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Sample records for numerical calculation method

  1. A numerical method for resonance integral calculations

    International Nuclear Information System (INIS)

    Tanbay, Tayfun; Ozgener, Bilge

    2013-01-01

    A numerical method has been proposed for resonance integral calculations and a cubic fit based on least squares approximation to compute the optimum Bell factor is given. The numerical method is based on the discretization of the neutron slowing down equation. The scattering integral is approximated by taking into account the location of the upper limit in energy domain. The accuracy of the method has been tested by performing computations of resonance integrals for uranium dioxide isolated rods and comparing the results with empirical values. (orig.)

  2. Nodal methods in numerical reactor calculations

    Energy Technology Data Exchange (ETDEWEB)

    Hennart, J.P. [UNAM, IIMAS, A.P. 20-726, 01000 Mexico D.F. (Mexico)]. e-mail: jean_hennart@hotmail.com; Valle, E. del [National Polytechnic Institute, School of Physics and Mathematics, Department of Nuclear Engineering, Mexico, D.F. (Mexico)

    2004-07-01

    The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)

  3. Nodal methods in numerical reactor calculations

    International Nuclear Information System (INIS)

    Hennart, J.P.; Valle, E. del

    2004-01-01

    The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)

  4. Numerical calculation of lubrication methods and programs

    CERN Document Server

    Huang, Ping

    2013-01-01

    This book describes basic lubrication problems and specific engineering applications. It focuses on the Reynolds equation, illustrating solutions with different conditions and discrete forms, such as dynamic bearing or grease lubrication. Thermal fluid lubrication problems are addressed by combining the Reynolds and energy equation solution, while the topic of elastohydrodynamic lubrication illustrates a combination of programs, join solution methods, and the Reynolds equation. Additional programs address lubrication for different parts with specific design, such as the magnetic hard disk/head

  5. MATH: A Scientific Tool for Numerical Methods Calculation and Visualization

    Directory of Open Access Journals (Sweden)

    Henrich Glaser-Opitz

    2016-02-01

    Full Text Available MATH is an easy to use application for various numerical methods calculations with graphical user interface and integrated plotting tool written in Qt with extensive use of Qwt library for plotting options and use of Gsl and MuParser libraries as a numerical and parser helping libraries. It can be found at http://sourceforge.net/projects/nummath. MATH is a convenient tool for use in education process because of its capability of showing every important step in solution process to better understand how it is done. MATH also enables fast comparison of similar method speed and precision.

  6. Numerical methods for calculating thermal residual stresses and hydrogen diffusion

    International Nuclear Information System (INIS)

    Leblond, J.B.; Devaux, J.; Dubois, D.

    1983-01-01

    Thermal residual stresses and hydrogen concentrations are two major factors intervening in cracking phenomena. These parameters were numerically calculated by a computer programme (TITUS) using the FEM, during the deposition of a stainless clad on a low-alloy plate. The calculation was performed with a 2-dimensional option in four successive steps: thermal transient calculation, metallurgical transient calculation (determination of the metallurgical phase proportions), elastic-plastic transient (plain strain conditions), hydrogen diffusion transient. Temperature and phase dependence of hydrogen diffusion coefficient and solubility constant. The following results were obtained: thermal calculations are very consistent with experiments at higher temperatures (due to the introduction of fusion and solidification latent heats); the consistency is not as good (by 70 degrees) for lower temperatures (below 650 degrees C); this was attributed to the non-introduction of gamma-alpha transformation latent heat. The metallurgical phase calculation indicates that the heat affected zone is almost entirely transformed into bainite after cooling down (the martensite proportion does not exceed 5%). The elastic-plastic calculations indicate that the stresses in the heat affected zone are compressive or slightly tensile; on the other hand, higher tensile stresses develop on the boundary of the heat affected zone. The transformation plasticity has a definite influence on the final stress level. The return of hydrogen to the clad during the bainitic transformation is but an incomplete phenomenon and the hydrogen concentration in the heat affected zone after cooling down to room temperature is therefore sufficient to cause cold cracking (if no heat treatment is applied). Heat treatments are efficient in lowering the hydrogen concentration. These results enable us to draw preliminary conclusions on practical means to avoid cracking. (orig.)

  7. Study on numerical calculation method for hydrodynamic parameters of WEC

    Directory of Open Access Journals (Sweden)

    Lijiao Shen

    2017-01-01

    Full Text Available For the effect of hydrodynamic parameters on the dynamic performance of wave energy devices is very significant, these parameters must be considered carefully when adjusting dynamic characteristics of devices. On the other hand calculating hydrodynamic parameter of devices accurately can guarantee rational dynamic property parameter adjustment. By using CFD technique and considering the definition of hydrodynamic parameters, the phase relationship between added mass and damp as well as the equation of forces, one new calculation method of hydrodynamic parameter was presented. Finally one example demonstrated the effectiveness of the new analysis method presented in this paper.

  8. Numerical calculation of elastohydrodynamic lubrication methods and programs

    CERN Document Server

    Huang, Ping

    2015-01-01

    The book not only offers scientists and engineers a clear inter-disciplinary introduction and orientation to all major EHL problems and their solutions but, most importantly, it also provides numerical programs on specific application in engineering. A one-stop reference providing equations and their solutions to all major elastohydrodynamic lubrication (EHL) problems, plus numerical programs on specific applications in engineering offers engineers and scientists a clear inter-disciplinary introduction and a concise program for practical engineering applications to most important EHL problems

  9. Comparison of Different Numerical Methods for Quality Factor Calculation of Nano and Micro Photonic Cavities

    DEFF Research Database (Denmark)

    Taghizadeh, Alireza; Mørk, Jesper; Chung, Il-Sug

    2014-01-01

    Four different numerical methods for calculating the quality factor and resonance wavelength of a nano or micro photonic cavity are compared. Good agreement was found for a wide range of quality factors. Advantages and limitations of the different methods are discussed.......Four different numerical methods for calculating the quality factor and resonance wavelength of a nano or micro photonic cavity are compared. Good agreement was found for a wide range of quality factors. Advantages and limitations of the different methods are discussed....

  10. A numerical method for calculation of electrostatic charge distribution induced on conducting surfaces

    OpenAIRE

    Saeed Hatamzadeh-Varmazyar; Zahra Masouri

    2014-01-01

    The focus of this article is on calculation of electrostatic charge distribution induced on conducting surfaces. For this purpose, the integral equation concept is used for mathematical modeling of the problem. A special set of exponential basis functions is introduced and defined to be used in formulation of a numerical method for solving the integral equation to obtain the charge distribution. The method is numerically evaluated via calculation of charge density for some structures by which...

  11. Numerical method for three dimensional steady-state two-phase flow calculations

    International Nuclear Information System (INIS)

    Raymond, P.; Toumi, I.

    1992-01-01

    This paper presents the numerical scheme which was developed for the FLICA-4 computer code to calculate three dimensional steady state two phase flows. This computer code is devoted to steady state and transient thermal hydraulics analysis of nuclear reactor cores 1,3 . The first section briefly describes the FLICA-4 flow modelling. Then in order to introduce the numerical method for steady state computations, some details are given about the implicit numerical scheme based upon an approximate Riemann solver which was developed for calculation of flow transients. The third section deals with the numerical method for steady state computations, which is derived from this previous general scheme and its optimization. We give some numerical results for steady state calculations and comparisons on required CPU time and memory for various meshing and linear system solvers

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

    Energy Technology Data Exchange (ETDEWEB)

    Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)

    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.

  13. Dose calculation using a numerical method based on Haar wavelets integration

    Energy Technology Data Exchange (ETDEWEB)

    Belkadhi, K., E-mail: khaled.belkadhi@ult-tunisie.com [Unité de Recherche de Physique Nucléaire et des Hautes Énergies, Faculté des Sciences de Tunis, Université Tunis El-Manar (Tunisia); Manai, K. [Unité de Recherche de Physique Nucléaire et des Hautes Énergies, Faculté des Sciences de Tunis, Université Tunis El-Manar (Tunisia); College of Science and Arts, University of Bisha, Bisha (Saudi Arabia)

    2016-03-11

    This paper deals with the calculation of the absorbed dose in an irradiation cell of gamma rays. Direct measurement and simulation have shown that they are expensive and time consuming. An alternative to these two operations is numerical methods, a quick and efficient way can furnish an estimation of the absorbed dose by giving an approximation of the photon flux at a specific point of space. To validate the numerical integration method based on the Haar wavelet for absorbed dose estimation, a study with many configurations was performed. The obtained results with the Haar wavelet method showed a very good agreement with the simulation highlighting good efficacy and acceptable accuracy. - Highlights: • A numerical integration method using Haar wavelets is detailed. • Absorbed dose is estimated with Haar wavelets method. • Calculated absorbed dose using Haar wavelets and Monte Carlo simulation using Geant4 are compared.

  14. On a method of numerical calculation of nonlinear radial pulsations of stars

    International Nuclear Information System (INIS)

    Kosovichev, A.G.

    1984-01-01

    Some features of using the finite difference method for numerical investigation of nonradial pulsations of stars were considered. The mathematical model of these pulsations is described by time-dependent gasdynaMic equations with gravity. A one-dimentional (spherically-symmetric) case is considered. It was obtained a two-parametric family of ultimate conservative difference schemes where the diffepence analogy of the main conservative laws as well as the additional relations for the balance to individual kinds of energy are performed. Such difference schemes provide more exact calculation of nonlinear flows with shocks as compared with the other difference schemes with the same order of approximation. The methods of numerical solution of implicit (absolute stable) difference schemes for a given family were considered. The coupled equations are solved through iterative Newton method Using martrix and separate successive eliminations. Numerical method can be used for calculation of large amplitude radial pulsations of stars

  15. A numerical calculation method of environmental impacts for the deep sea mining industry - a review.

    Science.gov (United States)

    Ma, Wenbin; van Rhee, Cees; Schott, Dingena

    2018-03-01

    Since the gradual decrease of mineral resources on-land, deep sea mining (DSM) is becoming an urgent and important emerging activity in the world. However, until now there has been no commercial scale DSM project in progress. Together with the reasons of technological feasibility and economic profitability, the environmental impact is one of the major parameters hindering its industrialization. Most of the DSM environmental impact research focuses on only one particular aspect ignoring that all the DSM environmental impacts are related to each other. The objective of this work is to propose a framework for the numerical calculation methods of the integrated DSM environmental impacts through a literature review. This paper covers three parts: (i) definition and importance description of different DSM environmental impacts; (ii) description of the existing numerical calculation methods for different environmental impacts; (iii) selection of a numerical calculation method based on the selected criteria. The research conducted in this paper provides a clear numerical calculation framework for DSM environmental impact and could be helpful to speed up the industrialization process of the DSM industry.

  16. Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods

    KAUST Repository

    Wang, Yi

    2016-07-21

    Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.

  17. An Efficient numerical method to calculate the conductivity tensor for disordered topological matter

    Science.gov (United States)

    Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.

    2015-03-01

    We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.

  18. A finite-volume numerical method to calculate fluid forces and rotordynamic coefficients in seals

    Science.gov (United States)

    Athavale, M. M.; Przekwas, A. J.; Hendricks, R. C.

    1992-01-01

    A numerical method to calculate rotordynamic coefficients of seals is presented. The flow in a seal is solved by using a finite-volume formulation of the full Navier-Stokes equations with appropriate turbulence models. The seal rotor is perturbed along a diameter such that the position of the rotor is a sinusoidal function of time. The resulting flow domain changes with time, and the time-dependent flow in the seal is solved using a space conserving moving grid formulation. The time-varying fluid pressure reaction forces are then linked with the rotor center displacement, velocity and acceleration to yield the rotordynamic coefficients. Results for an annular seal are presented, and compared with experimental data and other more simplified numerical methods.

