological and pathological conditions, as well as following various treatments, has always been an important part of neuroscience. The present paper evaluates three methods for numerical estimates of nerves in epithelium: I) unbiased nerve fiber profile and nerve fiber fragment estimation methods, II) the traditional method of counting whole nerve fibers, and III) the nerve fiber estimation method. In addition, an unbiased nerve length estimation method was evaluated. Of these four methods, the nerve length per volume method was theoretically optimal, but more time-consuming than the others. The numbers obtained with the methods of nerve fiber profile, nerve fragment and nerve fiber estimation are dependent on the thickness of the epithelium and the sections as well as certain shape factors of the counted fiber. However for those, the actual counting can readily be performed in the microscope and is consequently quick and relatively inexpensive. The statistical analysis showed a very good correlation (R > 0.96) between the three numerical methods, meaning that basically any method could be used. However, dependent on theoretical and practical considerations and the correlation statistics, it may be concluded that the nerve fiber profile or fragment estimation methods should be employed if differences in epithelial and section thickness and the nerve fibers shape factors can be controlled. Such drawbacks are not inherent in the nerve length estimation method and, thus, it can generally be applied. PMID:10197065

  17. Numerical integration of population models satisfying conservation laws: NSFD methods.

    PubMed

    Mickens, Ronald E

    2007-10-01

    Population models arising in ecology, epidemiology and mathematical biology may involve a conservation law, i.e. the total population is constant. In addition to these cases, other situations may occur for which the total population, asymptotically in time, approach a constant value. Since it is rarely the situation that the equations of motion can be analytically solved to obtain exact solutions, it follows that numerical techniques are needed to provide solutions. However, numerical procedures are only valid if they can reproduce fundamental properties of the differential equations modeling the phenomena of interest. We show that for population models, involving a dynamical conservation law the use of nonstandard finite difference (NSFD) methods allows the construction of discretization schemes such that they are dynamically consistent (DC) with the original differential equations. The paper will briefly discuss the NSFD methodology, the concept of DC, and illustrate their application to specific problems for population models. PMID:22876826

  18. A Numerical Method for Solving Elasticity Equations with Interfaces

    PubMed Central

    Li, Zhilin; Wang, Liqun; Wang, Wei

    2012-01-01

    Solving elasticity equations with interfaces is a challenging problem for most existing methods. Nonetheless, it has wide applications in engineering and science. An accurate and efficient method is desired. In this paper, an efficient non-traditional finite element method with non-body-fitting grids is proposed to solve elasticity equations with interfaces. The main idea is to choose the test function basis to be the standard finite element basis independent of the interface and to choose the solution basis to be piecewise linear satisfying the jump conditions across the interface. The resulting linear system of equations is shown to be positive definite under certain assumptions. Numerical experiments show that this method is second order accurate in the L∞ norm for piecewise smooth solutions. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interface corner. PMID:22707984

  19. Time-dependent corona models - A numerical method

    NASA Astrophysics Data System (ADS)

    Korevaar, P.; van Leer, B.

    1988-07-01

    A time-dependent numerical method for calculating gas flows is described. The method is implicit and especially suitable for finding stationary flow solutions. Although the method is general in its application to ideal compressible fluids, this paper applies it to a stellar atmosphere, heated to coronal temperatures by dissipation of mechanical energy. The integration scheme is based on conservative upwind spatial differencing. The upwind switching is provided by Van Leer's method of differentiable flux-splitting. It is shown that the code can handle large differences in density: up to 14 orders of magnitude. Special attention is paid to the boundary conditions, which are made completely transparent to disturbances. Besides some test-results, converged solutions for various values of the initial mechanical flux are presented which are in good agreement with previous time-independent calculations.

  20. Advanced numerical methods in mesh generation and mesh adaptation

    SciTech Connect

    Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A

    2010-01-01

    Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge

  1. Novel Parallel Numerical Methods for Radiation& Neutron Transport

    SciTech Connect

    Brown, P N

    2001-03-06

    In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both.

  2. Numerical Analysis of Blood Damage Potential of the HeartMate II and HeartWare HVAD Rotary Blood Pumps.

    PubMed

    Thamsen, Bente; Blümel, Bastian; Schaller, Jens; Paschereit, Christian O; Affeld, Klaus; Goubergrits, Leonid; Kertzscher, Ulrich

    2015-08-01

    Implantable left ventricular assist devices (LVADs) became the therapy of choice in treating end-stage heart failure. Although survival improved substantially and is similar in currently clinically implanted LVADs HeartMate II (HM II) and HeartWare HVAD, complications related to blood trauma are frequently observed. The aim of this study was to compare these two pumps regarding their potential blood trauma employing computational fluid dynamics. High-resolution structured grids were generated for the pumps. Newtonian flow was calculated, solving Reynolds-averaged Navier-Stokes equations with a sliding mesh approach and a k-ω shear stress transport turbulence model for the operating point of 4.5 L/min and 80 mm Hg. The pumps were compared in terms of volumes subjected to certain viscous shear stress thresholds, below which no trauma was assumed (von Willebrand factor cleavage: 9 Pa, platelet activation: 50 Pa, and hemolysis: 150 Pa), and associated residence times. Additionally, a hemolysis index was calculated based on a Eulerian transport approach. Twenty-two percent of larger volumes above 9 Pa were observed in the HVAD; above 50 Pa and 150 Pa the differences between the two pumps were marginal. Residence times were higher in the HVAD for all thresholds. The hemolysis index was almost equal for the HM II and HVAD. Besides the gap regions in both pumps, the inlet regions of the rotor and diffuser blades have a high hemolysis production in the HM II, whereas in the HVAD, the volute tongue is an additional site for hemolysis production. Thus, in this study, the comparison of the HM II and the HVAD using numerical methods indicated an overall similar tendency to blood trauma in both pumps. However, influences of turbulent shear stresses were not considered and effects of the pivot bearing in the HM II were not taken into account. Further in vitro investigations are required. PMID:26234447

  3. Numerical study of the Columbia high-beta device: Torus-II

    SciTech Connect

    Izzo, R.

    1981-01-01

    The ionization, heating and subsequent long-time-scale behavior of the helium plasma in the Columbia fusion device, Torus-II, is studied. The purpose of this work is to perform numerical simulations while maintaining a high level of interaction with experimentalists. The device is operated as a toroidal z-pinch to prepare the gas for heating. This ionization of helium is studied using a zero-dimensional, two-fluid code. It is essentially an energy balance calculation that follows the development of the various charge states of the helium and any impurities (primarily silicon and oxygen) that are present. The code is an atomic physics model of Torus-II. In addition to ionization, we include three-body and radiative recombination processes.

  4. Comparison of four stable numerical methods for Abel's integral equation

    NASA Technical Reports Server (NTRS)

    Murio, Diego A.; Mejia, Carlos E.

    1991-01-01

    The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.

  5. Numerical Analysis of a Finite Element/Volume Penalty Method

    NASA Astrophysics Data System (ADS)

    Maury, Bertrand

    The penalty method makes it possible to incorporate a large class of constraints in general purpose Finite Element solvers like freeFEM++. We present here some contributions to the numerical analysis of this method. We propose an abstract framework for this approach, together with some general error estimates based on the discretization parameter ɛ and the space discretization parameter h. As this work is motivated by the possibility to handle constraints like rigid motion for fluid-particle flows, we shall pay a special attention to a model problem of this kind, where the constraint is prescribed over a subdomain. We show how the abstract estimate can be applied to this situation, in the case where a non-body-fitted mesh is used. In addition, we describe how this method provides an approximation of the Lagrange multiplier associated to the constraint.

  6. Numerical Analyses on Transient Thermal Process of Gas - Cooled Current Leads in BEPC II

    NASA Astrophysics Data System (ADS)

    Zhang, X. B.; Yao, Z. L.; Wang, L.; Jia, L. X.

    2004-06-01

    A pair of high current leads will be used for the superconducting detector solenoid magnet and six pairs of low current leads will be used for the superconducting interaction quadruple magnets in the Beijing Electron-Positron Collider Upgrade (BEPC II). This paper reports the numerical analyses on the thermal processes in the current leads, including the power charging process and overloaded current case as well as the transient characteristic of the leads once the helium cooling is interrupted. The design parameters of the current leads are studied for the stable and unstable conditions.

  7. Numerical methods for high-dimensional probability density function equations

    NASA Astrophysics Data System (ADS)

    Cho, H.; Venturi, D.; Karniadakis, G. E.

    2016-01-01

    In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.

  8. Improved numerical method for subchannel cross-flow calculations

    SciTech Connect

    Kaya, S.; Anghaie, S.

    1986-01-01

    COBRA-OSU is a fast running computer code for coupled kinetic and thermal-hydraulic analysis of nuclear reactor core subchannels, currently under development at Oregon State University. This code is a modified version of COBRA-IV with two major improved features. First, COBRA-OSU uses the Gaussian elimination method instead of Gauss-Seidel iteration for subchannel cross-flow calculation. Second, COBRA-OSU has an additional model for regionwise point reactor kinetics which includes all major feedback reactivity effects on calculation of the axial power profile during the course of a transient. This paper summarizes the improved numerical features of the COBRA-OSU code.

  9. Optimization methods and silicon solar cell numerical models

    NASA Technical Reports Server (NTRS)

    Girardini, K.

    1986-01-01

    The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.

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

    SciTech Connect

    D. S. Lucas

    2004-10-01

    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.

  11. Validation of a numerical method for unsteady flow calculations

    SciTech Connect

    Giles, M.; Haimes, R. . Dept. of Aeronautics and Astronautics)

    1993-01-01

    This paper describes and validates a numerical method for the calculation of unsteady inviscid and viscous flows. A companion paper compares experimental measurements of unsteady heat transfer on a transonic rotor with the corresponding computational results. The mathematical model is the Reynolds-averaged unsteady Navier-Stokes equations for a compressible ideal gas. Quasi-three-dimensionality is included through the use of a variable streamtube thickness. The numerical algorithm is unusual in two respects: (a) For reasons of efficiency and flexibility, it uses a hybrid Navier-Stokes/Euler method, and (b) to allow for the computation of stator/rotor combinations with arbitrary pitch ratio, a novel space-time coordinate transformation is used. Several test cases are presented to validate the performance of the computer program, UNSFLO. These include: (a) unsteady, inviscid flat plate cascade flows (b) steady and unsteady, viscous flat plate cascade flows, (c) steady turbine heat transfer and loss prediction. In the first two sets of cases comparisons are made with theory, and in the third the comparison is with experimental data.

  12. Numerical modeling of spray combustion with an advanced VOF method

    NASA Technical Reports Server (NTRS)

    Chen, Yen-Sen; Shang, Huan-Min; Shih, Ming-Hsin; Liaw, Paul

    1995-01-01

    This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.

  13. Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part II. Practical applications

    SciTech Connect

    Saetta, Anna V.; Vitaliani, Renato V

    2005-05-01

    The mathematical-numerical method developed by the authors to predict the corrosion initiation time of reinforced concrete structures due to carbonation process, recalled in Part I of this work, is here applied to some real cases. The final aim is to develop and test a practical method for determining the durability characteristics of existing buildings liable to carbonation, as well as estimating the corrosion initiation time of a building at the design stage. Two industrial sheds with different ages and located in different areas have been analyzed performing both experimental tests and numerical analyses. Finally, a case of carbonation-induced failure in a prestressed r.c. beam is presented.

  14. Asymmetric MRI magnet design using a hybrid numerical method.

    PubMed

    Zhao, H; Crozier, S; Doddrell, D M

    1999-12-01

    This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. PMID:10579958

  15. A Coursewriter II Function (FCALC) For the Manipulation of Numerical and Algebraic Expressions. Systems Memo Number One.

    ERIC Educational Resources Information Center

    Smith, Authella; And Others

    Documentation of the Coursewriter II Function FCALC is provided. The function is designed for use on the IBM 1500 instructional system and has three major applications: 1) comparison of a numeric expression in buffer 5 with a numeric expression in buffer 0; 2) comparison of an algebraic expression in buffer 5 with an algebraic expression in buffer…

  16. A method for improving time-stepping numerics

    NASA Astrophysics Data System (ADS)

    Williams, P. D.

    2012-04-01

    In contemporary numerical simulations of the atmosphere, evidence suggests that time-stepping errors may be a significant component of total model error, on both weather and climate time-scales. This presentation will review the available evidence, and will then suggest a simple but effective method for substantially improving the time-stepping numerics at no extra computational expense. The most common time-stepping method is the leapfrog scheme combined with the Robert-Asselin (RA) filter. This method is used in the following atmospheric models (and many more): ECHAM, MAECHAM, MM5, CAM, MESO-NH, HIRLAM, KMCM, LIMA, SPEEDY, IGCM, PUMA, COSMO, FSU-GSM, FSU-NRSM, NCEP-GFS, NCEP-RSM, NSEAM, NOGAPS, RAMS, and CCSR/NIES-AGCM. Although the RA filter controls the time-splitting instability in these models, it also introduces non-physical damping and reduces the accuracy. This presentation proposes a simple modification to the RA filter. The modification has become known as the RAW filter (Williams 2011). When used in conjunction with the leapfrog scheme, the RAW filter eliminates the non-physical damping and increases the amplitude accuracy by two orders, yielding third-order accuracy. (The phase accuracy remains second-order.) The RAW filter can easily be incorporated into existing models, typically via the insertion of just a single line of code. Better simulations are obtained at no extra computational expense. Results will be shown from recent implementations of the RAW filter in various atmospheric models, including SPEEDY and COSMO. For example, in SPEEDY, the skill of weather forecasts is found to be significantly improved. In particular, in tropical surface pressure predictions, five-day forecasts made using the RAW filter have approximately the same skill as four-day forecasts made using the RA filter (Amezcua, Kalnay & Williams 2011). These improvements are encouraging for the use of the RAW filter in other models.