  19. Probability density of tunneled carrier states near heterojunctions calculated numerically by the scattering method.

    Energy Technology Data Exchange (ETDEWEB)

    Wampler, William R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Myers, Samuel M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Modine, Normand A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2017-09-01

    The energy-dependent probability density of tunneled carrier states for arbitrarily specified longitudinal potential-energy profiles in planar bipolar devices is numerically computed using the scattering method. Results agree accurately with a previous treatment based on solution of the localized eigenvalue problem, where computation times are much greater. These developments enable quantitative treatment of tunneling-assisted recombination in irradiated heterojunction bipolar transistors, where band offsets may enhance the tunneling effect by orders of magnitude. The calculations also reveal the density of non-tunneled carrier states in spatially varying potentials, and thereby test the common approximation of uniform- bulk values for such densities.

  20. Development of an atmospheric diffusion numerical model for a nuclear facility. Numerical calculation method incorporating building effects

    International Nuclear Information System (INIS)

    Sada, Koichi; Michioka, Takenobu; Ichikawa, Yoichi

    2002-01-01

    Because effluent gas is sometimes released from low positions, viz., near the ground surface and around buildings, the effects caused by buildings within the site area are not negligible for gas diffusion predictions. For these reasons, the effects caused by buildings for gas diffusion are considered under the terrain following calculation coordinate system in this report. Numerical calculation meshes on the ground surface are treated as the building with the adaptation of wall function techniques of turbulent quantities in the flow calculations using a turbulence closure model. The reflection conditions of released particles on building surfaces are taken into consideration in the diffusion calculation using the Lagrangian particle model. Obtained flow and diffusion calculation results are compared with those of wind tunnel experiments around the building. It was apparent that features observed in a wind tunnel, viz., the formation of cavity regions behind the building and the gas diffusion to the ground surface behind the building, are also obtained by numerical calculation. (author)

  1. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods

    International Nuclear Information System (INIS)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-01-01

    In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs

  2. A numerical method for the calculation of dynamic response and acoustic radiation from an underwater structure

    Science.gov (United States)

    Zhou, Q.; Joseph, P. F.

    2005-05-01

    An approach combining finite element with boundary element methods is proposed to calculate the elastic vibration and acoustic field radiated from an underwater structure. The FEM software NASTRAN is employed for computation of the structural vibration. An uncoupled boundary element method, based on the potential decomposition technique, is described to determine the acoustic added mass and damping coefficients that result due to fluid loading effects. The acoustic matrices of added mass and damping coefficients are then added to the structural mass and damping matrices, respectively, by the DMAP modules of NASTRAN. Numerical results are shown to be in good agreement with experimental data. The complex eigenvalue analyses of underwater structure are obtained by NASTRAN solution sequence SOL107. Results obtained from this study suggest that the natural frequencies of underwater structures are only weakly dependent on the acoustic frequency if the acoustic wavelength is roughly twice as large as the maximum structural dimension.

  3. A calculation method for RF couplers design based on numerical simulation by microwave studio

    International Nuclear Information System (INIS)

    Wang Rong; Pei Yuanji; Jin Kai

    2006-01-01

    A numerical simulation method for coupler design is proposed. It is based on the matching procedure for the 2π/3 structure given by Dr. R.L. Kyhl. Microwave Studio EigenMode Solver is used for such numerical simulation. the simulation for a coupler has been finished with this method and the simulation data are compared with experimental measurements. The results show that this numerical simulation method is feasible for coupler design. (authors)

  4. Study of plasma equilibrium in toroidal fusion devices using mesh-free numerical calculation method

    Energy Technology Data Exchange (ETDEWEB)

    Rasouli, C.; Abbasi Davani, F. [Radiation Application Department, Shahid Beheshti University, Tehran (Iran, Islamic Republic of); Rokrok, B. [Nuclear Safety and Radiological Protection Group, Nuclear Science and Technology Research Institute, Tehran (Iran, Islamic Republic of)

    2016-08-15

    Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation has been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.

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

    Science.gov (United States)

    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.

  6. Hybrid method for determining the parameters of condenser microphones from measured membrane velocities and numerical calculations

    DEFF Research Database (Denmark)

    Barrera Figueroa, Salvador; Rasmussen, Knud; Jacobsen, Finn

    2009-01-01

    Typically, numerical calculations of the pressure, free-field, and random-incidence response of a condenser microphone are carried out on the basis of an assumed displacement distribution of the diaphragm of the microphone; the conventional assumption is that the displacement follows a Bessel...

  7. Numerical methods to calculate solar radiation, validation through a new Graphic User Interface design

    International Nuclear Information System (INIS)

    Mesri, Mokhtaria

    2015-01-01

    Highlights: • Rare measuring networks in the developing world due to technical and fiscal reasons. • Insufficient attention is paid regarding to tools for solar energy systems design. • The new interface offers solutions to the insisting need for innovative decisions. • Comprehensive comparative studies are conducted using experimental measurements. • Results are with attractive margins of error in accordance with experimental data. - Abstract: The present paper is basically devoted to the estimation of solar radiation in order to provide data on the situation of solar applications in a given site; it also aims at contributing to the performance improvement of solar energy systems. I aim to show and evaluate the performance of the most appropriate models used to recover solar components at ground level, via confronting meteorological techniques to selected semi empirical methods. I have adopted an innovative approach to testing the theory through numerical simulation by providing a friendly user ergonomic Graphic User Interface ‘GUI’, carefully designed and that principally makes use of a large range of models for the calculation of solar components. In this article I may consider three numerical models namely: Lacis and Hansen, Atwater and Ball and Lui and Jordon, which are used here to elucidate the performance of such methods facing meteorological models such as those of Angstrom, Garg and Coppolino. I debate the advantages of these latest methods, and I argue that they are of big importance because the main variable that is used is sunshine duration. Some of them involve the water content in the atmosphere, a particularly important parameter which strongly absorbs solar radiation in the infrared region. They are also perfectly suited for locations where solar irradiance is not being measured by all hydrometeorological stations, and where only meteorological data are collected. I want to complete this paper by demonstrating the efficiency of the

  8. Paradoxes in numerical calculations

    Czech Academy of Sciences Publication Activity Database

    Brandts, J.; Křížek, Michal; Zhang, Z.

    2016-01-01

    Roč. 26, č. 3 (2016), s. 317-330 ISSN 1210-0552 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : round-off errors * numerical instability * recurrence formulae Subject RIV: BA - General Mathematics Impact factor: 0.394, year: 2016

  9. Analytical-numerical methods of calculations of energy and three-dimensional particle distributions in electromagnetic cascades

    Science.gov (United States)

    Ivanenko, I. P.; Kanevsky, B. L.; Roganova, T. M.; Sizov, V. V.; Triphonova, S. V.

    1985-01-01

    Analytical and numerical methods of calculation of the energy and three dimensional EPS characteristics are reported. The angular and lateral functions of electrons in EPS have been obtained by the Landau and small angle approximations A and B and compared with earlier data. A numerical method of solution of cascade equations for the EPS distribution function moments has been constructed. Considering the equilibrium rms angle as an example, errors appearing when approximating the elementary process cross sections by their asymptotic expressions are analyzed.

  10. The numerical method of inverse Laplace transform for calculation of overvoltages in power transformers and test results

    Directory of Open Access Journals (Sweden)

    Mikulović Jovan Č.

    2014-01-01

    Full Text Available A methodology for calculation of overvoltages in transformer windings, based on a numerical method of inverse Laplace transform, is presented. Mathematical model of transformer windings is described by partial differential equations corresponding to distributed parameters electrical circuits. The procedure of calculating overvoltages is applied to windings having either isolated neutral point, or grounded neutral point, or neutral point grounded through impedance. A comparative analysis of the calculation results obtained by the proposed numerical method and by analytical method of calculation of overvoltages in transformer windings is presented. The results computed by the proposed method and measured voltage distributions, when a voltage surge is applied to a three-phase 30 kVA power transformer, are compared. [Projekat Ministartsva nauke Republike Srbije, br. TR-33037 i br. TR-33020

  11. Numerical-analytical method of calculating insulated double-glazed units deflection under climatic (internal load

    Directory of Open Access Journals (Sweden)

    Plotnikov Aleksandr Aleksandrovich

    Full Text Available Glass unit consists of glasses hermetically-united together. The cavity of an insulating glass unit contains a fixed volume of air (gas. In the process of production regular air with atmospheric pressure and temperature is sealed inside a glass unit. During operation the atmospheric pressure is constantly changing, but the pressure inside remains constant (at a constant temperature. A change of temperature or of the external air pressure results in a pressure difference and therefore in a load on the glass panes. The action may exceed the usual load considerably. This pressure effects the glasses of the unit, deforms them, lowers the thermotechnical properties of glass units and can lead to their destruction. The action of the inside pressure can be seen all around as convex and concaved glasses, which destroys the architectural look of buildings. It is obvious that it is incorrect to calculate thin glass plates on such a load only by classical methods of strength of materials theory. In this case we need a special calculation method. The effects of a change in temperature, altitude or meteorological pressure are easily covered by the definition of an isochore pressure. This is necessary, to determine the change of pressure due to the temperature induced gas expansion in the cavity of the insulating glass according to the ideal gas law. After the integration of the analytical plate solution and the ideal gas law, the final pressure states can easily be calculated by coupling the change of volume and the change of pressure.

  12. VALIDATION OF NUMERICAL METHODS TO CALCULATE BYPASS FLOW IN A PRISMATIC GAS-COOLED REACTOR CORE

    Directory of Open Access Journals (Sweden)

    NAM-IL TAK

    2013-11-01

    Full Text Available For thermo-fluid and safety analyses of a High Temperature Gas-cooled Reactor (HTGR, intensive efforts are in progress in the developments of the GAMMA+ code of Korea Atomic Energy Research Institute (KAERI and the AGREE code of the University of Michigan (U of M. One of the important requirements for GAMMA+ and AGREE is an accurate modeling capability of a bypass flow in a prismatic core. Recently, a series of air experiments were performed at Seoul National University (SNU in order to understand bypass flow behavior and generate an experimental database for the validation of computer codes. The main objective of the present work is to validate the GAMMA+ and AGREE codes using the experimental data published by SNU. The numerical results of the two codes were compared with the measured data. A good agreement was found between the calculations and the measurement. It was concluded that GAMMA+ and AGREE can reliably simulate the bypass flow behavior in a prismatic core.

  13. Numerical method for calculation of 3D viscous turbomachine flow taking into account stator/rotor unsteady interaction

    Energy Technology Data Exchange (ETDEWEB)

    Rusanov, A.V.; Yershov, S.V. [Institute of Mechanical Engineering Problems of National Academy of Sciences of Ukraine Kharkov (Ukraine)

    1997-12-31

    The numerical method is suggested for the calculation of the 3D periodically unsteady viscous cascade flow evoked by the aerodynamics interaction of blade rows. Such flow is described by the thin-layer Reynolds-averaged unsteady Navier-Stokes equations. The turbulent effects are simulated with the modified Baldwin-Lomax turbulence model. The problem statement allows to consider an unsteady flow through either a single turbo-machine stage or a multi stage turbomachine. The sliding mesh techniques and the time-space non-oscillatory square interpolation are used in axial spacings to calculate the flow in a computational domain that contains the reciprocally moving elements. The gasdynamical equations are integrated numerically with the implicit quasi-monotonous Godunov`s type ENO scheme of the second or third order of accuracy. The suggested numerical method is incorporated in the FlowER code developed by authors for calculations of the 3D viscous compressible flows through multi stage turbomachines. The numerical results are presented for unsteady turbine stage throughflows. The method suggested is shown to simulate qualitatively properly the main unsteady cascade effects in particular the periodically blade loadings, the propagation of stator wakes through rotor blade passage and the unsteady temperature flowfields for stages with cooled stator blades. (author) 21 refs.