  17. Shear mixing in stellar radiative zones. II. Robustness of numerical simulations

    NASA Astrophysics Data System (ADS)

    Prat, V.; Guilet, J.; Viallet, M.; Müller, E.

    2016-07-01

    Context. Recent numerical simulations suggest that the model by Zahn (1992, A&A, 265, 115) for the turbulent mixing of chemical elements due to differential rotation in stellar radiative zones is valid. Aims: We investigate the robustness of this result with respect to the numerical configuration and Reynolds number of the flow. Methods: We compare results from simulations performed with two different numerical codes, including one that uses the shearing-box formalism. We also extensively study the dependence of the turbulent diffusion coefficient on the turbulent Reynolds number. Results: The two numerical codes used in this study give consistent results. The turbulent diffusion coefficient is independent of the size of the numerical domain if at least three large turbulent structures fit in the box. Generally, the turbulent diffusion coefficient depends on the turbulent Reynolds number. However, our simulations suggest that an asymptotic regime is obtained when the turbulent Reynolds number is larger than 103. Conclusions: Shear mixing in the regime of small Péclet numbers can be investigated numerically both with shearing-box simulations and simulations using explicit forcing. Our results suggest that Zahn's model is valid at large turbulent Reynolds numbers.

  18. Unsaturated Shear Strength and Numerical Analysis Methods for Unsaturated Soils

    NASA Astrophysics Data System (ADS)

    Kim, D.; Kim, G.; Kim, D.; Baek, H.; Kang, S.

    2011-12-01

    The angles of shearing resistance(φb) and internal friction(φ') appear to be identical in low suction range, but the angle of shearing resistance shows non-linearity as suction increases. In most numerical analysis however, a fixed value for the angle of shearing resistance is applied even in low suction range for practical reasons, often leading to a false conclusion. In this study, a numerical analysis has been undertaken employing the estimated shear strength curve of unsaturated soils from the residual water content of SWCC proposed by Vanapalli et al.(1996). The result was also compared with that from a fixed value of φb. It is suggested that, in case it is difficult to measure the unsaturated shear strength curve through the triaxial soil tests, the estimated shear strength curve using the residual water content can be a useful alternative. This result was applied for analyzing the slope stablity of unsaturated soils. The effects of a continuous rainfall on slope stability were analyzed using a commercial program "SLOPE/W", with the coupled infiltration analysis program "SEEP/W" from the GEO-SLOPE International Ltd. The results show that, prior to the infiltration by the intensive rainfall, the safety factors using the estimated shear strength curve were substantially higher than that from the fixed value of φb at all time points. After the intensive infiltration, both methods showed a similar behavior.

  19. Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods

    NASA Technical Reports Server (NTRS)

    Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark

    2002-01-01

    Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.

  20. A Hybrid Numerical Analysis Method for Structural Health Monitoring

    NASA Technical Reports Server (NTRS)

    Forth, Scott C.; Staroselsky, Alexander

    2001-01-01

    A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

  1. Space-time adaptive numerical methods for geophysical applications.

    PubMed

    Castro, C E; Käser, M; Toro, E F

    2009-11-28

    In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space-time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost. PMID:19840984

  2. Numerical method of characteristics for one-dimensional blood flow

    NASA Astrophysics Data System (ADS)

    Acosta, Sebastian; Puelz, Charles; Rivière, Béatrice; Penny, Daniel J.; Rusin, Craig G.

    2015-08-01

    Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.

  3. Development of numerical methods to problems of micromechanics

    NASA Astrophysics Data System (ADS)

    Garcia-Martinez, Jose Ramon

    In this dissertation we utilize the finite element method to investigate three micromechanical problems. In Chapter 2, we study the compliance contribution tensor H of multiple branched cracks. The cracks grow from a deltoid pore at their center into a triple crack. For plain strain conditions, two-dimensional models of the branched crack are modeled and solved in ABAQUS. The displacement field over the surface of the branched crack and the deltoid is curve fitted to carry out the integral surface of the compliance contribution tensor H. The predicted values are in good agreement with analytical solution. In Chapter 3 a three-dimensional finite element program using an unaligned mesh with an eight-node isoparametric element is developed to study the compliance contribution tensor H of cavities with superellipsoid shapes. A mesh clustering algorithm to increase the number of elements inside and near the superellipsoid surface to obtain a mesh independent solution is used. The numerical results are compared with the analytical solution of a sphere; the error of the numerical approximation varied from 8 to 11%. It is found that the number of elements inside the superellipsoid are insufficient. An algorithm to mesh independently the volumes inside and outside the cube is proposed to increase the accuracy in the calculation of H. As n1 and n2 increase, the numerical solutions show that, H1111 → 0 and H2211 → 0. Although, for these concave shapes no analytical solution exists a bound of 0 for the terms H 1111 and H2211 is suggested. Finally, in Chapter 4 a numerical verification of the cross-property connection between the effective fluid permeability and the effective electrical conductivity is study. A molecular dynamics algorithm is used to generate a set of different microstructural patterns. The volumetric average over a cubic volume is used to obtain the effective electrical conductivity and the effective fluid permeability. The tortuosity of the porous phase

  4. Simultaneous source-mask optimization: a numerical combining method

    NASA Astrophysics Data System (ADS)

    Mülders, Thomas; Domnenko, Vitaliy; Küchler, Bernd; Klimpel, Thomas; Stock, Hans-Jürgen; Poonawala, Amyn A.; Taravade, Kunal N.; Stanton, William A.

    2010-09-01

    A new method for simultaneous Source-Mask Optimization (SMO) is presented. In order to produce optimum imaging fidelity with respect to exposure lattitude, depth of focus (DoF) and mask error enhancement factor (MEEF) the presented method aims to leverage both, the available degrees of freedom of a pixelated source and those available for the mask layout. The approach described in this paper is designed as to work with dissected mask polygons. The dissection of the mask patterns is to be performed in advance (before SMO) with the Synopsys Proteus OPC engine, providing the available degrees of freedom for mask pattern optimization. This is similar to mask optimization done for optical proximity correction (OPC). Additionally, however, the illumination source will be simultaneously optimized. The SMO approach borrows many of the performance enhancement methods of OPC software for mask correction, but is especially designed as to simultaneously optimize a pixelated source shape as nowadays available in production environments. Designed as a numerical optimization approach the method is able to assess in acceptable times several hundreds of thousands source-mask combinations for small, critical layout snippets. This allows a global optimization scheme to be applied to the SMO problem which is expected to better explore the optimization space and thus to yield an improved solution quality compared to local optimizations methods. The method is applied to an example system for investigating the impact of source constraints on the SMO results. Also, it is investigated how well possibly conflicting goals of low MEEF and large DoF can be balanced.

  5. a Numerical Method for Stability Analysis of Pinned Flexible Mechanisms

    NASA Astrophysics Data System (ADS)

    Beale, D. G.; Lee, S. W.

    1996-05-01

    A technique is presented to investigate the stability of mechanisms with pin-jointed flexible members. The method relies on a special floating frame from which elastic link co-ordinates are defined. Energies are easily developed for use in a Lagrange equation formulation, leading to a set of non-linear and mixed ordinary differential-algebraic equations of motion with constraints. Stability and bifurcation analysis is handled using a numerical procedure (generalized co-ordinate partitioning) that avoids the tedious and difficult task of analytically reducing the system of equations to a number equalling the system degrees of freedom. The proposed method was then applied to (1) a slider-crank mechanism with a flexible connecting rod and crank of constant rotational speed, and (2) a four-bar linkage with a flexible coupler with a constant speed crank. In both cases, a single pinned-pinned beam bending mode is employed to develop resonance curves and stability boundaries in the crank length-crank speed parameter plane. Flip and fold bifurcations are common occurrences in both mechanisms. The accuracy of the proposed method was also verified by comparison with previous experimental results [1].

  6. Introduction to finite-difference methods for numerical fluid dynamics

    SciTech Connect

    Scannapieco, E.; Harlow, F.H.

    1995-09-01

    This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.

  7. Numerical performance of projection methods in finite element consolidation models

    NASA Astrophysics Data System (ADS)

    Gambolati, Giuseppe; Pini, Giorgio; Ferronato, Massimiliano

    2001-12-01

    Projection, or conjugate gradient like, methods are becoming increasingly popular for the efficient solution of large sparse sets of unsymmetric indefinite equations arising from the numerical integration of (initial) boundary value problems. One such problem is soil consolidation coupling a flow and a structural model, typically solved by finite elements (FE) in space and a marching scheme in time (e.g. the Crank-Nicolson scheme). The attraction of a projection method stems from a number of factors, including the ease of implementation, the requirement of limited core memory and the low computational cost if a cheap and effective matrix preconditioner is available. In the present paper, biconjugate gradient stabilized (Bi- CGSTAB) is used to solve FE consolidation equations in 2-D and 3-D settings with variable time integration steps. Three different nodal orderings are selected along with the preconditioner ILUT based on incomplete triangular factorization and variable fill-in. The overall cost of the solver is made up of the preconditioning cost plus the cost to converge which is in turn related to the number of iterations and the elementary operations required by each iteration. The results show that nodal ordering affects the perfor mance of Bi-CGSTAB. For normally conditioned consolidation problems Bi-CGSTAB with the best ILUT preconditioner may converge in a number of iterations up to two order of magnitude smaller than the size of the FE model and proves an accurate, cost-effective and robust alternative to direct methods.

  8. Advanced numerical methods and software approaches for semiconductor device simulation

    SciTech Connect

    CAREY,GRAHAM F.; PARDHANANI,A.L.; BOVA,STEVEN W.

    2000-03-23

    In this article the authors concisely present several modern strategies that are applicable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of upwind and artificial dissipation schemes, generalization of the traditional Scharfetter-Gummel approach, Petrov-Galerkin and streamline-upwind Petrov Galerkin (SUPG), entropy variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. They have included numerical examples from the recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and they emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, they briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.

  9. Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation

    DOE PAGESBeta

    Carey, Graham F.; Pardhanani, A. L.; Bova, S. W.

    2000-01-01

    In this article we concisely present several modern strategies that are applicable to driftdominated carrier transport in higher-order deterministic models such as the driftdiffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of “upwind” and artificial dissipation schemes, generalization of the traditional Scharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind Petrov Galerkin (SUPG), “entropy” variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of themore » methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.« less

  10. Numerical Simulations of Granular Dynamics: Method and Tests

    NASA Astrophysics Data System (ADS)

    Richardson, Derek C.; Walsh, K. J.; Murdoch, N.; Michel, P.; Schwartz, S. R.

    2010-10-01

    We present a new particle-based numerical method for the simulation of granular dynamics, with application to motions of particles (regolith) on small solar system bodies and planetary surfaces [1]. The method employs the parallel N-body tree code pkdgrav [2] to search for collisions and compute particle trajectories. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. Several tests of the method are presented, including a model granular "atmosphere” that achieves correct energy equipartition, and a series of tumbler simulations that compare favorably with actual laboratory experiments [3]. DCR and SRS acknowledge NASA Grant No. NNX08AM39G and NSF Grant No. AST0524875; KJW, the Poincaré Fellowship at OCA; NM, Thales Alenia Space and The Open University; and PM and NM, the French Programme National de Planétologie. References: [1] Richardson et al. (2010), Icarus, submitted; [2] Cf. Richardson et al. (2009), P&SS 57, 183 and references therein; [3] Brucks et al. (2007), PRE 75, 032301-1-032301-4.

  11. Numerical Comparison of Periodic MoM (Method of Moments) and BMIA (Banded Matrix Iteration Method)

    NASA Technical Reports Server (NTRS)

    Kim, Y.; Rodriguez, E.; Michel, T.

    1995-01-01

    The most popular numerical technique in rough surface scattering is the Method of Moments (MoM). Since the scattering patch size is finite, the edge current must be suppressed to obtain accurate scattering cross sections. Two standard ways to minimize the edge current are periodic boundary conditions and incident wave tapering. We compare the accuracy & computational requirements of these methods.

  12. Numerical methods for determining interstitial oxygen in silicon

    SciTech Connect

    Stevenson, J.O.; Medernach, J.W.

    1995-01-01

    The interstitial oxygen (O{sub i}) concentration in Czochralski silicon and the subsequent SiO{sub x} precipitation are important parameters for integrated circuit fabrication. Uncontrolled SiO{sub x} precipitation during processing can create detrimental mechanical and electrical effects that contribute to poor performance. An inability to consistently and accurately measure the initial O{sub i} concentration in heavily doped silicon has led to contradictory results regarding the effects of dopant type and concentration on SiO{sub x} precipitation. The authors have developed a software package for reliably determining and comparing O{sub i} in heavily doped silicon. The SiFTIR{copyright} code implements three independent oxygen analysis methods in a single integrated package. Routine oxygen measurements are desirable over a wide range of silicon resistivities, but there has been confusion concerning which of the three numerical methods is most suitable for the low resistivity portion of the continuum. A major strength of the software is an ability to rapidly produce results for all three methods using only a single Fourier Transform Infrared Spectroscopy (FTIR) spectrum as input. This ability to perform three analyses on a single data set allows a detailed comparison of the three methods across the entire range of resistivities in question. Integrated circuit manufacturers could use the enabling technology provided by SiFTIR{copyright} to monitor O{sub i} content. Early detection of O{sub i} using this diagnostic could be beneficial in controlling SiO{sub x} precipitation during integrated circuit processing.

  13. Numerical Methods for Forward and Inverse Problems in Discontinuous Media

    SciTech Connect

    Chartier, Timothy P.

    2011-03-08

    The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.