  14. Numerical methods

    CERN Document Server

    Dahlquist, Germund

    1974-01-01

    ""Substantial, detailed and rigorous . . . readers for whom the book is intended are admirably served."" - MathSciNet (Mathematical Reviews on the Web), American Mathematical Society.Practical text strikes fine balance between students' requirements for theoretical treatment and needs of practitioners, with best methods for large- and small-scale computing. Prerequisites are minimal (calculus, linear algebra, and preferably some acquaintance with computer programming). Text includes many worked examples, problems, and an extensive bibliography.

  15. Application of numerical method in calculating the internal rate of return of joint venture investment using diminishing musyarakah model

    Science.gov (United States)

    Ruslan, Siti Zaharah Mohd; Jaffar, Maheran Mohd

    2017-05-01

    Islamic banking in Malaysia offers variety of products based on Islamic principles. One of the concepts is a diminishing musyarakah. The concept of diminishing musyarakah helps Muslims to avoid transaction which are based on riba. The diminishing musyarakah can be defined as an agreement between capital provider and entrepreneurs that enable entrepreneurs to buy equity in instalments where profits and losses are shared based on agreed ratio. The objective of this paper is to determine the internal rate of return (IRR) for a diminishing musyarakah model by applying a numerical method. There are several numerical methods in calculating the IRR such as by using an interpolation method and a trial and error method by using Microsoft Office Excel. In this paper we use a bisection method and secant method as an alternative way in calculating the IRR. It was found that the diminishing musyarakah model can be adapted in managing the performance of joint venture investments. Therefore, this paper will encourage more companies to use the concept of joint venture in managing their investments performance.

  16. Numerical tables of anomalous scattering factors calculated by the Cromer and Liberman's method

    International Nuclear Information System (INIS)

    Sasaki, Satoshi.

    1989-02-01

    Anomalous scattering factors f' and f'' have been calculated for the atoms Li through Bi, plus U, using the relativistic treatment described by Cromer and Liberman. The final f' value does not include the Jensen's correction term on the magnetic scattering. The tables are presented with the f' and f'' values (i) at 0.01 A intervals in the wavelength range from 0.1 to 2.89 A and (ii) at 0.0001 A intervals in the neighborhood of the K, L 1 , L 2 , and L 3 absorption edges. (author)

  17. Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data

    Science.gov (United States)

    Daryabeigi, Kamran; Berry, Scott A.; Horvath, Thomas J.; Nowak, Robert J.

    2006-01-01

    The use of multi-dimensional finite volume heat conduction techniques for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the standard one-dimensional semi-infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the NASA Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody was investigated. An array of streamwise-orientated heating striations was generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients caused by striation patterns multi-dimensional heat transfer techniques were necessary to obtain more accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates compared to 2-D analysis because it did not account for lateral heat conduction in the model.

  18. The grid-based fast multipole method--a massively parallel numerical scheme for calculating two-electron interaction energies.

    Science.gov (United States)

    Toivanen, Elias A; Losilla, Sergio A; Sundholm, Dage

    2015-12-21

    Algorithms and working expressions for a grid-based fast multipole method (GB-FMM) have been developed and implemented. The computational domain is divided into cubic subdomains, organized in a hierarchical tree. The contribution to the electrostatic interaction energies from pairs of neighboring subdomains is computed using numerical integration, whereas the contributions from further apart subdomains are obtained using multipole expansions. The multipole moments of the subdomains are obtained by numerical integration. Linear scaling is achieved by translating and summing the multipoles according to the tree structure, such that each subdomain interacts with a number of subdomains that are almost independent of the size of the system. To compute electrostatic interaction energies of neighboring subdomains, we employ an algorithm which performs efficiently on general purpose graphics processing units (GPGPU). Calculations using one CPU for the FMM part and 20 GPGPUs consisting of tens of thousands of execution threads for the numerical integration algorithm show the scalability and parallel performance of the scheme. For calculations on systems consisting of Gaussian functions (α = 1) distributed as fullerenes from C20 to C720, the total computation time and relative accuracy (ppb) are independent of the system size.

  19. Development of numerical methods to calculate the propagation and the absorption of the hybrid wave in tokamaks

    International Nuclear Information System (INIS)

    Sebelin, E.

    1997-01-01

    Full-wave calculations based on trial functions are carried out for solving the lower hybrid current drive problem in tokamaks. A variational method is developed and provides an efficient system to describe in a global manner both the propagation and the absorption of the electromagnetic waves in plasmas. The calculation is fully carried out in the case of circular and concentric flux surfaces. The existence and uniqueness of the solution of the wave propagation equation is mathematically proved. The first realistic simulations are performed for the high aspect ratio tokamak TRIAM-1M. It is checked that the main features of the lower-hybrid wave dynamics are well described numerically. (A.C.)

  20. Numerical analysis of incompressible two-fluid model by finite element method. Numerical method and calculation of flow around a circular cylinder

    International Nuclear Information System (INIS)

    Uchiyama, Tomomi; Minemura, Kiyoshi

    1996-01-01

    A two-dimensional finite element method for an incompressible two-fluid model is developed in order to enhance the applicability of the two-fluid model to the analyses in arbitrarily shaped channels. The solution algorithm is based on the SMAC method for incompressible single-phase flows. Quadrilateral element with four nodes is employed. The velocities and volumetric fractions of both phases are defined on the nodes. The pressure is defined at a centroid of each element and assumed to be constant within the element. The Galerkin method is applied to the finite element formulations. Air-water two-phase flow around a circular cylinder is analyzed by the finite element method. The calculated distributions of the volumetric fraction of the gas-phase show good agreement with measurements. (author)

  1. Application of numerical inverse method in calculation of composition-dependent interdiffusion coefficients in finite diffusion couples

    DEFF Research Database (Denmark)

    Liu, Yuanrong; Chen, Weimin; Zhong, Jing

    2017-01-01

    The previously developed numerical inverse method was applied to determine the composition-dependent interdiffusion coefficients in single-phase finite diffusion couples. The numerical inverse method was first validated in a fictitious binary finite diffusion couple by pre-assuming four standard ...

  2. A testing procedure for triaxial tests and a numerical method for the calculation of powder flow properties

    NARCIS (Netherlands)

    Eelkman Rooda, J.; Haaker, G.

    1977-01-01

    A testing procedure for measuring flow properties of powders is developed which makes it possible to use results from triaxial tests in the Jenike bin theory. For the elaboration of the results a numerical method is used, based upon the Warren Spring equation (τ/C)N = (σ + T)/T. In this equation σ

  3. Numerical calculations of ultrasonic fields

    Science.gov (United States)

    Johnson, J. A.

    1982-02-01

    A code for calculating ultrasonic fields was developed by revising the thermal hydraulics code STEALTH. This code may be used in a wide variety of situations in which a detailed knowledge of a propagating wave field is required. Among the potential uses are interpretation of pulse echo or pitch catch ultrasonic signals in complicated geometries, ultrasonic transducer modeling and characterization; optimization and evaluation of transducer design; optimization and reliability of inspection procedures; investigation of the response of different types of reflectors; flaw modeling; and general theoretical acoustics. The code is described, and its limitations and potential are discussed. A discussion of the required input and of the general procedures for running the code is presented. Three sample problems illustrate the input and the use of the code.

  4. Spin--density-functional formalism for quantum mechanical calculations: test on diatomic molecules with an efficient numerical method

    International Nuclear Information System (INIS)

    Gunnarsson, O.; Johansson, P.

    1976-01-01

    The spin-density-functional (SDF) formalism with the local-spin-density (LSD) approximation is applied to a number of small molecules with the primary aim of testing the approximation for molecular applications. A new numerical method to solve the one-electron wave equation is developed, utilizing the special features of the SDF formalism. Energy curves, dissociation energies, and equilibrium distances for some diatomic molecules [H 2 + ( 2 Σ + /sub g/, 2 Σ + /sub u/), H 2 ( 1 Σ + /sub g/, 3 Σ + /sub u/), He 2 2+ ( 1 Σ + /sub g/), and He 2 ( 1 Σ + /sub g/)] and the vibrational frequencies of H 2 . The deviations from the experimental results are typically 1 / 2 eV for the energies and less than or equal to 0.1 A for the distances. The LSD approximation is discussed using the concept of an exchange-correlation hole and predictions about the applicability to other molecules are made. The LSD approximation is compared with the Hartree--Fock and multiple-scattering-Xα methods, and some difficulties in the latter methods are pointed out. It is argued that the SDF formalism within the LSD approximation has physical advantages compared to the Hartree--Fock and Xα methods and that it should provide a simple and useful method for a broad range of applications

  5. Numerical methods using Matlab

    CERN Document Server

    Lindfield, George

    2012-01-01

    Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board. Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of use

  6. Numerical precision calculations for LHC physics

    Energy Technology Data Exchange (ETDEWEB)

    Reuschle, Christian Andreas

    2013-02-05

    In this thesis I present aspects of QCD calculations, which are related to the fully numerical evaluation of next-to-leading order (NLO) QCD amplitudes, especially of the one-loop contributions, and the efficient computation of associated collider observables. Two interrelated topics have thereby been of concern to the thesis at hand, which give rise to two major parts. One large part is focused on the general group-theoretical behavior of one-loop QCD amplitudes, with respect to the underlying SU(N{sub c}) theory, in order to correctly and efficiently handle the color degrees of freedom in QCD one-loop amplitudes. To this end a new method is introduced that can be used in order to express color-ordered partial one-loop amplitudes with multiple quark-antiquark pairs as shuffle sums over cyclically ordered primitive one-loop amplitudes. The other large part is focused on the local subtraction of divergences off the one-loop integrands of primitive one-loop amplitudes. A method for local UV renormalization has thereby been developed, which uses local UV counterterms and efficient recursive routines. Together with suitable virtual soft and collinear subtraction terms, the subtraction method is extended to the virtual contributions in the calculations of NLO observables, which enables the fully numerical evaluation of the one-loop integrals in the virtual contributions. The method has been successfully applied to the calculation of jet rates in electron-positron annihilation to NLO accuracy in the large-N{sub c} limit.

  7. Numerical precision calculations for LHC physics

    International Nuclear Information System (INIS)

    Reuschle, Christian Andreas

    2013-01-01

    In this thesis I present aspects of QCD calculations, which are related to the fully numerical evaluation of next-to-leading order (NLO) QCD amplitudes, especially of the one-loop contributions, and the efficient computation of associated collider observables. Two interrelated topics have thereby been of concern to the thesis at hand, which give rise to two major parts. One large part is focused on the general group-theoretical behavior of one-loop QCD amplitudes, with respect to the underlying SU(N c ) theory, in order to correctly and efficiently handle the color degrees of freedom in QCD one-loop amplitudes. To this end a new method is introduced that can be used in order to express color-ordered partial one-loop amplitudes with multiple quark-antiquark pairs as shuffle sums over cyclically ordered primitive one-loop amplitudes. The other large part is focused on the local subtraction of divergences off the one-loop integrands of primitive one-loop amplitudes. A method for local UV renormalization has thereby been developed, which uses local UV counterterms and efficient recursive routines. Together with suitable virtual soft and collinear subtraction terms, the subtraction method is extended to the virtual contributions in the calculations of NLO observables, which enables the fully numerical evaluation of the one-loop integrals in the virtual contributions. The method has been successfully applied to the calculation of jet rates in electron-positron annihilation to NLO accuracy in the large-N c limit.