  14. Numerical Methods for Two-Dimensional Stem Cell Tissue Growth.

    PubMed

    Ovadia, Jeremy; Nie, Qing

    2014-01-01

    Growth of developing and regenerative biological tissues of different cell types is usually driven by stem cells and their local environment. Here, we present a computational framework for continuum tissue growth models consisting of stem cells, cell lineages, and diffusive molecules that regulate proliferation and differentiation through feedback. To deal with the moving boundaries of the models in both open geometries and closed geometries (through polar coordinates) in two dimensions, we transform the dynamic domains and governing equations to fixed domains, followed by solving for the transformation functions to track the interface explicitly. Clustering grid points in local regions for better efficiency and accuracy can be achieved by appropriate choices of the transformation. The equations resulting from the incompressibility of the tissue is approximated by high-order finite difference schemes and is solved using the multigrid algorithms. The numerical tests demonstrate an overall spatiotemporal second-order accuracy of the methods and their capability in capturing large deformations of the tissue boundaries. The methods are applied to two biological systems: stratified epithelia for studying the effects of two different types of stem cell niches and the scaling of a morphogen gradient with the size of the Drosophila imaginal wing disc during growth. Direct simulations of both systems suggest that that the computational framework is robust and accurate, and it can incorporate various biological processes critical to stem cell dynamics and tissue growth. PMID:24415847

  15. Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

    NASA Astrophysics Data System (ADS)

    Rangan, Aaditya V.; Cai, David; Tao, Louis

    2007-02-01

    Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of

  16. Hybrid Numerical Methods for Multiscale Simulations of Subsurface Biogeochemical Processes

    SciTech Connect

    Scheibe, Timothy D.; Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.; Redden, George D.; Meakin, Paul

    2007-08-01

    Many subsurface flow and transport problems of importance today involve coupled non-linear flow, transport, and reaction in media exhibiting complex heterogeneity. In particular, problems involving biological mediation of reactions fall into this class of problems. Recent experimental research has revealed important details about the physical, chemical, and biological mechanisms involved in these processes at a variety of scales ranging from molecular to laboratory scales. However, it has not been practical or possible to translate detailed knowledge at small scales into reliable predictions of field-scale phenomena important for environmental management applications. A large assortment of numerical simulation tools have been developed, each with its own characteristic scale including molecular (e.g., molecular dynamics), microbial (e.g., cellular automata or particle individual-based models), pore (e.g., lattice-Boltzmann, pore network models, and discrete particle methods such as smoothed particle hydrodynamics) and continuum scales (e.g., traditional partial differential equations solved by finite difference or finite element methods). While many problems can be effectively addressed by one of these models at a single scale, some problems may require explicit integration of models across multiple scales. We are developing a hybrid multi-scale subsurface reactive transport modeling framework that integrates models with diverse representations of physics, chemistry and biology at different scales (sub-pore, pore and continuum). The modeling framework is being designed to take advantage of advanced computational technologies including parallel code components using the Common Component Architecture, parallel solvers, gridding, data and workflow management, and visualization. This paper describes the specific methods/codes being used at each scale, techniques used to directly and adaptively couple across model scales, and preliminary results of application to a

  17. Numerical simulation of a low-emission gas turbine combustor using KIVA-II

    NASA Technical Reports Server (NTRS)

    Yang, S. L.; Chen, R.; Cline, M. C.; Nguyen, H. L.; Micklow, G. J.

    1992-01-01

    A modified version of the KIVA-II code was used to obtain a multidimensional numerical solution for the turbulent two-phase chemically reacting flows inside a staged turbine combustor (STC). The STC under consideration is equipped with an advanced airblast fuel nozzle and encompasses a fuel nozzle (FN), a rich-burn (RB) zone, a converging connecting pipe, a quick-quench (QQ) zone, a diverging connecting pipe, and a lean-combustion (LC) zone. The STC was divided into two subsystems, namely, FN/RB zone and QQ/LC zones, and the numerical solutions were obtained separately for each subsystem. Preliminary data characterize the major features of the flow and temperature fields inside the STC. Information on velocity, temperature, and some critical species in the FN/RB zone is presented. In the QQ/LC zones, formation of the co- and counter-rotating bulk flow and the sandwiched-ring-shaped temperature field can be clearly seen. The calculations of the mass-weighted standard deviation and the pattern factor of temperature indicated that the mixing performance of the STC is very promising.

  18. Numerical study of the semiclassical limit of the Davey-Stewartson II equations

    NASA Astrophysics Data System (ADS)

    Klein, C.; Roidot, K.

    2014-09-01

    We present the first detailed numerical study of the semiclassical limit of the Davey-Stewartson II equations both for the focusing and the defocusing variant. We concentrate on rapidly decreasing initial data with a single hump. The formal limit of these equations for vanishing semiclassical parameter ɛ, the semiclassical equations, is numerically integrated up to the formation of a shock. The use of parallelized algorithms allows one to determine the critical time tc and the critical solution for these 2 + 1-dimensional shocks. It is shown that the solutions generically break in isolated points similarly to the case of the 1 + 1-dimensional cubic nonlinear Schrödinger equation, i.e., cubic singularities in the defocusing case and square root singularities in the focusing case. For small values of ɛ, the full Davey-Stewartson II equations are integrated for the same initial data up to the critical time tc. The scaling in ɛ of the difference between these solutions is found to be the same as in the 1 + 1 dimensional case, proportional to ɛ2/7 for the defocusing case and proportional to ɛ2/5 in the focusing case. We document the Davey-Stewartson II solutions for small ɛ for times much larger than the critical time tc. It is shown that zones of rapid modulated oscillations are formed near the shocks of the solutions to the semiclassical equations. For smaller ɛ, the oscillatory zones become smaller and more sharply delimited to lens-shaped regions. Rapid oscillations are also found in the focusing case for initial data where the singularities of the solution to the semiclassical equations do not coincide. If these singularities do coincide, which happens when the initial data are symmetric with respect to an interchange of the spatial coordinates, no such zone is observed. Instead the initial hump develops into a blow-up of the L∞ norm of the solution. We study the dependence of the blow-up time on the semiclassical parameter ɛ.

  19. Micarta Propellers II : Method of Construction

    NASA Technical Reports Server (NTRS)

    Caldwell, F W; Clay, N S

    1924-01-01

    The methods used in manufacturing Micarta propellers differ considerably from those employed with wood propellers on account of the hardness of the materials. The propellers must be formed accurately to size in a mold and afterwards balanced without the customary trimming of the material from the tips. Described here are the pressing and molding processes, filing, boring, balancing, and curing.

  20. Chunking Method of Teaching and Studying: II.

    ERIC Educational Resources Information Center

    Furukawa, James M.; And Others

    Data from three general psychology classes were used in a study of the chunking method of teaching and studying. Two classes participated in a study on chunking study outline (CSO) length, and one in a study on retention rates. Results of students with high and low cognitive processing capacities (CPC) were also compared. It was found that a CSO…

  1. Trigonometrically fitted two step hybrid method for the numerical integration of second order IVPs

    NASA Astrophysics Data System (ADS)

    Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.

    2016-06-01

    In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct trigonometrically fitted two step hybrid methods. We apply the new methods on the numerical integration of several test problems.

  2. Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods.

    PubMed

    Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K

    2016-08-01

    In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption. PMID:27505799

  3. Extracting S-matrix poles for resonances from numerical scattering data: Type-II Padé reconstruction

    NASA Astrophysics Data System (ADS)

    Sokolovski, D.; Akhmatskaya, E.; Sen, S. K.

    2011-02-01

    residues of resonance poles from numerical scattering data supplied by the user. The data can then be used for quantitative analysis of interference patterns observed in elastic, inelastic and reactive integral and differential cross sections. Solution method: The S-matrix element is analytically continued in the complex plane of either energy or angular momentum with the help of Padé approximation of type II. Resonance (complex energy or Regge) poles are identified and their residues evaluated. Unusual features: Use of multiple precision MPFUN package (Bailey (1993) [45]). (Distributed with the PADE II code.) Running time: From several seconds to several minutes depending on the precision level chosen and the number of iterations performed.

  4. A Numerical Method for Determining Diffusivity from Annealing Experiments

    NASA Astrophysics Data System (ADS)

    Harris-Kuhlman, K. R.; Kulcinski, G. L.

    1998-12-01

    Terrestrial analogs of lunar ilmenite (FeTiO3) have been implanted with solar-wind energy 4He at 4 keV and 3He at 3 keV using Plasma Source Ion Implantation (PSII). Isochronal annealing of the samples revealed thermally induced 4He evolution similar to the helium release of the Apollo 11 regoliths reported by Pepin, et. al., [1970]. These annealing experiments are analyzed with a three dimensional numerical method based on Fick's law for diffusion. An iterative method is used to calculate the diffusivity. The code uses an assumed diffusivity to calculate the amount of gas released during a temperature step. The initial depth profile of the implanted species is generated using the TRIM electronic stopping code [Ziegler, 1996]. The calculated value is compared to the measured value and a linear regression is used to calculate a new diffusivity until there is convergence within a specified tolerance level. The diffusivity as a function of temperature is then fitted to an Arrhenius equation. Analysis of results for 4 keV 4He on ilmenite shows two distinct regions of Arrehnius behavior with activation energies of 0.5 +/- 0.1 eV at emperatures below 800 deg C and 1.5 +/- 0.2 eV at temperatures from 800 deg C to 1100 deg C. Pepin, R. O., L. E. Nyquist, D. Phinney, and D. C. Black (1970) "Rare Gases in Apollo 11 Lunar Material," Proceedings of the Apollo 11 Lunar Science Conference, 2, pp. 1435-1454. Ziegler, J. P. (1996) SRIM Instruction Manual: The Stopping and Range of Ions in Matter, (Yorktown, New York: IBM - Research); based on Ziegler, J. P., J. P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids, (New York: Pergamon Press, 1985).

  5. Spectrophotometric methods for the evaluation of acidity constants-I Numerical methods for single equilibria.

    PubMed

    Asuero, A G; Navas, M J; Jiminez-Trillo, J L

    1986-02-01

    The spectrophotometric methods applicable to the numerical evaluation of acidity constants of monobasic acids are briefly reviewed. The equations are presented in a form suitable for easy calculation with a programmable pocket calculator. The aim of this paper is to cover a gap in the education analytical literature. PMID:18964064

  6. Active Problem Solving and Applied Research Methods in a Graduate Course on Numerical Methods

    ERIC Educational Resources Information Center

    Maase, Eric L.; High, Karen A.

    2008-01-01

    "Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…

  7. Extending canonical Monte Carlo methods: II

    NASA Astrophysics Data System (ADS)

    Velazquez, L.; Curilef, S.

    2010-04-01

    We have previously presented a methodology for extending canonical Monte Carlo methods inspired by a suitable extension of the canonical fluctuation relation C = β2langδE2rang compatible with negative heat capacities, C < 0. Now, we improve this methodology by including the finite size effects that reduce the precision of a direct determination of the microcanonical caloric curve β(E) = ∂S(E)/∂E, as well as by carrying out a better implementation of the MC schemes. We show that, despite the modifications considered, the extended canonical MC methods lead to an impressive overcoming of the so-called supercritical slowing down observed close to the region of the temperature driven first-order phase transition. In this case, the size dependence of the decorrelation time τ is reduced from an exponential growth to a weak power-law behavior, \\tau (N)\\propto N^{\\alpha } , as is shown in the particular case of the 2D seven-state Potts model where the exponent α = 0.14-0.18.

  8. NUMERICAL METHODS FOR THE SIMULATION OF HIGH INTENSITY HADRON SYNCHROTRONS.

    SciTech Connect

    LUCCIO, A.; D'IMPERIO, N.; MALITSKY, N.

    2005-09-12

    Numerical algorithms for PIC simulation of beam dynamics in a high intensity synchrotron on a parallel computer are presented. We introduce numerical solvers of the Laplace-Poisson equation in the presence of walls, and algorithms to compute tunes and twiss functions in the presence of space charge forces. The working code for the simulation here presented is SIMBAD, that can be run as stand alone or as part of the UAL (Unified Accelerator Libraries) package.

  9. A Fast Numerical Method for a Nonlinear Black-Scholes Equation

    NASA Astrophysics Data System (ADS)

    Koleva, Miglena N.; Vulkov, Lubin G.

    2009-11-01

    In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed.

  10. Numerical Analysis on the Vortex Pattern and Flux Particle Dispersion in KR Method Using MPS Method

    NASA Astrophysics Data System (ADS)

    Hirata, N.; Xu, Y.; Anzai, K.

    2015-06-01

    The mechanically-stirring vessel is widely used in many fields, such as chemical reactor, bioreactor, and metallurgy, etc. The type of vortex mode that formed during impeller stirring has great effect on stirring efficiency, chemical reacting rate and air entrapment. Many efforts have been made to numerically simulate the fluid flow in the stirring vessel with classical Eulerian method. However, it is difficult to directly investigate the vortex mode and flux particle dispersion. Therefore, moving particle semi-implicit (MPS) method, which is based on Lagrangian method, is applied to simulate the fluid flow in a KR method in this practice. Top height and bottom heights of vortex surface in a steady state under several rotation speed was taken as key parameters to compare the results of numerical and published results. Flux particle dispersion behaviour under a rotation speed range from 80 to 480 rpm was also compared with the past study. The result shows that the numerical calculation has high consistency with experimental results. It is confirmed that the calculation using MPS method well reflected the vortex mode and flux particle dispersion in a mechanically-stirring vessel.

  11. SAMSAN- MODERN NUMERICAL METHODS FOR CLASSICAL SAMPLED SYSTEM ANALYSIS

    NASA Technical Reports Server (NTRS)

    Frisch, H. P.

    1994-01-01

    SAMSAN was developed to aid the control system analyst by providing a self consistent set of computer algorithms that support large order control system design and evaluation studies, with an emphasis placed on sampled system analysis. Control system analysts have access to a vast array of published algorithms to solve an equally large spectrum of controls related computational problems. The analyst usually spends considerable time and effort bringing these published algorithms to an integrated operational status and often finds them less general than desired. SAMSAN reduces the burden on the analyst by providing a set of algorithms that have been well tested and documented, and that can be readily integrated for solving control system problems. Algorithm selection for SAMSAN has been biased toward numerical accuracy for large order systems with computational speed and portability being considered important but not paramount. In addition to containing relevant subroutines from EISPAK for eigen-analysis and from LINPAK for the solution of linear systems and related problems, SAMSAN contains the following not so generally available capabilities: 1) Reduction of a real non-symmetric matrix to block diagonal form via a real similarity transformation matrix which is well conditioned with respect to inversion, 2) Solution of the generalized eigenvalue problem with balancing and grading, 3) Computation of all zeros of the determinant of a matrix of polynomials, 4) Matrix exponentiation and the evaluation of integrals involving the matrix exponential, with option to first block diagonalize, 5) Root locus and frequency response for single variable transfer functions in the S, Z, and W domains, 6) Several methods of computing zeros for linear systems, and 7) The ability to generate documentation "on demand". All matrix operations in the SAMSAN algorithms assume non-symmetric matrices with real double precision elements. There is no fixed size limit on any matrix in any

  12. Prospective phase II trial of regional hyperthermia and whole liver irradiation for numerous chemorefractory liver metastases from colorectal cancer

    PubMed Central

    Yu, Jeong Il; Choi, Doo Ho; Noh, Jae Myoung; Oh, Dongryul; Park, Jun Su; Chang, Ji Hyun; Kim, Seung Tae; Lee, Jeeyun; Park, Se Hoon; Park, Joon Oh; Park, Young Suk; Lim, Ho Yeong; Kang, Won Ki

    2016-01-01

    Purpose A prospective phase II trial was conducted to evaluate the effectiveness and toxicity of regional hyperthermia and whole liver irradiation (WLI) for numerous chemorefractory liver metastases from colorectal cancer. Materials and Methods Enrolled patients had numerous chemorefractory hepatic metastases from colorectal cancer. Five sessions of hyperthermia and seven fractions of 3-gray WLI were planned. Health-related quality of life (HRQoL) was determined using the Korean version of the European Organization for Research and Treatment of Cancer quality of life questionnaire C-30 and the Functional Assessment of Cancer Therapy-Hepatobiliary version 4.0. Objective and pain response was evaluated. Results A total of 12 patients consented to the study and the 10 who received WLI and hyperthermia were analyzed. WLI was completed as planned in nine patients and hyperthermia in eight. Pain response was partial in four patients and stable in four. Partial objective response was achieved in three patients (30.0%) and stable disease was seen in four patients at the 1-month follow-up. One patient died 1 month after treatment because of respiratory failure related to pleural metastasis progression. Other grade III or higher toxicities were detected in three patients; however, all severe toxicities were related to disease progression rather than treatment. No significant difference in HRQoL was noted at the time of assessment for patients who were available for questionnaires. Conclusion Combined WLI and hyperthermia were well tolerated without severe treatment-related toxicity with a promising response from numerous chemorefractory hepatic metastases from colorectal cancer. PMID:27104165

  13. Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method

    NASA Astrophysics Data System (ADS)

    Ying, Teh Yuan; Yaacob, Nazeeruddin

    2013-04-01

    In this paper, a new implicit Runge-Kutta method which based on a 4-point Gauss-Kronrod-Radau II quadrature formula is developed. The resulting implicit method is a 4-stage sixth order Gauss-Kronrod-Radau IIA method, or in brief as GKRM(4,6)-IIA. GKRM(4,6)-IIA requires four function of evaluations at each integration step and it gives accuracy of order six. In addition, GKRM(4,6)-IIA has stage order four and being L-stable. Numerical experiments compare the accuracy between GKRM(4,6)-IIA and the classical 3-stage sixth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKRM(4,6)-IIA is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-IIA has higher stage order.

  14. WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method

    NASA Astrophysics Data System (ADS)

    Crevoisier, David; Voltz, Marc

    2013-04-01

    To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute

  15. Analysis of the Numerical and Geometrical Parameters Influencing the Simulation of Mode I and Mode II Delamination Growth in Unidirectional and Textile Composites

    NASA Astrophysics Data System (ADS)

    Jacques, S.; De Baere, I.; Van Paepegem, W.

    2015-12-01

    The reliability of composite structures depends, among other damage mechanisms, on their ability to withstand delaminations. In order to have a better understanding of the cohesive zone method technique for delamination simulations, a complete analysis of the multiple parameters influencing the results is necessary. In this paper the work is concentrated on the cohesive zone method using cohesive elements. First a summary of the theory of the cohesive zone method is given. A numerical investigation on the multiple parameters influencing the numerical simulation of the mode I and mode II delamination tests has been performed. The parameters such as the stabilization method, the output frequency, the friction and the computational efficiency have been taken into account. The results will be compared to an analytical solution obtained by linear elastic fracture mechanics. Additionally the numerical simulation results will be compared to the experimental results of a glass-fibre reinforced composite material for the mode I Double Cantilever Beam (DCB) and to a carbon fibre 5-harness satin weave reinforced polyphenylene sulphide composite for the mode I DCB and mode II End Notched Flexure (ENF).

  16. An Improved Numerical Integration Method for Springback Predictions

    NASA Astrophysics Data System (ADS)

    Ibrahim, R.; Smith, L. M.; Golovashchenko, Sergey F.

    2011-08-01

    In this investigation, the focus is on the springback of steel sheets in V-die air bending. A full replication to a numerical integration algorithm presented rigorously in [1] to predict the springback in air bending was performed and confirmed successfully. Algorithm alteration and extensions were proposed here. The altered approach used in solving the moment equation numerically resulted in springback values much closer to the trend presented by the experimental data, Although investigation here extended to use a more realistic work-hardening model, the differences in the springback values obtained by both hardening models were almost negligible. The algorithm was extended to be applied on thin sheets down to 0.8 mm. Results show that this extension is possible as verified by FEA and other published experiments on TRIP steel sheets.

  17. Some variance reduction methods for numerical stochastic homogenization.

    PubMed

    Blanc, X; Le Bris, C; Legoll, F

    2016-04-28

    We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here. PMID:27002065

  18. Algorithms for the Fractional Calculus: A Selection of Numerical Methods

    NASA Technical Reports Server (NTRS)

    Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.

    2003-01-01

    Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

  19. On numerical methods in non-Newtonian flows

    NASA Astrophysics Data System (ADS)

    Fileas, G.

    1982-12-01

    The constitutive equations for non-Newtonian flows are presented and the various flow models derived from continuum mechanics and molecular theories are considered and evaluated. Detailed account is given of numerical simulation employing differential and integral models of different kinds of non-Newtonian flows using finite difference and finite element techniques. Procedures for computer set ups are described and references are given for finite difference, finite element and molecular theory based programs for several kinds of flow. Achievements and unreached goals in the field of numerical simulation of non-Newtonian flows are discussed and the lack of numerical work in the fields of suspension flows and heat transfer is pointed out. Finally, FFOCUS is presented as a newly built computer program which can simulate freezing flows of Newtonian fluids through various geometries and is aimed to be further developed to handle non-Newtonian freezing flows and certain types of suspension phenomena involved in corium flow after a hypothetical core melt down accident in a pressurized water reactor.

  20. A Numerical Method for Calculating Stellar Occultation Light Curves from an Arbitrary Atmospheric Model

    NASA Technical Reports Server (NTRS)

    Chamberlain, D. M.; Elliot, J. L.

    1997-01-01

    We present a method for speeding up numerical calculations of a light curve for a stellar occultation by a planetary atmosphere with an arbitrary atmospheric model that has spherical symmetry. This improved speed makes least-squares fitting for model parameters practical. Our method takes as input several sets of values for the first two radial derivatives of the refractivity at different values of model parameters, and interpolates to obtain the light curve at intermediate values of one or more model parameters. It was developed for small occulting bodies such as Pluto and Triton, but is applicable to planets of all sizes. We also present the results of a series of tests showing that our method calculates light curves that are correct to an accuracy of 10(exp -4) of the unocculted stellar flux. The test benchmarks are (i) an atmosphere with a l/r dependence of temperature, which yields an analytic solution for the light curve, (ii) an atmosphere that produces an exponential refraction angle, and (iii) a small-planet isothermal model. With our method, least-squares fits to noiseless data also converge to values of parameters with fractional errors of no more than 10(exp -4), with the largest errors occurring in small planets. These errors are well below the precision of the best stellar occultation data available. Fits to noisy data had formal errors consistent with the level of synthetic noise added to the light curve. We conclude: (i) one should interpolate refractivity derivatives and then form light curves from the interpolated values, rather than interpolating the light curves themselves; (ii) for the most accuracy, one must specify the atmospheric model for radii many scale heights above half light; and (iii) for atmospheres with smoothly varying refractivity with altitude, light curves can be sampled as coarsely as two points per scale height.

  1. Numerical and experimental analysis of factors leading to suture dehiscence after Billroth II gastric resection.

    PubMed

    Cvetkovic, Aleksandar M; Milasinovic, Danko Z; Peulic, Aleksandar S; Mijailovic, Nikola V; Filipovic, Nenad D; Zdravkovic, Nebojsa D

    2014-11-01

    The main goal of this study was to numerically quantify risk of duodenal stump blowout after Billroth II (BII) gastric resection. Our hypothesis was that the geometry of the reconstructed tract after BII resection is one of the key factors that can lead to duodenal dehiscence. We used computational fluid dynamics (CFD) with finite element (FE) simulations of various models of BII reconstructed gastrointestinal (GI) tract, as well as non-perfused, ex vivo, porcine experimental models. As main geometrical parameters for FE postoperative models we have used duodenal stump length and inclination between gastric remnant and duodenal stump. Virtual gastric resection was performed on each of 3D FE models based on multislice Computer Tomography (CT) DICOM. According to our computer simulation the difference between maximal duodenal stump pressures for models with most and least preferable geometry of reconstructed GI tract is about 30%. We compared the resulting postoperative duodenal pressure from computer simulations with duodenal stump dehiscence pressure from the experiment. Pressure at duodenal stump after BII resection obtained by computer simulation is 4-5 times lower than the dehiscence pressure according to our experiment on isolated bowel segment. Our conclusion is that if the surgery is performed technically correct, geometry variations of the reconstructed GI tract by themselves are not sufficient to cause duodenal stump blowout. Pressure that develops in the duodenal stump after BII resection using omega loop, only in the conjunction with other risk factors can cause duodenal dehiscence. Increased duodenal pressure after BII resection is risk factor. Hence we recommend the routine use of Roux en Y anastomosis as a safer solution in terms of resulting intraluminal pressure. However, if the surgeon decides to perform BII reconstruction, results obtained with this methodology can be valuable. PMID:25201585

  2. Spectral methods in general relativity and large Randall-Sundrum II black holes

    SciTech Connect

    Abdolrahimi, Shohreh; Cattoën, Céline; Page, Don N.; Yaghoobpour-Tari, Shima E-mail: celine.cattoen-gilbert@canterbury.ac.nz E-mail: yaghoobp@ualberta.ca

    2013-06-01

    Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS{sub 5}-CFT{sub 4} solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS{sub 5}-CFT{sub 4} solution, showing that our solution agrees closely with theirs. We have obtained a closed-form approximation to the metric of the black hole on the brane. We have also deduced the new results that to first order in 1/(−ΛM{sup 2}), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(−Λ)

  3. Magnetohydrodynamic (MHD) modelling of solar active phenomena via numerical methods

    NASA Technical Reports Server (NTRS)

    Wu, S. T.

    1988-01-01

    Numerical ideal MHD models for the study of solar active phenomena are summarized. Particular attention is given to the following physical phenomena: (1) local heating of a coronal loop in an isothermal and stratified atmosphere, and (2) the coronal dynamic responses due to magnetic field movement. The results suggest that local heating of a magnetic loop will lead to the enhancement of the density of the neighboring loops through MHD wave compression. It is noted that field lines can be pinched off and may form a self-contained magnetized plasma blob that may move outward into interplanetary space.

  4. Achieving better cooling of turbine blades using numerical simulation methods

    NASA Astrophysics Data System (ADS)

    Inozemtsev, A. A.; Tikhonov, A. S.; Sendyurev, C. I.; Samokhvalov, N. Yu.

    2013-02-01

    A new design of the first-stage nozzle vane for the turbine of a prospective gas-turbine engine is considered. The blade's thermal state is numerically simulated in conjugate statement using the ANSYS CFX 13.0 software package. Critical locations in the blade design are determined from the distribution of heat fluxes, and measures aimed at achieving more efficient cooling are analyzed. Essentially lower (by 50-100°C) maximal temperature of metal has been achieved owing to the results of the performed work.

  5. Path Integrals and Exotic Options:. Methods and Numerical Results

    NASA Astrophysics Data System (ADS)

    Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.

    2005-09-01

    In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.

  6. Numerical methods for a general class of porous medium equations

    SciTech Connect

    Rose, M. E.

    1980-03-01

    The partial differential equation par. deltau/par. deltat + par. delta(f(u))/par. deltax = par. delta(g(u)par. deltau/par. deltax)/par. deltax, where g(u) is a non-negative diffusion coefficient that may vanish for one or more values of u, was used to model fluid flow through a porous medium. Error estimates for a numerical procedure to approximate the solution are derived. A revised version of this report will appear in Computers and Mathematics with Applications.

  7. Projection methods for the numerical solution of Markov chain models

    NASA Technical Reports Server (NTRS)

    Saad, Youcef

    1989-01-01

    Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

  8. Method for numerical simulation of two-term exponentially correlated colored noise

    SciTech Connect

    Yilmaz, B.; Ayik, S.; Abe, Y.; Gokalp, A.; Yilmaz, O.

    2006-04-15

    A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications.

  9. Numerical conformal mapping methods for exterior and doubly connected regions

    SciTech Connect

    DeLillo, T.K.; Pfaltzgraff, J.A.