  8. Numerical method to calculate the quantum transmission, resonance and eigenvalue energies: application to a biased multibarrier systems

    Energy Technology Data Exchange (ETDEWEB)

    Maiz, F., E-mail: fethimaiz@gmail.com [University of Cartage, Nabeul Engineering Preparatory Institute, Merazka, 8000 Nabeul (Tunisia); King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413 (Saudi Arabia)

    2015-04-15

    A novel method to calculate the quantum transmission, resonance and eigenvalue energies forming the sub-bands structure of non-symmetrical, non-periodical semiconducting heterostructure potential has been proposed in this paper. The method can be applied on a multilayer system with varying thickness of the layer and effective mass of electrons and holes. Assuming an approximated effective mass and using Bastard's boundary conditions, Schrödinger equation at each media is solved and then using a confirmed recurrence method, the transmission and reflection coefficients and the energy quantification condition are expressed. They are simple combination of coupled equations. Schrödinger's equation solutions are Airy functions or plane waves, depending on the electrical potential energy slope. To illustrate the feasibility of the proposed method, the N barriers – (N−1) wells structure for N=3, 5, 8, 9, 17 and 35 are studied. All results show very good agreements with previously published results obtained from applying different methods on similar systems.

  9. Validation of numeric methods for calculating interactions between district heating pipelines and the surrounding soil; Validierung numerischer Verfahren zur Berechnung des Interaktionsverhaltens 'Fernwaermeleitung - Baugrund'

    Energy Technology Data Exchange (ETDEWEB)

    Salveter, G.

    2000-07-01

    In this thesis, the results of experimental research work on global bearing behaviour with respect to the existing theoretical basis are systematically analysed for the evaluation and interpretation of measuring results. Among other things, the geometry of the pipeline route, the compactness of the backfilling material and the temperature dependence are considered. The mutual influence of friction and bedding resistances in the region of bends could not yet be determined for a local analysis by existing numerical models. This requires the determination of the induced stress distribution on the pipe perimeter due to lateral displacement of the pipe. The influence is therefore described by a numerical consideration of relative displacements between the pipe and the surrounding soil. Ultimately, relative displacements are verified on the basis of our own complementary results from experimental research carried out in a laboratory for soil mechanics with specially designed test equipment. The global analysis of bearing loads and displacements is done with a numerical model, in which the plastic jacked pipe is idealized as a beam, and the effect of the soil is idealized by spring elements with non-linear force displacement characteristics. An existing numerical model is extended with regard to the new findings and while taking vertical displacements into account. It is used for numerical simulations of selected tests on the global bearing behaviour of underground district heating pipelines which were carried out as part of the research cooperation project. Apart from a good correspondence between calculated results and test results this also provides a plausible description of interrelations. At the same time, however, it also makes itclear that further research is necessary. This thesis provides a contribution to the validation of recent methods for the calculated modelling of the interaction between a district heating pipeline and the subsoil on the basis of

  10. Analysis of numerical methods

    CERN Document Server

    Isaacson, Eugene

    1994-01-01

    This excellent text for advanced undergraduates and graduate students covers norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation, and other topics. It offers a careful analysis and stresses techniques for developing new methods, plus many examples and problems. 1966 edition.

  11. Numerical Methods in Linguistics

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 10; Issue 1. Numerical Methods in Linguistics - An Introduction to Glottochronology. Raamesh Gowri Raghavan. General Article Volume 10 Issue 1 January 2005 pp 17-24. Fulltext. Click here to view fulltext PDF. Permanent link:

  12. Aerodynamic losses calculation of a turbine blade with film cooling with forward and backward injection by numerical method

    Science.gov (United States)

    Prajapati, Anil

    Thermal efficiency and power output of gas turbines can be increased by increasing the turbine blade inlet temperature. However, the main problem is the durability of the turbine blade due to the thermal stress on it at high temperature. This has led to the development of film cooling technology, in which coolant is injected from a series of cooling holes made on the blade surface to form an insulating blanket over the blade surface. However, it has to pay the aerodynamic penalties due to the injection of coolant, which are not fully understood. Pressure loss coefficient is one of the easy and widely used parameters to determine the aerodynamic loss occurred on a turbine blade. The losses occurred on the turbine blade with forward injection and backward injection cooling are studied at a different blowing ratios by a numerical simulation, which shows that the loss is higher in the case of backward injection than in forward injection. Fan-shaped cooling holes are also considered to compare with the cylindrical holes. It is observed that the loss is increased due to the fan-shaped holes in the forward injection whereas there is not a substantial difference due to the fan-shaped holes in the backward injection. The aerodynamic loss due to the location of coolant injection is studied by using injection from the leading edge, pressure side, suction side and trailing edge respectively. The study is performed to determine the effect of incidence angles and coolant injection angles on the aerodynamic loss.

  13. The numerical field calculation in structures with the space-uniform quadruple focusing by the method of auxiliary charges

    CERN Document Server

    Tishkin, S S

    2001-01-01

    In the paper the procedure of solving integral equations with the use of auxiliary charges is used. The electrostatic field potential is presented in the form of superposition of the fields of point sources located out of the investigated region at some distance from it. The values of N charges are determined from the boundary conditions at N points of the boundary. The definition of the point sources is equivalent to using some function of the charge density at the boundary of the region.This approach was used for the calculation of structures with the space-uniform quadruple focusing with sinusoidal and trapezoidal modulation, and also a section of the transverse matching of the 'funnel'.

  14. Numerical calculations of potential distribution in non-ideal ...

    Indian Academy of Sciences (India)

    A quadrupole ion trap consisting of electrode structures symmetric about -axis is an important tool for conducting several precision experiments. In practice the field inside the trap does not remain purely quadrupolar, and can be calculated using numerical methods. We have used boundary element method to calculate the ...

  15. A Fast Numerical Method for the Calculation of the Equilibrium Isotopic Composition of a Transmutation System in an Advanced Fuel Cycle

    Directory of Open Access Journals (Sweden)

    F. Álvarez-Velarde

    2012-01-01

    Full Text Available A fast numerical method for the calculation in a zero-dimensional approach of the equilibrium isotopic composition of an iteratively used transmutation system in an advanced fuel cycle, based on the Banach fixed point theorem, is described in this paper. The method divides the fuel cycle in successive stages: fuel fabrication, storage, irradiation inside the transmutation system, cooling, reprocessing, and incorporation of the external material into the new fresh fuel. The change of the fuel isotopic composition, represented by an isotope vector, is described in a matrix formulation. The resulting matrix equations are solved using direct methods with arbitrary precision arithmetic. The method has been successfully applied to a double-strata fuel cycle with light water reactors and accelerator-driven subcritical systems. After comparison to the results of the EVOLCODE 2.0 burn-up code, the observed differences are about a few percents in the mass estimations of the main actinides.

  16. Numerical effects in the neutron flux calculations into WWER-type reactor vessels by Monte Carlo method

    International Nuclear Information System (INIS)

    Alvarez Cardona, C.M.; Rodriguez Gual, M.; Hernandez Valle, S.

    2001-01-01

    The calculation of neutron fluxes and fluence into reactor pressure vessel is a regulatory requirement in the stages of the design, operation and plan lifetime extension. The reactor vessel is considered a unique and non-substitutable part of the NPP that undergoes degradation. The main source of the aging comes from the fast neutron damage induced in the steel crystalline lattice. Due to the proximity of the core edge to the vessel inner surface; the vessel steel is exposed to high fast neutron fluence. The effect of this irradiation on the mechanical properties becomes more acute because of the impurities measured in the Russian steel alloys. In the present paper, a PC version of the Monte Carlo 3-D HEXANN-EVALU system is used for the estimation of the WWER reactor pressure vessel irradiation. It was selected on the basis of its flexible options that on the other hand need to be quantified in connection with the desired magnitudes. The parameters that control the random walk of neutrons as well as the efficiency increasing options included in the code are studied in order to identify their impact in the final results for fluxes and fluence in the reactor pressure vessel. As a result an optimal set of parameters is suggested. (authors)

  17. Numerical calculations of the probabilities for quantum transitions in atoms and molecules by the path integral method

    Science.gov (United States)

    Biryukov, Alexander; Degtyareva, Yana

    2017-10-01

    The probabilities of molecular quantum transitions induced by electromagnetic field are expressed as path integrals of a real alternating functional. We propose a new method for computing these integrals by means of recurrence relations. We apply this approach to description of the two-photon Rabi oscillations.

  18. Numerical calculation of impurity charge state distributions

    International Nuclear Information System (INIS)

    Crume, E.C.; Arnurius, D.E.

    1977-09-01

    The numerical calculation of impurity charge state distributions using the computer program IMPDYN is discussed. The time-dependent corona atomic physics model used in the calculations is reviewed, and general and specific treatments of electron impact ionization and recombination are referenced. The complete program and two examples relating to tokamak plasmas are given on a microfiche so that a user may verify that his version of the program is working properly. In the discussion of the examples, the corona steady-state approximation is shown to have significant defects when the plasma environment, particularly the electron temperature, is changing rapidly

  19. Numerical calculation of impurity charge state distributions

    Energy Technology Data Exchange (ETDEWEB)

    Crume, E. C.; Arnurius, D. E.

    1977-09-01

    The numerical calculation of impurity charge state distributions using the computer program IMPDYN is discussed. The time-dependent corona atomic physics model used in the calculations is reviewed, and general and specific treatments of electron impact ionization and recombination are referenced. The complete program and two examples relating to tokamak plasmas are given on a microfiche so that a user may verify that his version of the program is working properly. In the discussion of the examples, the corona steady-state approximation is shown to have significant defects when the plasma environment, particularly the electron temperature, is changing rapidly.

  20. FIESTA 2: Parallelizeable multiloop numerical calculations

    Science.gov (United States)

    Smirnov, A. V.; Smirnov, V. A.; Tentyukov, M.

    2011-03-01

    The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin-Barnes representations. Other important improvements to the code are complete parallelization (even to multiple computers), high-precision arithmetics (allowing to calculate integrals which were undoable before), new integrators, Speer sectors as a strategy, the possibility to evaluate more general parametric integrals. Program summaryProgram title:FIESTA 2 Catalogue identifier: AECP_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECP_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL version 2 No. of lines in distributed program, including test data, etc.: 39 783 No. of bytes in distributed program, including test data, etc.: 6 154 515 Distribution format: tar.gz Programming language: Wolfram Mathematica 6.0 (or higher) and C Computer: From a desktop PC to a supercomputer Operating system: Unix, Linux, Windows, Mac OS X Has the code been vectorised or parallelized?: Yes, the code has been parallelized for use on multi-kernel computers as well as clusters via Mathlink over the TCP/IP protocol. The program can work successfully with a single processor, however, it is ready to work in a parallel environment and the use of multi-kernel processor and multi-processor computers significantly speeds up the calculation; on clusters the calculation speed can be improved even further. RAM: Depends on the complexity of the problem Classification: 4.4, 4.12, 5, 6.5 Catalogue identifier of previous version: AECP_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 735 External routines: QLink [1], Cuba library [2], MPFR [3] Does the new version supersede the previous version?: Yes Nature of problem: The sector

  1. Numerical calculations of potential distribution in non-ideal ...

    Indian Academy of Sciences (India)

    Abstract. A quadrupole ion trap consisting of electrode structures symmetric about z- axis is an important tool for conducting several precision experiments. In practice the field inside the trap does not remain purely quadrupolar, and can be calculated using numer- ical methods. We have used boundary element method to ...