    1996-12-31

    Methods are presented and analyzed for approximating the conformal map from the exterior of the disk to the exterior a smooth, simple closed curve and from an annulus to a bounded, doubly connected region with smooth boundaries. The methods are Newton-like methods for computing the boundary correspondences and conformal moduli similar to Fornberg`s method for the interior of the disk. We show that the linear systems are discretizations of the identity plus a compact operator and, hence, that the conjugate gradient method converges superlinearly.

  10. Analysis of free turbulent shear flows by numerical methods

    NASA Technical Reports Server (NTRS)

    Korst, H. H.; Chow, W. L.; Hurt, R. F.; White, R. A.; Addy, A. L.

    1973-01-01

    Studies are described in which the effort was essentially directed to classes of problems where the phenomenologically interpreted effective transport coefficients could be absorbed by, and subsequently extracted from (by comparison with experimental data), appropriate coordinate transformations. The transformed system of differential equations could then be solved without further specifications or assumptions by numerical integration procedures. An attempt was made to delineate different regimes for which specific eddy viscosity models could be formulated. In particular, this would account for the carryover of turbulence from attached boundary layers, the transitory adjustment, and the asymptotic behavior of initially disturbed mixing regions. Such models were subsequently used in seeking solutions for the prescribed two-dimensional test cases, yielding a better insight into overall aspects of the exchange mechanisms.

  11. Numerical method to digital photoelasticity using plane polariscope.

    PubMed

    Júnior, P A A Magalhães; Vieira, F G; Magalhães, C A; Ribeiro, J S; Rios, I G

    2016-06-13

    This research aims to find a new way to get the intensity equations for the phase-shifting model in digital photoelasticity. The procedure is based on the rotation of the analyzer itself. From the intensity equations, the isoclinic and isochromatic equations parameters are deduced by applying a new numerical technique. This approach can be done to calculate how many images allow the resolution of the polariscope. Each image indicates the stress forces in the object. In this study the plane polariscope was used. The amount of images will determinate the number of errors and uncertainties of the study, due to the observation that the veracity of the equations increases considerably with a large amout of images. Several analyses are performed with different amounts of photographic images. The results showed the possibility to measure stress forces with high precision using plane polariscopes. PMID:27410283

  12. MODELING COLLISIONAL CASCADES IN DEBRIS DISKS: THE NUMERICAL METHOD

    SciTech Connect

    Gaspar, Andras; Psaltis, Dimitrios; Oezel, Feryal; Rieke, George H.; Cooney, Alan E-mail: dpsaltis@as.arizona.edu E-mail: grieke@as.arizona.edu

    2012-04-10

    We develop a new numerical algorithm to model collisional cascades in debris disks. Because of the large dynamical range in particle masses, we solve the integro-differential equations describing erosive and catastrophic collisions in a particle-in-a-box approach, while treating the orbital dynamics of the particles in an approximate fashion. We employ a new scheme for describing erosive (cratering) collisions that yields a continuous set of outcomes as a function of colliding masses. We demonstrate the stability and convergence characteristics of our algorithm and compare it with other treatments. We show that incorporating the effects of erosive collisions results in a decay of the particle distribution that is significantly faster than with purely catastrophic collisions.

  13. A Numerical Simulation of Cosmic Ray Modulation Near the Heliopause. II. Some Physical Insights

    NASA Astrophysics Data System (ADS)

    Luo, Xi; Potgieter, Marius S.; Zhang, Ming; Pogorelov, Nikolai V.; Feng, Xueshang; du Toit Strauss, R.

    2016-08-01

    Cosmic ray (CR) transport near the heliopause (HP) is studied using a hybrid transport model, with the parameters constrained by observations from the Voyager 1 spacecraft. We simulate the CR radial flux along different directions in the heliosphere. There is no well-defined thin layer between the solar wind region and the interstellar region along the tail and polar directions of the heliosphere. By analyzing the radial flux curve along the direction of Voyager 2, together with its trajectory information, the crossing time of the HP by Voyager 2 is predicted to be in 2017.14. We simulate the CR radial flux for different energy values along the direction of Voyager 1. We find that there is only a modest modulation region of about 10 au wide beyond the HP, so that Voyager 1 observing the Local Interstellar Spectra is justified in numerical modeling. We analyze the heliospheric exit information of pseudo-particles in our stochastic numerical (time-backward) method, conjecturing that they represent the behavior of CR particles, and we find that pseudo-particles that have been traced from the nose region exit in the tail region. This implies that many CR particles diffuse directly from the heliospheric tail region to the nose region near the HP. In addition, when pseudo-particles were traced from the Local Interstellar Medium (LISM), it is found that their exit location (entrance for real particles) from the simulation domain is along the prescribed Interstellar Magnetic Field direction. This indicates that parallel diffusion dominates CR particle transport in the LISM.

  14. On a New Numerical Method for Solving General Variational Inequalities

    NASA Astrophysics Data System (ADS)

    Bnouhachem, Abdellah; Noor, Muhammad Aslam; Khalfaoui, Mohamed; Sheng, Zhaohan

    In this paper, we suggest and analyze a new extragradient method for solving the general variational inequalities involving two operators. We also prove the global convergence of the proposed modified method under certain mild conditions. We used a self-adaptive technique to adjust parameter ρ at each iteration. It is proved theoretically that the lower-bound of the progress obtained by the proposed method is greater than that by the extragradient method. An example is given to illustrate the efficiency and its comparison with the extragradient method. Since the general variational inequalities include the classical variational inequalities and complementarity problems as special cases, our results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as an improvement and refinement of the previously known results in this field.

  15. Probabilistic Fracture Analysis of Functionally Graded Materials--Part II: Implementation and Numerical Examples

    SciTech Connect

    Nguyen, Tam H.; Song, Junho; Paulino, Glaucio H.

    2008-02-15

    Probabilistic fracture analyses are performed for investigating uncertain fracture response of Functionally Graded Material (FGM) structures. The First-Order-Reliability-Method (FORM) is implemented into an existing Finite Element code for FGM (FE-FGM), which was previously developed at the University of Illinois at Urbana-Champaign. The computational simulation will be used in order to estimate the probability of crack initiation with uncertainties in the material properties only. The two-step probability analysis method proposed in the companion paper is illustrated by a numerical example of a composite strip with an edge crack. First, the reliability index of a crack initiation event is estimated as we vary the mean and standard deviation of the slope and the location of the inflection point of the spatial profile of Young's modulus. Secondly, the reliability index is estimated as we vary the standard deviation and the correlation length of the random field that characterize the random spatial fluctuation of Young's modulus. Also investigated is the relative importance of the uncertainties in the toughness compared to those in Young's modulus.

  16. Biphasic indentation of articular cartilage--II. A numerical algorithm and an experimental study.

    PubMed

    Mow, V C; Gibbs, M C; Lai, W M; Zhu, W B; Athanasiou, K A

    1989-01-01

    Part I (Mak et al., 1987, J. Biomechanics 20, 703-714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus. Poisson's ratio and permeability for young bovine femoral condylar cartilage in situ to be HA = 0.90 MPa, vs = 0.39 and k = 0.44 x 10(-15) m4/Ns respectively, and those for patellar groove cartilage to be HA = 0.47 MPa, vs = 0.24, k = 1.42 x 10(-15) m4/Ns. One surprising finding from this study is that the in situ Poisson's ratio of cartilage (0.13-0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40-0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments. PMID:2613721

  17. A numerical model of non-equilibrium thermal plasmas. II. Governing equations

    SciTech Connect

    Li HePing; Zhang XiaoNing; Xia Weidong

    2013-03-15

    Governing equations and the corresponding physical properties of the plasmas are both prerequisites for studying the fundamental processes in a non-equilibrium thermal plasma system numerically. In this paper, a kinetic derivation of the governing equations used for describing the complicated thermo-electro-magneto-hydrodynamic-chemical coupling effects in non-equilibrium thermal plasmas is presented. This derivation, which is achieved using the Chapman-Enskog method, is completely consistent with the theory of the transport properties reported in the previous paper by the same authors. It is shown, based on this self-consistent theory, that the definitions of the specific heat at constant pressure and the reactive thermal conductivity of two-temperature plasmas are not necessary. The governing equations can be reduced to their counterparts under local thermodynamic equilibrium (LTE) and local chemical equilibrium (LCE) conditions. The general method for the determination of the boundary conditions of the solved variables is also discussed briefly. The two papers establish a self-consistent physical-mathematical model that describes the complicated physical and chemical processes in a thermal plasma system for the cases both in LTE or LCE conditions and under non-equilibrium conditions.

  18. Ab initio theory of superconductivity in a magnetic field. II. Numerical solution

    NASA Astrophysics Data System (ADS)

    Linscheid, A.; Sanna, A.; Gross, E. K. U.

    2015-07-01

    We numerically investigate the spin density functional theory for superconductors (SpinSCDFT) and the approximated exchange-correlation functional, derived and presented in the preceding Paper I [A. Linscheid et al., Phys. Rev. B 92, 024505 (2015), 10.1103/PhysRevB.92.024505]. As a test system, we employ a free-electron gas featuring an exchange splitting, a phononic pairing field, and a Coulomb repulsion. SpinSCDFT results are compared with Sarma, the Bardeen-Cooper-Schrieffer theory, and with an Eliashberg type of approach. We find that the spectrum of the superconducting Kohn-Sham SpinSCDFT system is not in agreement with the true quasiparticle structure. Therefore, starting from the Dyson equation, we derive a scheme that allows to compute the many-body excitations of the superconductor and represents the extension to superconductivity of the G0W0 method in band-structure theory. This superconducting G0W0 method vastly improves the predicted spectra.

  19. The impact of Seasat-A scatterometer data on the numerical prediction of the Queen Elizabeth II storm

    NASA Astrophysics Data System (ADS)

    Duffy, D. G.; Atlas, R.

    1986-02-01

    The development of the Queen Elizabeth II storm from 1200 UT on September 9, 1978, to 0000 UT on September 11, 1978, is forecast with a limited-area, fine resolution (100 km) numerical weather prediction model. Forecasts from initial conditions that include and exclude Seasat scatterometer surface winds are performed. When the Seasat winds are allowed to influence the upper levels of the atmosphere, a large positive impact is found.

  20. The impact of Seasat-A scatterometer data on the numerical prediction of the Queen Elizabeth II storm

    NASA Technical Reports Server (NTRS)

    Duffy, D. G.; Atlas, R.

    1986-01-01

    The development of the Queen Elizabeth II storm from 1200 UT on September 9, 1978, to 0000 UT on September 11, 1978, is forecast with a limited-area, fine resolution (100 km) numerical weather prediction model. Forecasts from initial conditions that include and exclude Seasat scatterometer surface winds are performed. When the Seasat winds are allowed to influence the upper levels of the atmosphere, a large positive impact is found.

  1. Exploring the Use of Discontinuous Galerkin Methods for Numerical Relativity

    NASA Astrophysics Data System (ADS)

    Hebert, Francois; Kidder, Lawrence; Teukolsky, Saul; SXS Collaboration

    2015-04-01

    The limited accuracy of relativistic hydrodynamic simulations constrains our insight into several important research problems, including among others our ability to generate accurate template waveforms for black hole-neutron star mergers, or our understanding of supernova explosion mechanisms. In many codes the algorithms used to evolve the matter, based on the finite volume method, struggle to reach the desired accuracy. We aim to show improved accuracy by using a discontinuous Galerkin method. This method's attractiveness comes from its combination of spectral convergence properties for smooth solutions and robust stability properties for shocks. We present the status of our work implementing a testbed GR-hydro code using discontinuous Galerkin.

  2. A numerical method for eigenvalue problems in modeling liquid crystals

    SciTech Connect

    Baglama, J.; Farrell, P.A.; Reichel, L.; Ruttan, A.; Calvetti, D.

    1996-12-31

    Equilibrium configurations of liquid crystals in finite containments are minimizers of the thermodynamic free energy of the system. It is important to be able to track the equilibrium configurations as the temperature of the liquid crystals decreases. The path of the minimal energy configuration at bifurcation points can be computed from the null space of a large sparse symmetric matrix. We describe a new variant of the implicitly restarted Lanczos method that is well suited for the computation of extreme eigenvalues of a large sparse symmetric matrix, and we use this method to determine the desired null space. Our implicitly restarted Lanczos method determines adoptively a polynomial filter by using Leja shifts, and does not require factorization of the matrix. The storage requirement of the method is small, and this makes it attractive to use for the present application.

  3. Numerical Stability and Convergence of Approximate Methods for Conservation Laws

    NASA Astrophysics Data System (ADS)

    Galkin, V. A.

    We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.

  4. Numerical Solutions of Electromagnetic Problems by Integral Equation Methods and Finite-Difference Time - Method.

    NASA Astrophysics Data System (ADS)

    Min, Xiaoyi

    This thesis first presents the study of the interaction of electromagnetic waves with three-dimensional heterogeneous, dielectric, magnetic, and lossy bodies by surface integral equation modeling. Based on the equivalence principle, a set of coupled surface integral equations is formulated and then solved numerically by the method of moments. Triangular elements are used to model the interfaces of the heterogeneous body, and vector basis functions are defined to expand the unknown current in the formulation. The validity of this formulation is verified by applying it to concentric spheres for which an exact solution exists. The potential applications of this formulation to a partially coated sphere and a homogeneous human body are discussed. Next, this thesis also introduces an efficient new set of integral equations for treating the scattering problem of a perfectly conducting body coated with a thin magnetically lossy layer. These electric field integral equations and magnetic field integral equations are numerically solved by the method of moments (MoM). To validate the derived integral equations, an alternative method to solve the scattering problem of an infinite circular cylinder coated with a thin magnetic lossy layer has also been developed, based on the eigenmode expansion. Results for the radar cross section and current densities via the MoM and the eigenmode expansion method are compared. The agreement is excellent. The finite difference time domain method is subsequently implemented to solve a metallic object coated with a magnetic thin layer and numerical results are compared with that by the MoM. Finally, this thesis presents an application of the finite-difference time-domain approach to the problem of electromagnetic receiving and scattering by a cavity -backed antenna situated on an infinite conducting plane. This application involves modifications of Yee's model, which applies the difference approximations of field derivatives to differential

  5. Validation of a Numerical Method for Determining Liner Impedance

    NASA Technical Reports Server (NTRS)

    Watson, Willie R.; Jones, Michael G.; Tanner, Sharon E.; Parrott, Tony L.