  2. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods; Calculo Numerico de Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Metodos Numericos

    Energy Technology Data Exchange (ETDEWEB)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-10-12

    In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs.

  3. Excel spreadsheet in teaching numerical methods

    Science.gov (United States)

    Djamila, Harimi

    2017-09-01

    One of the important objectives in teaching numerical methods for undergraduates’ students is to bring into the comprehension of numerical methods algorithms. Although, manual calculation is important in understanding the procedure, it is time consuming and prone to error. This is specifically the case when considering the iteration procedure used in many numerical methods. Currently, many commercial programs are useful in teaching numerical methods such as Matlab, Maple, and Mathematica. These are usually not user-friendly by the uninitiated. Excel spreadsheet offers an initial level of programming, which it can be used either in or off campus. The students will not be distracted with writing codes. It must be emphasized that general commercial software is required to be introduced later to more elaborated questions. This article aims to report on a teaching numerical methods strategy for undergraduates engineering programs. It is directed to students, lecturers and researchers in engineering field.

  4. Improvement of fire-tube boilers calculation methods by the numerical modeling of combustion processes and heat transfer in the combustion chamber

    Science.gov (United States)

    Komarov, I. I.; Rostova, D. M.; Vegera, A. N.

    2017-11-01

    This paper presents the results of study on determination of degree and nature of influence of operating conditions of burner units and flare geometric parameters on the heat transfer in a combustion chamber of the fire-tube boilers. Change in values of the outlet gas temperature, the radiant and convective specific heat flow rate with appropriate modification of an expansion angle and a flare length was determined using Ansys CFX software package. Difference between values of total heat flow and bulk temperature of gases at the flue tube outlet calculated using the known methods for thermal calculation and defined during the mathematical simulation was determined. Shortcomings of used calculation methods based on the results of a study conducted were identified and areas for their improvement were outlined.

  5. Numerical challenges of short range wake field calculations

    Energy Technology Data Exchange (ETDEWEB)

    Lau, Thomas; Gjonaj, Erion; Weiland, Thomas [Technische Universitaet Darmstadt (Germany). Institut fuer Theorie Elektromagnetischer Felder (TEMF)

    2011-07-01

    For present and future accelerator projects with ultra short bunches the accurate and reliable calculation of short range wake fields is an important issue. However, the numerical calculation of short range wake fields is a numerical challenging task. The presentation gives an overview over the numerical challenges and techniques for short range wake field calculations. Finally, some simulation results obtained by the program PBCI developed at the TU Darmstadt are presented.

  6. Development of numerical methods to calculate the propagation and the absorption of the hybrid wave in tokamaks; Developpement des methodes numeriques pour la resolution de la propagation et de l`absorption de l`onde hybride dans les tokamaks

    Energy Technology Data Exchange (ETDEWEB)

    Sebelin, E

    1997-12-15

    Full-wave calculations based on trial functions are carried out for solving the lower hybrid current drive problem in tokamaks. A variational method is developed and provides an efficient system to describe in a global manner both the propagation and the absorption of the electromagnetic waves in plasmas. The calculation is fully carried out in the case of circular and concentric flux surfaces. The existence and uniqueness of the solution of the wave propagation equation is mathematically proved. The first realistic simulations are performed for the high aspect ratio tokamak TRIAM-1M. It is checked that the main features of the lower-hybrid wave dynamics are well described numerically. (A.C.) 81 refs.

  7. Application of a numerical transport correction in diffusion calculations

    International Nuclear Information System (INIS)

    Tomatis, Daniele; Dall'Osso, Aldo

    2011-01-01

    Full core calculations by ordinary transport methods can demand considerable computational time, hardly acceptable in the industrial work frame. However, the trend of next generation nuclear cores goes toward more heterogeneous systems, where transport phenomena of neutrons become very important. On the other hand, using diffusion solvers is more practical allowing faster calculations, but a specific formulation of the diffusion coefficient is requested to reproduce the scalar flux with reliable physical accuracy. In this paper, the Ronen method is used to evaluate numerically the diffusion coefficient in the slab reactor. The new diffusion solution is driven toward the solution of the integral neutron transport equation by non linear iterations. Better estimates of currents are computed and diffusion coefficients are corrected at node interfaces, still assuming Fick's law. This method enables obtaining closer results to the transport solution by a common solver in multigroup diffusion. (author)

  8. Broyden's method in nuclear structure calculations

    International Nuclear Information System (INIS)

    Baran, Andrzej; Bulgac, Aurel; Forbes, Michael McNeil; Hagen, Gaute; Nazarewicz, Witold; Schunck, Nicolas; Stoitsov, Mario V.

    2008-01-01

    Broyden's method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the unitary gas problem, the nuclear density functional theory with Skyrme functionals, and the nuclear coupled-cluster theory. The stability of the method, its ease of use, and its rapid convergence rates make Broyden's method a tool of choice for large-scale nuclear structure calculations

  9. Parallelization method for three dimensional MOC calculation

    International Nuclear Information System (INIS)

    Zhang Zhizhu; Li Qing; Wang Kan

    2013-01-01

    A parallelization method based on angular decomposition for the three dimensional MOC was designed. To improve the parallel efficiency, the directions were pre-grouped and the groups were assembled to minimize the communication. The improved parallelization method was applied to the three dimensional MOC code TCM. The numerical results show that the calculation results of parallelization method are agreed with serial calculation results. The parallel efficiency gets obvious increase after the communication optimized and load balance. (authors)

  10. Physics-compatible numerical methods

    OpenAIRE

    Barry, Koren; Abgrall, Remi; Pavel, Bochev; Jason, Frank; Blair, Perrot

    2014-01-01

    International audience; Physics-compatible numerical methods are methods that aim to preserve key mathematical and physical properties of continuum physics models in their finite-dimensional algebraic representations. They include methods which preserve properties such as energy, monotonicity, maximum principles, symmetries, and involutions of the continuum models. Examples are mimetic methods for spatial discretizations, variational and geometric integrators, conservative finite-volume and f...

  11. Determination of hydrogen cluster velocities and comparison with numerical calculations

    International Nuclear Information System (INIS)

    Täschner, A.; Köhler, E.; Ortjohann, H.-W.; Khoukaz, A.

    2013-01-01

    The use of powerful hydrogen cluster jet targets in storage ring experiments led to the need of precise data on the mean cluster velocity as function of the stagnation temperature and pressure for the determination of the volume density of the target beams. For this purpose a large data set of hydrogen cluster velocity distributions and mean velocities was measured at a high density hydrogen cluster jet target using a trumpet shaped nozzle. The measurements have been performed at pressures above and below the critical pressure and for a broad range of temperatures relevant for target operation, e.g., at storage ring experiments. The used experimental method is described which allows for the velocity measurement of single clusters using a time-of-flight technique. Since this method is rather time-consuming and these measurements are typically interfering negatively with storage ring experiments, a method for a precise calculation of these mean velocities was needed. For this, the determined mean cluster velocities are compared with model calculations based on an isentropic one-dimensional van der Waals gas. Based on the obtained data and the presented numerical calculations, a new method has been developed which allows to predict the mean cluster velocities with an accuracy of about 5%. For this two cut-off parameters defining positions inside the nozzle are introduced, which can be determined for a given nozzle by only two velocity measurements

  12. Numerical methods problems and solutions

    CERN Document Server

    Jain, MK

    2004-01-01

    About the Book: Is an outline series containing brief text of numerical solution of transcendental and polynomial equations, system of linear algebraic equations and eigenvalue problems, interpolation and approximation, differentiation and integration, ordinary differential equations and complete solutions to about 300 problems. Most of these problems are given as unsolved problems in the authors earlier book. User friendly Turbo Pascal programs for commonly used numerical methods are given in the Appendix. This book can be used as a text/help book both by teachers and students. Contents:

  13. Numerical methods in multibody dynamics

    CERN Document Server

    Eich-Soellner, Edda

    1998-01-01

    Today computers play an important role in the development of complex mechanical systems, such as cars, railway vehicles or machines. Efficient simulation of these systems is only possible when based on methods that explore the strong link between numerics and computational mechanics. This book gives insight into modern techniques of numerical mathematics in the light of an interesting field of applications: multibody dynamics. The important interaction between modeling and solution techniques is demonstrated by using a simplified multibody model of a truck. Different versions of this mechanical model illustrate all key concepts in static and dynamic analysis as well as in parameter identification. The book focuses in particular on constrained mechanical systems. Their formulation in terms of differential-algebraic equations is the backbone of nearly all chapters. The book is written for students and teachers in numerical analysis and mechanical engineering as well as for engineers in industrial research labor...

  14. Numerical calculation of economic uncertainty by intervals and fuzzy numbers

    DEFF Research Database (Denmark)

    Schjær-Jacobsen, Hans

    2010-01-01

    This paper emphasizes that numerically correct calculation of economic uncertainty with intervals and fuzzy numbers requires implementation of global optimization techniques in contrast to straightforward application of interval arithmetic. This is demonstrated by both a simple case from managerial...

  15. Numerical calculation of beam coupling impedances in synchrotron accelerators

    Energy Technology Data Exchange (ETDEWEB)

    Haenichen, Lukas

    2016-07-01

    Beams of charged particles are of interest in various fields of research including particle and nuclear physics, material and medical science and many more. In synchrotron accelerators the accelerating section is passed periodically. A closed loop trajectory is enforced, by increasing the frequency of the accelerating electric field and the magnitude of the dipolar magnetic guide field synchronously. A synchrotron therefore consists of a circular assembly of various beamline elements which serve the purposes of accelerating and guiding the particle beam. For the flawless operation of such a machine it has to be assured that the particles perform a controlled motion along predefined trajectories. Amongst others, the fulfillment of the corresponding stability criteria is in close conjuction with the so-called beam coupling impedances which are an important figure of merit for collective effects in synchrotron accelerators. This work focuses on analytical and numerical methods for the calculation of beam coupling impedances. One of the primary objectives is to gain a better understanding of the electrodynamics related to charged particle beams, furthermore to recapitulate the mathematical description of charged particle beams in both time and frequency domain and finally establish the links between actual physics and numerical modeling. Analytical methods are usually restricted to symmetrical geometry and may solely serve for the approximate determination of the field distribution in real geometries or to validate certain numerical methods. More accurate prognosis is only possible with three-dimensional simulation models. Numerical simulation techniques have been established in the second half of the last century accompanying the evolution of many particle accelerators. Classical time domain codes were the prevailing simulation tools where the actual process of the particle motion sequence is reproduced. For the present case of a heavy ion synchrotron accelerator

  16. Analyzed method for calculating the distribution of electrostatic field

    International Nuclear Information System (INIS)

    Lai, W.

    1981-01-01

    An analyzed method for calculating the distribution of electrostatic field under any given axial gradient in tandem accelerators is described. This method possesses satisfactory accuracy compared with the results of numerical calculation

  17. Numerical methods for turbulent flow

    Science.gov (United States)

    Turner, James C., Jr.

    1988-01-01

    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.