    1996-01-01

    This paper reports the initial results of a test series to evaluate a method for determining the normal incidence impedance of a locally reacting acoustically absorbing liner, located on the lower wall of a duct in a grazing incidence, multi-modal, non-progressive acoustic wave environment without flow. This initial evaluation is accomplished by testing the methods' ability to converge to the known normal incidence impedance of a solid steel plate, and to the normal incidence impedance of an absorbing test specimen whose impedance was measured in a conventional normal incidence tube. The method is shown to converge to the normal incident impedance values and thus to be an adequate tool for determining the impedance of specimens in a grazing incidence, multi-modal, nonprogressive acoustic wave environment for a broad range of source frequencies.

  6. Improved numerical methods for turbulent viscous recirculating flows

    NASA Technical Reports Server (NTRS)

    Turan, A.; Vandoormaal, J. P.

    1988-01-01

    The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.

  7. Numerical solution of 2D-vector tomography problem using the method of approximate inverse

    NASA Astrophysics Data System (ADS)

    Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna

    2016-08-01

    We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.

  8. Early electromagnetic waves from earthquake rupturing: II. validation and numerical experiments

    NASA Astrophysics Data System (ADS)

    Gao, Yongxin; Chen, Xiaofei; Hu, Hengshan; Zhang, Jie

    2013-03-01

    We validate the branch-cut integration (BCI) technique presented in the companion paper. The numerical result shows that the early electromagnetic (EM) signal calculated by the BCI method is in good agreement with that in the full waveform calculated by the real-axis integration method. We further find that to calculate the early EM signal only the integrals along the vertical branch cuts that are around the k0 and kem branch points are needed, whereas neither the integrals along the vertical branch cuts around the Pf(P), S and Ps branch points nor the residues of the poles are necessary. We conduct numerical experiments to analyse the early EM signal generated by an earthquake in a porous half-space, including its component analysis, sensitivities to the conductivity, viscosity and recording depth, and radiation pattern. The component analysis shows that the total early EM (emTotal) signal is not a single wave but a combination of three kinds of EM waves, namely, the direct emd wave radiated from the source, the reflected emr waves converted from the emd wave, the direct P and S waves at the free surface and the critically refracted EM0 waves which are also converted from the emd wave, the direct P and S waves at the free surface. Three pulses, namely, the emd-, P- and S-converted pulses are identified in the emTotal signal according to their different arrival times. The emd-converted pulse arrives immediately after the occurrence of the earthquake and it is a combination of the emd wave, the emr and EM0 waves converted from the emd wave at the free surface. The P-converted (S-converted, respectively) pulse owns an arrival time approximately equal to that spent by the P wave (S wave, respectively) travelling from the hypocentre to the epicentre, and it is a combination of the emr and EM0 waves converted from the P wave (S wave, respectively) at the free surface. The P-converted pulse is usually weaker than the S- and emd-converted pulses in the electrogram and is

  9. Eulerian-Lagrangian numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods

    USGS Publications Warehouse

    Cox, T.J.; Runkel, R.L.

    2008-01-01

    Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.

  10. A finite volume method for numerical grid generation

    NASA Astrophysics Data System (ADS)

    Beale, S. B.

    1999-07-01

    A novel method to generate body-fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables , and is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re-zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid-correction procedure. The scalar variables are re-mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet-Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local-boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point-by-point and whole-field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright

  11. Evaluating numerical ODE/DAE methods, algorithms and software

    NASA Astrophysics Data System (ADS)

    Soderlind, Gustaf; Wang, Lina

    2006-01-01

    Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one method is better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris paribus conditions. Moreover, testing is an empirical science and as such requires a formal test protocol; without it conclusions are questionable, invalid or even false.We argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. The goals are computational stability, reproducibility, and improved software quality. We also focus on different error criteria and norms, and discuss modifications to DASPK and RADAU5. Finally, some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems.

  12. A survey of numerical methods for shock physics applications

    SciTech Connect

    Hertel, E.S. Jr.

    1997-10-01

    Hydrocodes or more accurately, shock physics analysis packages, have been widely used in the US Department of Energy (DOE) laboratories and elsewhere around the world for over 30 years. Initial applications included weapons effects studies where the pressure levels were high enough to disregard the material strength, hence the term hydrocode. Over the last 30 years, Sandia has worked extensively to develop and apply advanced hydrocodes to armor/anti-armor interactions, warhead design, high explosive initiation, and nuclear weapon safety issues. The needs of the DOE have changed over the last 30 years, especially over the last decade. A much stronger emphasis is currently placed on the details of material deformation and high explosive initiation phenomena. The hydrocodes of 30 years ago have now evolved into sophisticated analysis tools that can replace testing in some situations and complement it in all situations. A brief history of the development of hydrocodes in the US will be given. The author also discusses and compares the four principal methods in use today for the solution of the conservation equations of mass, momentum, and energy for shock physics applications. The techniques discussed are the Eulerian methods currently employed by the Sandia multi-dimensional shock physics analysis package known as CTH; the element based Lagrangian method currently used by codes like DYNA; the element free Lagrangian method (also known as smooth particle hydrodynamics) used by codes like the Los Alamos code SPHINX; and the Arbitrary Lagrangian Eulerian methods used by codes like the Lawrence Livermore code CALE or the Sandia code ALEGRA.

  13. Applications of numerical methods to simulate the movement of contaminants in groundwater.

    PubMed Central

    Sun, N Z

    1989-01-01

    This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

  14. Numerical design method for thermally loaded plate-cylinder intersections

    SciTech Connect

    Baldur, R.; Laberge, C.A.; Lapointe, D. )

    1988-11-01

    This paper is an extension of work on stresses in corner radii described by the authors previously. Whereas the original study concerned itself with pressure effects only and the second reference gave the initial version of the work dealing with the thermal effects, this report gives more recent results concerning specifically thermal loads. As before, the results are limited to inside corner radii between cylinders and flat heat closures. Similarly, the analysis is based on a systematic series of finite element calculations with the significant parameters covering the field of useful design boundaries. The results are condensed into a rapid method for the determination of peak stresses needed for performing fatigue analysis in pressure vessels subjected to a significant, variable thermal load. The paper takes into account the influence of the film coefficient, temporal temperature variations, and material properties. A set of coefficients provides a convenient method of stress evaluation suitable for design purposes.

  15. Numerical optimization methods for critical currents in superconductors

    NASA Astrophysics Data System (ADS)

    Kimmel, Gregory; Sadovskyy, Ivan; Koshelev, Alex; Glatz, Andreas

    In this work, I present optimization methods for maximizing the critical current in high-temperature superconductors for energy applications. The critical current in the presence of an external magnetic field is mostly defined by the pinning landscape (pinscape) within the superconductor, which prevents magnetic vortices from moving and, therefore, increases its critical current. Our approach is to generate different pinscapes and obtain the resulting critical current by large-scale time-dependent Ginzburg-Landau equations. Pinning centers could be any combination of defects, including spherical and columnar defects. The parameters controlling the pinscape are adaptively adjusted in order to find the optimal parameter set, which maximizes the critical current. Here, we compare different optimization methods and discuss their performance. Work was supported by the Scientific Discovery through Advanced Computing (SciDAC) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences.

  16. Extremal polynomials and methods of optimization of numerical algorithms

    NASA Astrophysics Data System (ADS)

    Lebedev, V. I.

    2004-10-01

    Chebyshëv-Markov-Bernstein-Szegö polynomials C_n(x) extremal on \\lbrack -1,1 \\rbrack with weight functions w(x)=(1+x)^\\alpha(1- x)^\\beta/\\sqrt{S_l(x)} where \\alpha,\\beta=0,\\frac12 and S_l(x)=\\prod_{k=1}^m(1-c_kT_{l_k}(x))>0 are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight p(x)=w^2(x)(1-x^2)^{-1/2}. The parameters of optimal Chebyshëv iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko-Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshëv filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.

  17. Extremal polynomials and methods of optimization of numerical algorithms

    SciTech Connect

    Lebedev, V I

    2004-10-31

    Chebyshev-Markov-Bernstein-Szegoe polynomials C{sub n}(x) extremal on [-1,1] with weight functions w(x)=(1+x){sup {alpha}}(1- x){sup {beta}}/{radical}(S{sub l}(x)) where {alpha},{beta}=0,1/2 and S{sub l}(x)={pi}{sub k=1}{sup m}(1-c{sub k}T{sub l{sub k}}(x))>0 are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight p(x)=w{sup 2}(x)(1-x{sup 2}){sup -1/2}. The parameters of optimal Chebyshev iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko-Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshev filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.

  18. Numerical simulation of fluid-structure interactions with stabilized finite element method

    NASA Astrophysics Data System (ADS)

    Sváček, Petr

    2016-03-01

    This paper is interested to the interactions of the incompressible flow with a flexibly supported airfoil. The bending and the torsion modes are considered. The problem is mathematically described. The numerical method is based on the finite element method. A combination of the streamline-upwind/Petrov-Galerkin and pressure stabilizing/Petrov-Galerkin method is used for the stabilization of the finite element method. The numerical results for a three-dimensional problem of flow over an airfoil are shown.

  19. A novel method for preparation of cobalt(II) and lead(II) carbonates

    NASA Astrophysics Data System (ADS)

    Refat, M. S.; Teleb, S. M.; Sadeek, S. A.

    2004-10-01

    Cobalt(II) carbonate, CoCO 3·4H 2O and lead(II) carbonate, PbCO 3·2H 2O were synthesis by a new simple method during the reaction of aqueous solutions of CoX 2 (X = Cl -, NO 3- and CH 3COO -) and PbX 2 (X = NO 3- or CH 3COO -), respectively, with urea at ˜85 °C for 2 h. The infrared spectra of the reaction products clearly indicates the absence of the bands due to coordinated urea, but show the characteristic bands of ionic carbonate. A general mechanisms describing the formation of cobalt and lead carbonates are suggested.

  20. Design of braided composite tubes by numerical analysis method

    SciTech Connect

    Hamada, Hiroyuki; Fujita, Akihiro; Maekawa, Zenichiro; Nakai, Asami; Yokoyama, Atsushi

    1995-11-01

    Conventional composite laminates have very poor strength through thickness and as a result are limited in their application for structural parts with complex shape. In this paper, the design for braided composite tube was proposed. The concept of analysis model which involved from micro model to macro model was presented. This method was applied to predict bending rigidity and initial fracture stress under bending load of the braided tube. The proposed analytical procedure can be included as a unit in CAE system for braided composites.

  1. Fast Numerical Methods for the Design of Layered Photonic Structures with Rough Interfaces

    NASA Technical Reports Server (NTRS)

    Komarevskiy, Nikolay; Braginsky, Leonid; Shklover, Valery; Hafner, Christian; Lawson, John

    2011-01-01

    Modified boundary conditions (MBC) and a multilayer approach (MA) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with arbitrary permittivity tensor. MBC and MA are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.

  2. Two Different Methods for Numerical Solution of the Modified Burgers' Equation

    PubMed Central

    Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi

    2014-01-01

    A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM. PMID:25162064

  3. Transforming Mean and Osculating Elements Using Numerical Methods

    NASA Technical Reports Server (NTRS)

    Ely, Todd A.

    2010-01-01

    Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order

  4. Transforming Mean and Osculating Elements Using Numerical Methods

    NASA Astrophysics Data System (ADS)

    Ely, Todd A.

    2015-03-01

    Mean element propagation of perturbed two body orbits has as its mathematical basis the averaging theory of nonlinear dynamical systems. Mean elements define an orbit's long-term evolution characteristics consisting of both secular and long-period effects. Using averaging theory, a near-identity transformation can be found that transforms between the mean elements and their osculating counterparts that augment the mean elements with short period effects. The ability to perform the conversion is necessary so that orbit design conducted in either mean elements or osculating can be effectively converted between each element type. In the present work, the near-identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the mean or osculating elements to first-order.

  5. On the numerical dispersion and the spectral fidelity of the Particle-In-Cell method

    NASA Astrophysics Data System (ADS)

    Huang, Chengkun; Meyers, M. D.; Zeng, Y.; Yi, S.; Albright, B. J.

    2015-11-01

    The Particle-In-Cell (PIC) method is widely used in plasma modeling. However, the PIC method exhibits grid type numerical instabilities, including the finite grid instability and the numerical Cherenkov instability that can render unphysical simulation results or disrupt the simulation. A faithful numerical dispersion of the electromagnetic PIC algorithm is obtained and analyzed to obtain the insight about the numerical instabilities inherent in such a computation model. Using this dispersion, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. Compared with the gridless model, we show that the lack of spectral fidelity relative to the real system due to the aliasing effect is a major cause of the numerical instabilities in the PIC model. Work supported by the U.S. Department of Energy through the LDRD program at Los Alamos National Laboratory.

  6. IMPROVED NUMERICAL METHODS FOR MODELING RIVER-AQUIFER INTERACTION.

    SciTech Connect

    Tidwell, Vincent C.; Sue Tillery; Phillip King

    2008-09-01

    A new option for Local Time-Stepping (LTS) was developed to use in conjunction with the multiple-refined-area grid capability of the U.S. Geological Survey's (USGS) groundwater modeling program, MODFLOW-LGR (MF-LGR). The LTS option allows each local, refined-area grid to simulate multiple stress periods within each stress period of a coarser, regional grid. This option is an alternative to the current method of MF-LGR whereby the refined grids are required to have the same stress period and time-step structure as the coarse grid. The MF-LGR method for simulating multiple-refined grids essentially defines each grid as a complete model, then for each coarse grid time-step, iteratively runs each model until the head and flux changes at the interfacing boundaries of the models are less than some specified tolerances. Use of the LTS option is illustrated in two hypothetical test cases consisting of a dual well pumping system and a hydraulically connected stream-aquifer system, and one field application. Each of the hypothetical test cases was simulated with multiple scenarios including an LTS scenario, which combined a monthly stress period for a coarse grid model with a daily stress period for a refined grid model. The other scenarios simulated various combinations of grid spacing and temporal refinement using standard MODFLOW model constructs. The field application simulated an irrigated corridor along the Lower Rio Grande River in New Mexico, with refinement of a small agricultural area in the irrigated corridor.The results from the LTS scenarios for the hypothetical test cases closely replicated the results from the true scenarios in the refined areas of interest. The head errors of the LTS scenarios were much smaller than from the other scenarios in relation to the true solution, and the run times for the LTS models were three to six times faster than the true models for the dual well and stream-aquifer test cases, respectively. The results of the field application

  7. A numerical method for the study of the circulation of the world ocean

    SciTech Connect

    Bryan, K.

    1997-08-01

    This paper describes a detail computational procedure involving a finite difference numerical schemes to study the circulation models of the world oceans. To obtain an efficient numerical method for low-frequency, large-scale current systems, surfaces gravity-inertial waves are filtered out by the rigid-lid approximation. Special features of the ocean circulation are resolved in the numerical model by allowing for a variable spacing in either the zonal or meridional direction. 20 refs., 5 figs., 1 tab.

  8. A New High-Order Stable Numerical Method for Matrix Inversion

    PubMed Central

    Haghani, F. Khaksar; Soleymani, F.

    2014-01-01

    A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfth-order convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding Moore-Penrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples. PMID:24688436

  9. Numerical methods for the design and analysis of wings at supersonic speeds

    NASA Technical Reports Server (NTRS)

    Carlson, H. W.; Miller, D. S.

    1974-01-01

    Numerical methods for the design and analysis of arbitrary-planform wings at supersonic speeds are reviewed. Certain deficiencies are revealed, particularly in application to wings with slightly subsonic leading edges. Recently devised numerical techniques which overcome the major part of these deficiencies are presented. The original development as well as the more recent revisions are subjected to a thorough review.

  10. A study of numerical methods for hyperbolic conservation laws with stiff source terms

    NASA Technical Reports Server (NTRS)

    Leveque, R. J.; Yee, H. C.

    1988-01-01

    The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.

  11. Some numerical methods for integrating systems of first-order ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Clark, N. W.

    1969-01-01

    Report on numerical methods of integration includes the extrapolation methods of Bulirsch-Stoer and Neville. A comparison is made nith the Runge-Kutta and Adams-Moulton methods, and circumstances are discussed under which the extrapolation method may be preferred.

  12. Conservation properties of numerical integration methods for systems of ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Rosenbaum, J. S.

    1976-01-01

    If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

  13. Advanced numerical methods for three dimensional two-phase flow calculations

    SciTech Connect

    Toumi, I.; Caruge, D.

    1997-07-01

    This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.

  14. EFFECTS OF ELECTROOSMOSIS ON SOIL TEMPERATURE AND HYDRAULIC HEAD: II. NUMERICAL SIMULATION

    EPA Science Inventory

    A numerical model to simulate the distributions of voltage, soil temperature, and hydraulic head during the field test of electroosmosis was developed. The two-dimensional governing equations for the distributions of voltage, soil temperature, and hydraulic head within a cylindri...

  15. Equilibrium gas flow computations. II - An analysis of numerical formulations of conservation laws

    NASA Technical Reports Server (NTRS)

    Vinokur, Marcel; Liu, Yen

    1988-01-01

    Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, equilibrium gas laws. Generalizations of the Beam-Warming scheme, Steger-Warming and van Leer flux-vector splittings, and Roe's approximate Riemann solver are presented for three-dimensional, time-varying grids. The approximations inherent in previous generalizations are discussed.

  16. Numerical Databases: Their Vital Role in Information Science. Part II: A Call to Action.

    ERIC Educational Resources Information Center

    Carter, G. C.

    1985-01-01

    In this second of two installments, a discussion of role of information science (IS) in numerical databases (NDBs) and vice versa highlights two elements of IS needed to develop NDBs: technical (hardware, software, artificial intelligence, degree of database reliability); social (man-machine interface, social infrastructure). Research requirements…

  17. On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. II: numerical algorithm

    NASA Astrophysics Data System (ADS)

    Wang, Jiong; Steinmann, Paul

    2016-05-01

    This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample's response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated.

  18. On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

    NASA Technical Reports Server (NTRS)

    Gottlieb, D.; Turkel, E.

    1980-01-01

    New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

  19. Modelling LARES temperature distribution and thermal drag II: Numerical computation of current-epoch thermal forces

    NASA Astrophysics Data System (ADS)

    Brooks, Jason W.; Matzner, Richard

    2016-07-01

    The LARES satellite is a laser-ranged space experiment to contribute to geophysics observation, and to measure the general relativistic Lense-Thirring effect. LARES consists of a solid tungsten alloy sphere, into which 92 fused-silica Cube Corner Reflectors (CCRs) are set in colatitude circles ("rows"). During its first four months in orbit it was observed to undergo an anomalous along-track orbital acceleration of approximately -0.4 pm/s2 (pm: = picometer). The first paper in this series (Eur. Phys. J. Plus 130, 206 (2015) - Paper I) computed the thermally induced along-track "thermal drag" on the LARES satellite during the first 126 days after launch. The results there suggest that the IR absorbance α and emissivity ɛ of the CCRs equal 0.60, a possible value for silica with slight surface contamination subjected to the space environment. Paper I computed an average thermal drag acceleration of -0.36 pm/s2 for a 120-day period starting with the 7th day after launch. The heating and the resultant along-track acceleration depend on the plane of the orbit, the sun position, and in particular on the occurrence of eclipses, all of which are functions of time. Thus we compute the thermal drag for specific days. The satellite is heated from two sources: sunlight and Earth's infrared (IR) radiation. Paper I worked in the fast-spin regime, where CCRs with the same colatitude can be taken to have the same temperature. Further, since all temperature variations (temporal or spatial) were small in this regime, Paper I linearized the Stefan-Boltzmann law and performed a Fourier series analysis. However, the spin rate of the satellite is expected currently ( ≈ day 1500) to be slow, of order ≈ 5 /orbit, so the "fast-spin equal-temperatures in a row" assumption is suspect. In this paper, which considers epochs up to 1580 days after launch, we do not linearize and we use direct numerical integration instead of Fourier methods. In addition to the along-track drag, this code

  20. A numerical method for approximating antenna surfaces defined by discrete surface points

    NASA Technical Reports Server (NTRS)

    Lee, R. Q.; Acosta, R.

    1985-01-01

    A simple numerical method for the quadratic approximation of a discretely defined reflector surface is described. The numerical method was applied to interpolate the surface normal of a parabolic reflector surface from a grid of nine closest surface points to the point of incidence. After computing the surface normals, the geometrical optics and the aperture integration method using the discrete Fast Fourier Transform (FFT) were applied to compute the radiaton patterns for a symmetric and an offset antenna configurations. The computed patterns are compared to that of the analytic case and to the patterns generated from another numerical technique using the spline function approximation. In the paper, examples of computations are given. The accuracy of the numerical method is discussed.

  1. Numerical methods for simulating blood flow at macro, micro, and multi scales.

    PubMed

    Imai, Yohsuke; Omori, Toshihiro; Shimogonya, Yuji; Yamaguchi, Takami; Ishikawa, Takuji

    2016-07-26

    In the past decade, numerical methods for the computational biomechanics of blood flow have progressed to overcome difficulties in diverse applications from cellular to organ scales. Such numerical methods may be classified by the type of computational mesh used for the fluid domain, into fixed mesh methods, moving mesh (boundary-fitted mesh) methods, and mesh-free methods. The type of computational mesh used is closely related to the characteristics of each method. We herein provide an overview of numerical methods recently used to simulate blood flow at macro and micro scales, with a focus on computational meshes. We also discuss recent progress in the multi-scale modeling of blood flow. PMID:26705108

  2. The Cooperative Lifestyle Intervention Program-II (CLIP-II): Design and Methods

    PubMed Central

    Marsh, Anthony P.; Janssen, James A.; Ambrosius, Walter T.; Burdette, Jonathan H.; Gaukstern, Jill E.; Morgan, Ashley R.; Nesbit, Beverly A.; Paolini, J. Brielle; Sheedy, Jessica L.; Rejeski, W. Jack

    2013-01-01

    A complication of cardiovascular disease (CVD) and the metabolic syndrome (MetS) among older adults is loss of mobility. The American Heart Association has identified weight management as a core component of secondary prevention programs for CVD and is an important risk factor for physical disability. The American Society for Nutrition and the Obesity Society have highlighted the need for long-term randomized clinical trials to evaluate the independent and additive effects of diet-induced weight loss (WL) and physical activity in older persons on outcomes such as mobility, muscle function, and obesity related diseases. Here we describe the rationale, design, and methods of a translational study, the Cooperative Lifestyle Intervention Program-II (CLIP-II). CLIP-II will randomize 252 obese, older adults with CVD or MetS to a weight loss only treatment (WL), aerobic exercise training (AT)+WL, or resistance exercise training (RT)+WL for 18 months. The dual primary outcomes are mobility and knee extensor strength. The interventions will be delivered by YMCA community partners with our staff as trainers and advisers. This study will provide the first large scale trial to evaluate the effects of diet-induced WL on mobility in obese, older adults with CVD or MetS as compared to WL combined with two different modes of physical activity (AT and RT). Because uncertainty exists about the best approach for promoting WL in older adults due to concerns with the loss of lean mass, the design also permits a contrast between AT+WL and RT+WL on muscle strength. PMID:23974035

  3. Chaotic structures of nonlinear magnetic fields. I - Theory. II - Numerical results

    NASA Technical Reports Server (NTRS)

    Lee, Nam C.; Parks, George K.

    1992-01-01

    A study of the evolutionary properties of nonlinear magnetic fields in flowing MHD plasmas is presented to illustrate that nonlinear magnetic fields may involve chaotic dynamics. It is shown how a suitable transformation of the coupled equations leads to Duffing's form, suggesting that the behavior of the general solution can also be chaotic. Numerical solutions of the nonlinear magnetic field equations that have been cast in the form of Duffing's equation are presented.

  4. Extended RKN-type methods for numerical integration of perturbed oscillators

    NASA Astrophysics Data System (ADS)

    Yang, Hongli; Wu, Xinyuan; You, Xiong; Fang, Yonglei

    2009-10-01

    In this paper, extended Runge-Kutta-Nyström-type methods for the numerical integration of perturbed oscillators with low frequencies are presented, which inherit the framework of RKN methods and make full use of the special feature of the true flows for both the internal stages and the updates. Following the approach of J. Butcher, E. Hairer and G. Wanner, we develop a new kind of tree set to derive order conditions for the extended Runge-Kutta-Nyström-type methods. The numerical stability and phase properties of the new methods are analyzed. Numerical experiments are accompanied to show the applicability and efficiency of our new methods in comparison with some well-known high quality methods proposed in the scientific literature.

  5. Numerical method for estimating the size of chaotic regions of phase space

    SciTech Connect

    Henyey, F.S.; Pomphrey, N.

    1987-10-01

    A numerical method for estimating irregular volumes of phase space is derived. The estimate weights the irregular area on a surface of section with the average return time to the section. We illustrate the method by application to the stadium and oval billiard systems and also apply the method to the continuous Henon-Heiles system. 15 refs., 10 figs. (LSP)

  6. Exploring tidal effects of coalescing binary neutron stars in numerical relativity. II. Long-term simulations

    NASA Astrophysics Data System (ADS)

    Hotokezaka, Kenta; Kyutoku, Koutarou; Okawa, Hirotada; Shibata, Masaru

    2015-03-01

    We perform new long-term (15-16 orbits) simulations of coalescing binary neutron stars in numerical relativity using an updated Einstein equation solver, employing low-eccentricity initial data, and modeling the neutron stars by a piecewise polytropic equation of state. A convergence study shows that our new results converge more rapidly than the third order, and using the determined convergence order, we construct an extrapolated waveform for which the estimated total phase error should be less than one radian. We then compare the extrapolated waveforms with those calculated by the latest effective-one-body (EOB) formalism in which the so-called tidal deformability, higher post-Newtonian corrections, and gravitational self-force effects are taken into account. We show that for a binary of compact neutron stars with their radius 11.1 km, the waveform by the EOB formalism agrees quite well with the numerical waveform so that the total phase error is smaller than one radian for the total phase of ˜200 radian up to the merger. By contrast, for a binary of less compact neutron stars with their radius 13.6 km, the EOB and numerical waveforms disagree with each other in the last few wave cycles, resulting in the total phase error of approximately three radian.

  7. Application of numerical methods for diffusion-based modeling of skin permeation.

    PubMed

    Frasch, H Frederick; Barbero, Ana M

    2013-02-01

    The application of numerical methods for mechanistic, diffusion-based modeling of skin permeation is reviewed. Methods considered here are finite difference, method of lines, finite element, finite volume, random walk, cellular automata, and smoothed particle hydrodynamics. First the methods are briefly explained with rudimentary mathematical underpinnings. Current state of the art numerical models are described, and then a chronological overview of published models is provided. Key findings and insights of reviewed models are highlighted. Model results support a primarily transcellular pathway with anisotropic lipid transport. Future endeavors would benefit from a fundamental analysis of drug/vehicle/skin interactions. PMID:22261307

  8. Preparation of ZrO II/nano-TiO II composite powder by sol-gel method

    NASA Astrophysics Data System (ADS)

    Baharvandi, H. R.; Mohammadi, E.; Abdizadeh, H.; Hadian, A. M.; Ehsani, N.