  18. Numerical methods for metamaterial design

    CERN Document Server

    2013-01-01

    This book describes a relatively new approach for the design of electromagnetic metamaterials.  Numerical optimization routines are combined with electromagnetic simulations to tailor the broadband optical properties of a metamaterial to have predetermined responses at predetermined wavelengths. After a review of both the major efforts within the field of metamaterials and the field of mathematical optimization, chapters covering both gradient-based and derivative-free design methods are considered.  Selected topics including surrogate-base optimization, adaptive mesh search, and genetic algorithms are shown to be effective, gradient-free optimization strategies.  Additionally, new techniques for representing dielectric distributions in two dimensions, including level sets, are demonstrated as effective methods for gradient-based optimization.  Each chapter begins with a rigorous review of the optimization strategy used, and is followed by numerous examples that combine the strategy with either electromag...

  19. Numerical methods for multibody systems

    Science.gov (United States)

    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.

  20. Friction and wear calculation methods

    CERN Document Server

    Kragelsky, I V; Kombalov, V S

    1981-01-01

    Friction and Wear: Calculation Methods provides an introduction to the main theories of a new branch of mechanics known as """"contact interaction of solids in relative motion."""" This branch is closely bound up with other sciences, especially physics and chemistry. The book analyzes the nature of friction and wear, and some theoretical relationships that link the characteristics of the processes and the properties of the contacting bodies essential for practical application of the theories in calculating friction forces and wear values. The effect of the environment on friction and wear is a

  1. Numerical calculation of the cross section by the solution of the wave equation

    International Nuclear Information System (INIS)

    Drewko, J.

    1982-01-01

    A numerical method of solving of the wave equation is described for chosen vibrational eigenfunctions. A prepared program calculates the total cross sections for the resonant vibrational excitation for diatomic molecules on the basis of introduced molecular data. (author)

  2. Comment on 'Shang S. 2012. Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step. Hydrological Processes 26: 3338-3343. DOI: 10.1002/hyp.8405'

    Science.gov (United States)

    Yatheendradas, Soni; Narapusetty, Balachandrudu; Peters-Lidard, Christa; Funk, Christopher; Verdin, James

    2014-01-01

    A previous study analyzed errors in the numerical calculation of actual crop evapotranspiration (ET(sub a)) under soil water stress. Assuming no irrigation or precipitation, it constructed equations for ET(sub a) over limited soil-water ranges in a root zone drying out due to evapotranspiration. It then used a single crop-soil composite to provide recommendations about the appropriate usage of numerical methods under different values of the time step and the maximum crop evapotranspiration (ET(sub c)). This comment reformulates those ET(sub a) equations for applicability over the full range of soil water values, revealing a dependence of the relative error in numerical ET(sub a) on the initial soil water that was not seen in the previous study. It is shown that the recommendations based on a single crop-soil composite can be invalid for other crop-soil composites. Finally, a consideration of the numerical error in the time-cumulative value of ET(sub a) is discussed besides the existing consideration of that error over individual time steps as done in the previous study. This cumulative ET(sub a) is more relevant to the final crop yield.

  3. Strongly correlated systems numerical methods

    CERN Document Server

    Mancini, Ferdinando

    2013-01-01

    This volume presents, for the very first time, an exhaustive collection of those modern numerical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and material science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciate consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possi...

  4. Methods for calculating nonconcave entropies

    International Nuclear Information System (INIS)

    Touchette, Hugo

    2010-01-01

    Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: (i) microcanonical contraction, (ii) metastable branches of the free energy, (iii) generalized canonical ensembles with specific illustrations involving the so-called Gaussian and Betrag ensembles, (iv) the restricted canonical ensemble, and (v) the inverse Laplace transform. A simple long-range spin model having a nonconcave entropy is used to illustrate each method

  5. Spectral Methods for Numerical Relativity

    Directory of Open Access Journals (Sweden)

    Grandclément Philippe

    2009-01-01

    Full Text Available Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole–binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole–binary mergers.

  6. Numeric calculation of celestial bodies with spreadsheet analysis

    Science.gov (United States)

    Koch, Alexander

    2016-04-01

    The motion of the planets and moons in our solar system can easily be calculated for any time by the Kepler laws of planetary motion. The Kepler laws are a special case of the gravitational law of Newton, especially if you consider more than two celestial bodies. Therefore it is more basic to calculate the motion by using the gravitational law. But the problem is, that by gravitational law it is not possible to calculate the state of motion with only one step of calculation. The motion has to be numerical calculated for many time intervalls. For this reason, spreadsheet analysis is helpful for students. Skills in programmes like Excel, Calc or Gnumeric are important in professional life and can easily be learnt by students. These programmes can help to calculate the complex motions with many intervalls. The more intervalls are used, the more exact are the calculated orbits. The sutdents will first get a quick course in Excel. After that they calculate with instructions the 2-D-coordinates of the orbits of Moon and Mars. Step by step the students are coding the formulae for calculating physical parameters like coordinates, force, acceleration and velocity. The project is limited to 4 weeks or 8 lessons. So the calcualtion will only include the calculation of one body around the central mass like Earth or Sun. The three-body problem can only be shortly discussed at the end of the project.

  7. Biased calculations: Numeric anchors influence answers to math equations

    Directory of Open Access Journals (Sweden)

    Andrew R. Smith

    2011-02-01

    Full Text Available People must often perform calculations in order to produce a numeric estimate (e.g., a grocery-store shopper estimating the total price of his or her shopping cart contents. The current studies were designed to test whether estimates based on calculations are influenced by comparisons with irrelevant anchors. Previous research has demonstrated that estimates across a wide range of contexts assimilate toward anchors, but none has examined estimates based on calculations. In two studies, we had participants compare the answers to math problems with anchors. In both studies, participants' estimates assimilated toward the anchor values. This effect was moderated by time limit such that the anchoring effects were larger when the participants' ability to engage in calculations was limited by a restrictive time limit.

  8. Ability of aphasic individuals to perform numerical processing and calculation tasks

    Directory of Open Access Journals (Sweden)

    Gabriela De Luccia

    2014-03-01

    Full Text Available Objective To compare performance on EC301 battery calculation task between aphasic subjects and normal controls of the same sex, age, and education. Method Thirty-two aphasic patients who had suffered a single left hemisphere stroke were evaluated. Forty-four healthy volunteers were also selected. All subjects underwent a comprehensive arithmetic battery to assess their numerical and calculation skills. Performances on numerical processing and calculation tasks were then analyzed. Results Aphasic individuals showed changes in their ability to perform numerical processing and calculation tasks that were not observed in the healthy population. Conclusion Compared with healthy subjects of the same age and education level, individuals with aphasia had difficulty performing various tasks that involved numerical processing and calculation.

  9. Numerical kinematic transformation calculations for a parallel link manipulator

    International Nuclear Information System (INIS)

    Killough, S.M.

    1993-01-01

    Parallel link manipulators are often considered for particular robotic applications because of the unique advantages they provide. Unfortunately, they have significant disadvantages with respect to calculating the kinematic transformations because of the high-order equations that must be solved. Presented is a manipulator design that exploits the mechanical advantages of parallel links yet also has a corresponding numerical kinematic solution that can be solved in real time on common microcomputers

  10. Numerical Calculation of Interaction Between Plane Jet and Subsonic Flow

    Directory of Open Access Journals (Sweden)

    V. O. Moskalenko

    2016-01-01

    Full Text Available The paper makes numerical calculation of interaction between plane jet and subsonic flow. Its aim is to determine the jet trajectory, velocity profiles, distribution of pressure coefficient on the plate surface at different jet angles, namely ωj=45°; 90°; 105° and at low blowing strengths ( ≤1.5 as well as a to make comparison with the experimental data of other authors.To simulate a two-dimensional jet in the subsonic flow the software package “CAD SolidWorks Flow Simulation” has been used. Initially, the test task was solved with its calculation results compared with experimental ones [6.8] in order to improve the convergence; the size of the computational domain and a computational grid within the k-ε turbulence model were selected. As a result of the calculation, were identified and analysed the pressure values, jet trajectories, and velocity profiles. In the graphs the solid lines show calculation results, and dots represent experimental data.From the calculation results it is seen that, with increasing intensity of the reduced mass flow ¯q in the above range, the change of the jet pressure coefficient p¯ distribution behind a slotted nozzle is almost linear and significant. Before the nozzle, with increasing ¯q the pressure coefficient increases slightly.Analysis of results has shown that blowing of jets with ωj>90ω, provides a greater perturbation of the subsonic flow. Thus, the jet penetrates into the flow deeper, forms a dead region of the greater length, and more significantly redistributes the pressure coefficient on the surface of the plate.The calculation results are in good compliance with the experimental data both for the jet axis and for the pressure coefficient distribution on the plate surface. The research results can be used in the designing the jet control of aircrafts.

  11. Self-Consistent Constricted Variational Theory RSCF-CV(∞)-DFT and Its Restrictions To Obtain a Numerically Stable ΔSCF-DFT-like Method: Theory and Calculations for Triplet States.

    Science.gov (United States)

    Park, Young Choon; Senn, Florian; Krykunov, Mykhaylo; Ziegler, Tom

    2016-11-08

    In this paper, the relaxed self-consistent field infinite order constricted variational density functional theory (RSCF-CV(∞)-DFT) for triplet calculations is presented. Here, we focus on two main features of our implementation. First, as an extension of our previous work by Krykunov and Ziegler ( J. Chem. Theory Comput. 2013 , 9 , 2761 ), the optimization of the transition matrix representing the orbital transition is implemented and applied for vertical triplet excitations. Second, restricting the transition matrix, we introduce RSCF-CV(∞)-DFT-based numerically stable ΔSCF-DFT-like methods, the most general of them being SVD-RSCF-CV(∞)-DFT. The reliability of the different methods, RSCF-CV(∞)-DFT and its restricted versions, is examined using the benchmark test set of Silva-Junior et al. ( J. Chem. Phys. 2008 , 129 , 104103 ). The obtained excitation energies validate our approach and implementation for RSCF-CV(∞)-DFT and also show that SVD-RSCF-CV(∞)-DFT mimics very well ΔSCF-DFT, as the root-mean-square deviations between these methods are less than 0.1 eV for all functionals examined.

  12. Mathematica with a Numerical Methods Course

    Science.gov (United States)

    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.

  13. A numerical approach to calculate the induced voltage in the case of conduced perturbations

    International Nuclear Information System (INIS)

    Andretzko, J.P.; Hedjiedj, A.; Babouri, A.; Guendouz, L.; Nadi, M.

    2006-01-01

    This paper presents a method of numerical simulation that makes it possible to calculate the induced tension to the terminals of the cardiac pacemaker subjected to conduced disturbances. The physical model used for simulation is an experimental test bed which makes it possible to study the behaviour of pacemaker, in vitro, subjected to electromagnetic disturbances in low frequencies range (50 hz - 500 khz). The test bed in which the pacemaker is implanted is described in this article. The process of calculation uses the admittance method adapted to the case of conducted disturbances. Results obtained by numerical simulation are close to experimental values. (authors)

  14. A numerical approach to calculate the induced voltage in the case of conduced perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Andretzko, J.P.; Hedjiedj, A.; Babouri, A.; Guendouz, L.; Nadi, M. [Nancy-1 Univ. Henri Poincare, Lab. d' Instrumentation Electronique de Nancy, Faculte des Sciences, 54 - Vandoeuvre les Nancy (France)

    2006-07-01

    This paper presents a method of numerical simulation that makes it possible to calculate the induced tension to the terminals of the cardiac pacemaker subjected to conduced disturbances. The physical model used for simulation is an experimental test bed which makes it possible to study the behaviour of pacemaker, in vitro, subjected to electromagnetic disturbances in low frequencies range (50 hz - 500 khz). The test bed in which the pacemaker is implanted is described in this article. The process of calculation uses the admittance method adapted to the case of conducted disturbances. Results obtained by numerical simulation are close to experimental values. (authors)

  15. Numerical methods in software and analysis

    CERN Document Server

    Rice, John R

    1992-01-01

    Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithm

  16. An introduction to numerical methods and analysis

    CERN Document Server

    Epperson, James F

    2013-01-01

    Praise for the First Edition "". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.""-Zentralblatt MATH "". . . carefully structured with many detailed worked examples.""-The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to

  17. Isogeometric methods for numerical simulation

    CERN Document Server

    Bordas, Stéphane

    2015-01-01

    The book presents the state of the art in isogeometric modeling and shows how the method has advantaged. First an introduction to geometric modeling with NURBS and T-splines is given followed by the implementation into computer software. The implementation in both the FEM and BEM is discussed.