    2007-07-01

    The effects of concentration of TTIP, amount of distilled water, and calcination temperature on morphology and particle size distribution of ZrO II/nano-TiO II catalysts were investigated. Mixed ZrO II/nano-TiO II powders were prepared by a modified sol-gel method by varying the mole fraction of TTIP from 0.002 to 0.01, H IIO/TTIP fraction from 2 to 8, and various stirring time (2, 4, and 10 h). The prepared ZrO II/nano-TiO II powders have been characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), and TG/DTA. Each oxide was calcined at the temperature between 110 and 1000°C. The results showed that the calcinations temperature has a pronounced effect on the phase formation and particle size of the calcined zirconium titanate (ZT) powders.

  9. Critical study of higher order numerical methods for solving the boundary-layer equations

    NASA Technical Reports Server (NTRS)

    Wornom, S. F.

    1978-01-01

    A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.

  10. Application of higher-order numerical methods to the boundary-layer equations

    NASA Technical Reports Server (NTRS)

    Wornom, S. F.

    1978-01-01

    A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

  11. The hydrodynamics of aspherical planetary nebulae. II - Numerical modelling of the early evolution

    NASA Astrophysics Data System (ADS)

    Icke, Vincent; Balick, Bruce; Frank, Adam

    1992-01-01

    Initial results are presented from numerical hydrodynamic calculations of the early evolution of aspherical planetary nebulae. It is found that the interacting winds produce the customary triple discontinuity, and that the outer shock's morphology conforms with remarkable fidelity to the analytic expectations. The inner shock develops in transient fashion, due to a reflection off the equatorial belt in which the shock deflects and focuses the fast wind. The shapes of the contact discontinuity and the flow behind the leading shock indicate two qualitatively distinct patterns.

  12. Resonant Absorption of Transverse Oscillations and Associated Heating in a Solar Prominence. II. Numerical Aspects

    NASA Astrophysics Data System (ADS)

    Antolin, P.; Okamoto, T. J.; De Pontieu, B.; Uitenbroek, H.; Van Doorsselaere, T.; Yokoyama, T.

    2015-08-01

    Transverse magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere and may be responsible for generating the Sun’s million-degree outer atmosphere. However, direct evidence of the dissipation process and heating from these waves remains elusive. Through advanced numerical simulations combined with appropriate forward modeling of a prominence flux tube, we provide the observational signatures of transverse MHD waves in prominence plasmas. We show that these signatures are characterized by a thread-like substructure, strong transverse dynamical coherence, an out-of-phase difference between plane-of-the-sky motions and line-of-sight velocities, and enhanced line broadening and heating around most of the flux tube. A complex combination between resonant absorption and Kelvin-Helmholtz instabilities (KHIs) takes place in which the KHI extracts the energy from the resonant layer and dissipates it through vortices and current sheets, which rapidly degenerate into turbulence. An inward enlargement of the boundary is produced in which the turbulent flows conserve the characteristic dynamics from the resonance, therefore guaranteeing detectability of the resonance imprints. We show that the features described in the accompanying paper through coordinated Hinode and Interface Region Imaging Spectrograph observations match the numerical results well.

  13. Numerical analysis of gas separator with thermal transpiration in micro channels II

    NASA Astrophysics Data System (ADS)

    Nakaye, Shoeji; Sugimoto, Hiroshi

    2014-12-01

    A membrane gas separator which operates with only a small temperature difference across a membrane is designed, and its capability is numerically proved. The separator system consists of three Knudsen pumps - a motionless pump that utilizes the thermal transpiration of the rarefied gas. Each pump is composed of a porous membrane and one channel along each of the two surfaces of the membrane. Two of the pumps induce a variation of mole fraction using a combination of the thermal transpiration and pressure driven flow through the membrane, and the other one provides the former two pumps with a required pressure difference. This paper reports the first numerical calculations that demonstrate a neon-argon binary gas mixture can be separated into pure neon gas and argon gas with the proposed design. The temperature difference is no more than 90 K, and the total length of the membrane is ˜ 15 cm at standard ambient temperature and pressure. The production rate of the separator is proportional to the width of the membrane. For example, when the width is 10 cm, the flow rates of the product gases are 0.8 sccm for argon and 1.9 sccm for neon.

  14. Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime

    NASA Astrophysics Data System (ADS)

    Bao, WeiZhu; Cai, YongYong; Jia, XiaoWei; Yin, Jia

    2016-08-01

    We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation in the nonrelativistic limit regime, involving a small dimensionless parameter $0<\\varepsilon\\ll 1$ which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e. there are propagating waves with wavelength $O(\\varepsilon^2)$ and $O(1)$ in time and space, respectively. We begin with the conservative Crank-Nicolson finite difference (CNFD) method and establish rigorously its error estimate which depends explicitly on the mesh size $h$ and time step $\\tau$ as well as the small parameter $0<\\varepsilon\\le 1$. Based on the error bound, in order to obtain `correct' numerical solutions in the nonrelativistic limit regime, i.e. $0<\\varepsilon\\ll 1$, the CNFD method requests the $\\varepsilon$-scalability: $\\tau=O(\\varepsilon^3)$ and $h=O(\\sqrt{\\varepsilon})$. Then we propose and analyze two numerical methods for the discretization of the nonlinear Dirac equation by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and time-splitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their $\\varepsilon$-scalability is improved to $\\tau=O(\\varepsilon^2)$ and $h=O(1)$ when $0<\\varepsilon\\ll 1$ compared with the CNFD method. Extensive numerical results are reported to confirm our error estimates.

  15. A method for estimating vertical distibution of the SAGE II opaque cloud frequency

    SciTech Connect

    Wang, P.; Mccormick, M.P.; Minnis, P.; Kent, G.S.; Yue, G.K.; Skeens, K.M. |

    1995-02-01

    A method is developed to infer the vertical distribution of the occurrence frequency of clouds that are opaque to the Stratospheric Aerosol and Gas Experiment (SAGE) II instrument. An application of the method to the 1986 SAGE II observations is included in this paper. The 1986 SAGE II results are compared with the 1952-1981 cloud climatology of Warren et al. (1986, 1988)

  16. A method for estimating vertical distibution of the SAGE II opaque cloud frequency

    NASA Technical Reports Server (NTRS)

    Wang, Pi-Huan; Mccormick, M. Patrick; Minnis, Patrick; Kent, Geoffrey S.; Yue, Glenn K.; Skeens, Kristi M.

    1995-01-01

    A method is developed to infer the vertical distribution of the occurrence frequency of clouds that are opaque to the Stratospheric Aerosol and Gas Experiment (SAGE) II instrument. An application of the method to the 1986 SAGE II observations is included in this paper. The 1986 SAGE II results are compared with the 1952-1981 cloud climatology of Warren et al. (1986, 1988)

  17. Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles. Part 2: Applications

    NASA Technical Reports Server (NTRS)

    Thomas, P. D.

    1980-01-01

    A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.

  18. A numerical adjoint parabolic equation (PE) method for tomography and geoacoustic inversion in shallow water

    NASA Astrophysics Data System (ADS)

    Hermand, Jean-Pierre; Berrada, Mohamed; Meyer, Matthias; Asch, Mark

    2005-09-01

    Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK '94 experimental conditions.

  19. Numerical solution of a diffusion problem by exponentially fitted finite difference methods.

    PubMed

    D'Ambrosio, Raffaele; Paternoster, Beatrice

    2014-01-01

    This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver. PMID:26034665

  20. A critical study of higher-order numerical methods for solving the boundary-layer equations

    NASA Technical Reports Server (NTRS)

    Wornom, S. F.

    1977-01-01

    A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

  1. A numerical method for the time coarsening of transport processes at the atomistic scale

    NASA Astrophysics Data System (ADS)

    Gonzalez-Ferreiro, B.; Romero, I.; Ortiz, M.

    2016-05-01

    We propose a novel numerical scheme for the simulation of slow transport processes at the atomistic scale. The scheme is based on a model for non-equilibrium statistical thermodynamics recently proposed by the authors, and extends it by formulating a variational integrator, i.e. a discrete functional whose optimality conditions provide all the governing equations of the problem. The method is employed to study surface segregation of AuAg alloys and its convergence is confirmed numerically.

  2. A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

    NASA Technical Reports Server (NTRS)

    Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.

    1992-01-01

    The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

  3. Development of mathematical models and numerical methods for aerodynamic design on multiprocessor computers

    NASA Astrophysics Data System (ADS)

    Maksimov, F. A.; Churakov, D. A.; Shevelev, Yu. D.

    2011-02-01

    Complex-geometry design and grid generation are addressed. The gasdynamic equations are solved, and the numerical results are compared with experimental data. For aerodynamic problems, a suite of mathematical and information technology tools is proposed for the support and management of geometric models of actual objects. Based on the mathematical modeling methods developed, numerical experiments can be performed for a wide class of geometric forms and the aerodynamic properties of aircraft can be predicted with allowance for the viscosity effects.

  4. Steady and Unsteady Numerical Solution of Generalized Newtonian Fluids Flow by Runge-Kutta method

    NASA Astrophysics Data System (ADS)

    Keslerová, R.; Kozel, K.; Prokop, V.

    2010-09-01

    In this paper the laminar viscous incompressible flow for generalized Newtonian (Newtonian and non-Newtonian) fluids is considered. The governing system of equations is the system of Navier-Stokes equations and the continuity equation. The steady and unsteady numerical solution for this system is computed by finite volume method combined with an artificial compressibility method. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. The dual time-stepping method is considered for unsteady computation. The high artificial compressibility coefficient is used in the artificial compressibility method applied in the dual time τ. The steady and unsteady numerical results of Newtonian and non-Newtonian (shear thickening and shear thinning) fluids flow in the branching channel are presented.

  5. Numerical simulation of stratified shear flow using a higher order Taylor series expansion method

    SciTech Connect

    Iwashige, Kengo; Ikeda, Takashi

    1995-09-01

    A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.

  6. A study of numerical methods for hyperbolic conservation laws with stiff source terms

    NASA Technical Reports Server (NTRS)

    Leveque, R. J.; Yee, H. C.

    1990-01-01

    In the present study of the behavior of typical numerical methods in the case of a model advection equation having a parameter-dependent source term, two approaches to the incorporation of the source terms are used: MacCormack-type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. The latter are found to perform slightly better. The model scalar equation is used to show that the incorrectness of the propagation speeds of discontinuities observed in the stiff case is due to the introduction of nonequilibrium values through numerical dissipation in the advection step.

  7. Numerical implementation of the method of fictitious domains for elliptic equations

    NASA Astrophysics Data System (ADS)

    Temirbekov, Almas N.

    2016-08-01

    In the paper, we study the elliptical type equation with strongly changing coefficients. We are interested in studying such equation because the given type equations are yielded when we use the fictitious domain method. In this paper we suggest a special method for numerical solution of the elliptic equation with strongly changing coefficients. We have proved the theorem for the assessment of developed iteration process convergence rate. We have developed computational algorithm and numerical calculations have been done to illustrate the effectiveness of the suggested method.

  8. Evolution of planetesimals. I - Dynamics: Relaxation in a thin disk. II - Numerical simulations

    NASA Astrophysics Data System (ADS)

    Palmer, P. L.; Lin, D. N. C.; Aarseth, S. J.

    1993-01-01

    The study examines the effects of density inhomogeneity and differential rotation as well as inelastic collisions on the dynamical evolution of planetesimals. Consideration is given to a three-step analysis: the dynamical evolution of the planetesimals, collisions and mass accumulation, and interaction with gas. It is shown that the velocity dispersion of a cold system of planetesimals increases rapidly due to elastic gravitational scattering. When the dispersion in the epicycle amplitude becomes comparable to the planetesimals' Roche radius, energy is transferred from the systematic Keplerian shear to the dispersive motion. With a numerical N-body scheme, gravitational scattering and physical collisions among a system of planetesimals is simulated. It is shown that dynamical equilibrium is attained with a velocity dispersion comparable to the surface escape velocity of those planetesimals which contribute most of the system mass.

  9. Partial Synchronization in Pulse-Coupled Oscillator Networks II: A Numerical Study

    NASA Astrophysics Data System (ADS)

    Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato

    We use high-precision numerical simulations, to compute the dynamics of N identical integrate and fire model neurons coupled in an all-to-all network through α-function pulses. In particular, we determine the discrete evolution of the state of our system from spike to spike. In addition to traditional fully synchronous and splay states, we exhibit multiple competing partially synchronized ordered states, which are fixed points and limit cycles in the phase space. Close examinations reveal the bifurcations among different states. By varying the parameters, we map out the phase diagram of stable fixed points. Our results illustrate the power of dimensional reduction in complex dynamical systems, and shed light on the collective behaviors of neural networks. Work supported by NSF DMS 1413020.

  10. A numerical simulation of barotropic instability. II Wave-wave interaction

    NASA Technical Reports Server (NTRS)

    Nielsen, J. E.; Schoeberl, M. R.

    1984-01-01

    A fully nonlinear numerical model of the point jet barotropic instability is used to test and confirm the hypothesis that the magnitude of the wave vorticity does not exceed the magnitude of the initial shear. This result arises directly from the local conservation of vorticity following a parcel and the fact that unstable waves are principally confined to the region where the zonal mean vorticity can be smoothed by the wave so as to eliminate the instability. Comparisons are made between fully nonlinear and quasi-linear models of the point jet instability and their tracer transport properties. Differences become particularly evident after wave saturation. The most important effect neglected by the wave-mean flow model appears to be the advection of wave vorticity by the most unstable mode. However, as equilibration of the instability proceeds, the globally averaged properties of both models are found to be similar.