  18. Implicit Numerical Methods in Meteorology

    Science.gov (United States)

    Augenbaum, J.

    1984-01-01

    The development of a fully implicit finite-difference model, whose time step is chosen solely to resolve accurately the physical flow of interest is discussed. The method is based on an operator factorization which reduces the dimensionality of the implicit approach: at each time step only (spatially) one-dimensional block-tridiagonal linear systems must be solved. The scheme uses two time levels and is second-order accurate in time. Compact implicit spatial differences are used, yielding fourth-order accuracy both vertically and horizontally. In addition, the development of a fully interactive computer code is discussed. With this code the user will have a choice of models, with various levels of accuracy and sophistication, which are imbedded, as subsets of the fully implicit 3D code.

  19. Calculation Methods for Wallenius’ Noncentral Hypergeometric Distribution

    DEFF Research Database (Denmark)

    Fog, Agner

    2008-01-01

    is the conditional distribution of independent binomial variates given their sum. No reliable calculation method for Wallenius' noncentral hypergeometric distribution has hitherto been described in the literature. Several new methods for calculating probabilities from Wallenius' noncentral hypergeometric...

  20. Numerical Methods For Chemically Reacting Flows

    Science.gov (United States)

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

    1990-01-01

    Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.

  1. Numerical calculations of 2D transonic flow in GAMM channel and over the profile

    Directory of Open Access Journals (Sweden)

    Slouka Martin

    2017-01-01

    Full Text Available The aim of this work is to make a 2D numerical model of the solution of the transonic inviscid and viscous compressible flow around the profile. In a case of viscous flow several turbulent models are used. For the verification of the calculation Baldwin-Lomax model is compared with Wilcox k-omega model and SST turbulent model. Calculations are done in GAMM channel computational domain with 10% DCA profile and in the turbine cascade computational domain with 8% DCA profile. Numerical methods are based on a finite volume solution. Comparisons are done with the experimental data for the 8% DCA profile.

  2. Numerical calculations of 2D transonic flow in GAMM channel and over the profile

    Science.gov (United States)

    Slouka, Martin; Kozel, Karel

    The aim of this work is to make a 2D numerical model of the solution of the transonic inviscid and viscous compressible flow around the profile. In a case of viscous flow several turbulent models are used. For the verification of the calculation Baldwin-Lomax model is compared with Wilcox k-omega model and SST turbulent model. Calculations are done in GAMM channel computational domain with 10% DCA profile and in the turbine cascade computational domain with 8% DCA profile. Numerical methods are based on a finite volume solution. Comparisons are done with the experimental data for the 8% DCA profile.

  3. Numerical calculations of ultrasonic fields. 1: Transducer near fields

    Science.gov (United States)

    Johnson, J. A.

    1982-04-01

    A computer code for the calculation of linear acoustic wave propagation in homogeneous fluid and solid materials has been derived from the thermal hydraulics code STEALTH. The code uses finite difference techniques in a two dimensional mesh made up of arbitrarily shaped quadrilaterals. Problems with two dimensional plane strain or two dimensional axial symmetries can be solved. Free, fixed or stressed boundaries can be used. Transducers can be modeled by time dependent boundary conditions or by moving pistons. A brief description of the method is given and the results of the calculation of the near fields of circular flat and focused transducers are shown. These results agree with analytic theory along the axis of symmetry and with other codes that use a Huygens' reconstruction technique off axis.

  4. Perception of numerical methods in rarefied gasdynamics

    Science.gov (United States)

    Bird, G. A.

    1989-01-01

    The relationships between various numerical methods applied to problems in rarefied gasdynamics are discussed, with emphasis on conflicting viewpoints and computational requirements associated with physical simulation versus the numerical solution of the Boltzmann equation. The basic differences between the molecular dynamics and direct simulation methods are shown to affect their applicability to dense and rarefied flows. Methods for the probabilistic selection of representative collision in the direct simulation Monte Carlo method are reviewed. A method combining the most desirable features of the earlier methods is presented.

  5. Numerical Methods for Partial Differential Equations

    CERN Document Server

    Guo, Ben-yu

    1987-01-01

    These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.

  6. Numerical Calculation on Cavitation Pressure Pulsation in Centrifugal Pump

    Directory of Open Access Journals (Sweden)

    Weidong Shi

    2014-02-01

    Full Text Available In order to study the internal flow in centrifugal pump when cavitation occurs, numerical calculation of the unsteady flow field in the WP7 automobile centrifugal pump is conducted based on the Navier-Stokes equations with the RNG k – ε turbulence model and Zwart-Gerber-Belamri cavitation model. The distributions of bubble volume fraction and pressure pulsation laws in the pump are analyzed when cavitation occurs. The conclusions are as follows: the bubble volume fraction is larger on the suction side of impeller blade near the inlet edge, which is consistent with the low-pressure region distribution. Bubble volume is determined by the growth rate and collapse rate of every bubble in the bubble group. The cavitation degree changes over time with the impeller rotation and the bubble growth and collapse coexist in the impeller flow channels. The main pulsation results from the cyclic and static coupling between the impeller and the tongue, while the fluctuating amplitude is increased by the cavitation.

  7. Exact numerical calculation of fixation probability and time on graphs.

    Science.gov (United States)

    Hindersin, Laura; Möller, Marius; Traulsen, Arne; Bauer, Benedikt

    2016-12-01

    The Moran process on graphs is a popular model to study the dynamics of evolution in a spatially structured population. Exact analytical solutions for the fixation probability and time of a new mutant have been found for only a few classes of graphs so far. Simulations are time-expensive and many realizations are necessary, as the variance of the fixation times is high. We present an algorithm that numerically computes these quantities for arbitrary small graphs by an approach based on the transition matrix. The advantage over simulations is that the calculation has to be executed only once. Building the transition matrix is automated by our algorithm. This enables a fast and interactive study of different graph structures and their effect on fixation probability and time. We provide a fast implementation in C with this note (Hindersin et al., 2016). Our code is very flexible, as it can handle two different update mechanisms (Birth-death or death-Birth), as well as arbitrary directed or undirected graphs. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

  8. Methods in nuclear reactors calculations

    International Nuclear Information System (INIS)

    Velarde, G.

    1966-01-01

    Studies are made of the neutron transport equation corresponding to the the real and virtual reactors, as well as the starting hypotheses. Methods are developed to solve the transport equation in slab geometry, and P l ; B l ; M l ; S n and discrete ordinates approximations. (Author)

  9. Numerical methods for stochastic differential equations.

    Science.gov (United States)

    Wilkie, Joshua

    2004-01-01

    Stochastic differential equations (SDE's) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes for solving stochastic equations is outlined here. High-order numerical methods are developed for the integration of stochastic differential equations with strong solutions. We demonstrate the accuracy of the resulting integration schemes by computing the errors in approximate solutions for SDE's which have known exact solutions.

  10. Development of 3-D FBR heterogeneous core calculation method based on characteristics method

    International Nuclear Information System (INIS)

    Takeda, Toshikazu; Maruyama, Manabu; Hamada, Yuzuru; Nishi, Hiroshi; Ishibashi, Junichi; Kitano, Akihiro

    2002-01-01

    A new 3-D transport calculation method taking into account the heterogeneity of fuel assemblies has been developed by combining the characteristics method and the nodal transport method. In the axial direction the nodal transport method is applied, and the characteristics method is applied to take into account the radial heterogeneity of fuel assemblies. The numerical calculations have been performed to verify 2-D radial calculations of FBR assemblies and partial core calculations. Results are compared with the reference Monte-Carlo calculations. A good agreement has been achieved. It is shown that the present method has an advantage in calculating reaction rates in a small region

  11. Design of heat exchangers by numerical methods

    International Nuclear Information System (INIS)

    Konuk, A.A.

    1981-01-01

    Differential equations describing the heat tranfer in shell - and tube heat exchangers are derived and solved numerically. The method of ΔT sub(lm) is compared with the proposed method in cases where the specific heat at constant pressure, Cp and the overall heat transfer coefficient, U, vary with temperature. The error of the method of ΔT sub (lm) for the computation of the exchanger lenght is less than + 10%. However, the numerical method, being more accurate and at the same time easy to use and economical, is recommended for the design of shell-and-tube heat exchangers. (Author) [pt

  12. Numerical analysis in electromagnetics the TLM method

    CERN Document Server

    Saguet, Pierre

    2013-01-01

    The aim of this book is to give a broad overview of the TLM (Transmission Line Matrix) method, which is one of the "time-domain numerical methods". These methods are reputed for their significant reliance on computer resources. However, they have the advantage of being highly general.The TLM method has acquired a reputation for being a powerful and effective tool by numerous teams and still benefits today from significant theoretical developments. In particular, in recent years, its ability to simulate various situations with excellent precision, including complex materials, has been

  13. Turn function and vorticity method for numerical fluid dynamics

    International Nuclear Information System (INIS)

    O'Rourke, P.J.

    1984-01-01

    A numerical method is presented that solves in a consistent fashion, conservation equations for both vorticity and linear momentum in multidimensional fluid-dynamics calculations. The equations are given in both two- and three-dimensional Cartesian geometry, and it is shown how the method can be easily implemented in a two-dimensional Eulerian fluid-dynamics code. The results of example calculations, which were performed with and without the new method, show the large errors that can arise when the vorticity equation is not solved in compressible flow calculations

  14. Pile Load Capacity – Calculation Methods

    Directory of Open Access Journals (Sweden)

    Wrana Bogumił

    2015-12-01

    Full Text Available The article is a review of the current problems of the foundation pile capacity calculations. The article considers the main principles of pile capacity calculations presented in Eurocode 7 and other methods with adequate explanations. Two main methods are presented: α – method used to calculate the short-term load capacity of piles in cohesive soils and β – method used to calculate the long-term load capacity of piles in both cohesive and cohesionless soils. Moreover, methods based on cone CPTu result are presented as well as the pile capacity problem based on static tests.

  15. Numerical groundwater flow calculations at the Finnsjoen site

    International Nuclear Information System (INIS)

    Lindbom, B.; Boghammar, A.; Lindberg, H.; Bjelkaas, J.

    1991-02-01

    The Swedish Nuclear Fuel and Waste Management Company (SKB) has initiated a research project called SKB 91, which is related to performance assessment of repositories for high level waste from nuclear power plants. Specifically the Finnsjoen site is of concern. As part of this research project, the report describes groundwater flow calculations at the Finnsjoen site, located in northern Uppland, approximately 150 km north of Stockholm. The calculations have been performed with the finite element method applying the porous media approach. The project comprises three steps, the first of which is concerned with the presence of salt below a hydraulically significant structure. This step was modelled in two dimensions in a semi-generic fashion, while the two following steps comprised three-dimensional modelling of the site at a semi-regional and a local scale. The semi-regional model covered approximately 43 square km while the area of the local model was roughly 6.6 square km. The semi-regional model included well expressed regional fracture zones that were explicitly modelled in deterministic manner. The modelling was performed with the finite element code NAMMU, used together with the program-package HYPAC. The latter was used for pre- and postprocessing purposes. The modelling was performed with 8-noded brick elements for the three-dimensional calculations, and the two-dimensional model involved the use of 8-noded rectangular elements. The present report is a revised version of a report previously published as a working report. The difference between the present report and the previous one, is that the present report describes the conclusions more site-specifically, the presentation of a number of the cases tackled has been pruned down, some editorial effort has been put into having the volume of the report reduced, and finally the summary has been edited and cut down. (authors)

  16. Numerical methods in astrophysics an introduction

    CERN Document Server

    Bodenheimer, Peter; Rozyczka, Michal; Plewa, Tomasz; Yorke, Harold W; Yorke, Harold W

    2006-01-01

    Basic Equations The Boltzmann Equation Conservation Laws of Hydrodynamics The Validity of the Continuous Medium Approximation Eulerian and Lagrangian Formulation of Hydrodynamics Viscosity and Navier-Stokes Equations Radiation Transfer Conducting and Magnetized Media Numerical Approximations to Partial Differential Equations Numerical Modeling with Finite-Difference Equations Difference Quotient Discrete Representation of Variables, Functions, and Derivatives Stability of Finite-Difference Methods Physical Meaning of Stability Criterion A Useful Implicit Scheme Diffusion

  17. Numerical methods and modelling for engineering

    CERN Document Server

    Khoury, Richard

    2016-01-01

    This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems. Uses a “building-block” approach, starting with simpler mathemati...

  18. Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

    Energy Technology Data Exchange (ETDEWEB)

    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.

  19. Numerical calculations of effective elastic properties of two cellular structures

    International Nuclear Information System (INIS)

    Tuncer, Enis

    2005-01-01

    Young's moduli of regular two-dimensional truss-like and eye-shaped structures are simulated using the finite element method. The structures are idealizations of soft polymeric materials used in ferro-electret applications. In the simulations, the length scales of the smallest representative units are varied, which changes the dimensions of the cell walls in the structures. A power-law expression with a quadratic as the exponent term is proposed for the effective Young's moduli of the systems as a function of the solid volume fraction. The data are divided into three regions with respect to the volume fraction: low, intermediate and high. The parameters of the proposed power-law expression in each region are later represented as a function of the structural parameters, the unit-cell dimensions. The expression presented can be used to predict a structure/property relationship in materials with similar cellular structures. The contribution of the cell-wall thickness to the elastic properties becomes significant at concentrations >0.15. The cell-wall thickness is the most significant factor in predicting the effective Young's modulus of regular cellular structures at high volume fractions of solid. At lower concentrations of solid, the eye-shaped structure yields a lower Young's modulus than a truss-like structure with similar anisotropy. Comparison of the numerical results with those of experimental data for poly(propylene) show good agreement regarding the influence of cell-wall thickness on elastic properties of thin cellular films

  20. Mesoscale modelling in China: Risø DTU numerical wind atlas calculation for NE China (Dongbei)

    DEFF Research Database (Denmark)

    Badger, Jake; Larsén, Xiaoli Guo; Hahmann, Andrea N.

    of the wind resource for Dongbei south of 50oN. The results of the numerical wind atlas show a wind resource over the region of interest modulated mainly by topographic features. These are principally elevated terrain features, giving high resources on exposed ridges and lower resources adjacent to the low......This document reports on the methods and findings of project “A01 Mesoscale Modelling”, part of the CMA component of the Wind Energy Development (WED) programme, focusing mainly on the methods and work undertaken by Risø DTU. The KAMM/WAsP methodology for numerical wind atlas calculation....... The major new aspects of the project were the large number of KAMM/WAsP sensitivity studies, comparison with WRF, and the CMA’s numerical wind atlas method (WERAS). Additionally, the reliability of the input data for the methodology, and the wave-number spectra properties of the output data were...

  1. Improvement of methods for calculation of sound insulation in buildings

    OpenAIRE

    Mašović, Draško B.

    2015-01-01

    The main object of this work are the methods for calculation of sound insulation based on the classical model of sound propagation in buildings and single-number rating of sound insulation. The aim of the work is inspection of the possibilities for improvement of standard methods for quantification and calculation of sound insulation, in order to achieve higher accuracy of the obtained numerical values and their correlation with subjective impression of the acoustic comfort in buildings. Proc...

  2. NUMERICAL CALCULATIONS IN GEOMECHANICS APPLICABLE TO LINEAR STRUCTURES

    Directory of Open Access Journals (Sweden)

    Vlasov Aleksandr Nikolaevich

    2012-10-01

    Full Text Available The article covers the problem of applicability of finite-element and engineering methods to the development of a model of interaction between pipeline structures and the environment in the complex conditions with a view to the simulation and projection of exogenous geological processes, trustworthy assessment of their impacts on the pipeline, and the testing of varied calculation methodologies. Pipelining in the areas that have a severe continental climate and permafrost soils is accompanied by cryogenic and exogenous processes and developments. It may also involve the development of karst and/or thermokarst. The adverse effect of the natural environment is intensified by the anthropogenic impact produced onto the natural state of the area, causing destruction of forests and other vegetation, changing the ratio of soils in the course of the site planning, changing the conditions that impact the surface and underground waters, and causing the thawing of the bedding in the course of the energy carrier pumping, etc. The aforementioned consequences are not covered by effective regulatory documents. The latter constitute general and incomplete recommendations in this respect. The appropriate mathematical description of physical processes in complex heterogeneous environments is a separate task to be addressed. The failure to consider the above consequences has repeatedly caused both minor damages (denudation of the pipeline, insulation stripping and substantial accidents; the rectification of their consequences was utterly expensive. Pipelining produces a thermal impact on the environment; it may alter the mechanical properties of soils and de-frost the clay. The stress of the pipeline is one of the principal factors that determines its strength and safety. The pipeline stress exposure caused by loads and impacts (self-weight, internal pressure, etc. may be calculated in advance, and the accuracy of these calculations is sufficient for practical

  3. Numerical calculation of transient field effects in quenching superconducting magnets

    Energy Technology Data Exchange (ETDEWEB)

    Schwerg, Juljan Nikolai

    2010-07-01

    The maximum obtainable magnetic induction of accelerator magnets, relying on normal conducting cables and iron poles, is limited to around 2 T because of ohmic losses and iron saturation. Using superconducting cables, and employing permeable materials merely to reduce the fringe field, this limit can be exceeded and fields of more than 10 T can be obtained. A quench denotes the sudden transition from the superconducting to the normal conducting state. The drastic increase in electrical resistivity causes ohmic heating. The dissipated heat yields a temperature rise in the coil and causes the quench to propagate. The resulting high voltages and excessive temperatures can result in an irreversible damage of the magnet - to the extend of a cable melt-down. The quench behavior of a magnet depends on numerous factors, e.g. the magnet design, the applied magnet protection measures, the external electrical network, electrical and thermal material properties, and induced eddy current losses. The analysis and optimization of the quench behavior is an integral part of the construction of any superconducting magnet. The dissertation is divided in three complementary parts, i.e. the thesis, the detailed treatment and the appendix. In the thesis the quench process in superconducting accelerator magnets is studied. At first, we give an overview over features of accelerator magnets and physical phenomena occurring during a quench. For all relevant effects numerical models are introduced and adapted. The different models are weakly coupled in the quench algorithm and solved by means of an adaptive time-stepping method. This allows to resolve the variation of material properties as well as time constants. The quench model is validated by means of measurement data from magnets of the Large Hadron Collider. In a second step, we show results of protection studies for future accelerator magnets. The thesis ends with a summary of the results and a critical outlook on aspects which could

  4. An improved algorithm for numerical calculation of seismic response spectra

    Directory of Open Access Journals (Sweden)

    Chengwang Liao

    2016-03-01

    Full Text Available The information of seismic response spectra is key to many problems concerned with aseismic structure and is also helpful for earthquake disaster relief if it is generated in time when earthquake happens. While current numerical calculation methods suffer from poor precision, especially in frequency band near Nyquist frequency, we present a set of improved parameters for precision improvement. It is shown that precision of displacement and velocity response spectra are both further improved compared to current numerical algorithms. A uniform fitting formula is given for computing these parameters for damping ratio range of 0.01–0.9, quite convenient for practical application.

  5. FORECASTING PILE SETTLEMENT ON CLAYSTONE USING NUMERICAL AND ANALYTICAL METHODS

    Directory of Open Access Journals (Sweden)

    Ponomarev Andrey Budimirovich

    2016-06-01

    Full Text Available In the article the problem of designing pile foundations on claystones is reviewed. The purpose of this paper is comparative analysis of the analytical and numerical methods for forecasting the settlement of piles on claystones. The following tasks were solved during the study: 1 The existing researches of pile settlement are analyzed; 2 The characteristics of experimental studies and the parameters for numerical modeling are presented, methods of field research of single piles’ operation are described; 3 Calculation of single pile settlement is performed using numerical methods in the software package Plaxis 2D and analytical method according to the requirements SP 24.13330.2011; 4 Experimental data is compared with the results of analytical and numerical calculations; 5 Basing on these results recommendations for forecasting pile settlement on claystone are presented. Much attention is paid to the calculation of pile settlement considering the impacted areas in ground space beside pile and the comparison with the results of field experiments. Basing on the obtained results, for the prediction of settlement of single pile on claystone the authors recommend using the analytical method considered in SP 24.13330.2011 with account for the impacted areas in ground space beside driven pile. In the case of forecasting the settlement of single pile on claystone by numerical methods in Plaxis 2D the authors recommend using the Hardening Soil model considering the impacted areas in ground space beside the driven pile. The analyses of the results and calculations are presented for examination and verification; therefore it is necessary to continue the research work of deep foundation at another experimental sites to improve the reliability of the calculation of pile foundation settlement. The work is of great interest for geotechnical engineers engaged in research, design and construction of pile foundations.

  6. Assessment of seismic margin calculation methods

    International Nuclear Information System (INIS)

    Kennedy, R.P.; Murray, R.C.; Ravindra, M.K.; Reed, J.W.; Stevenson, J.D.

    1989-03-01

    Seismic margin review of nuclear power plants requires that the High Confidence of Low Probability of Failure (HCLPF) capacity be calculated for certain components. The candidate methods for calculating the HCLPF capacity as recommended by the Expert Panel on Quantification of Seismic Margins are the Conservative Deterministic Failure Margin (CDFM) method and the Fragility Analysis (FA) method. The present study evaluated these two methods using some representative components in order to provide further guidance in conducting seismic margin reviews. It is concluded that either of the two methods could be used for calculating HCLPF capacities. 21 refs., 9 figs., 6 tabs

  7. Comparison of methods for calculating water erosion

    OpenAIRE

    SVOBODOVÁ, Pavlína

    2011-01-01

    Bachelor thesis presents a comparison of methods for calculating water erosion. The aim is to summarize available evidence concerning the problems of water erosion. There are presented some methods how to calculate average annual erosion of soils, and selected models for calculating the erosion immediately. There are also listed possible erosion control measures through which we can at least slow the effects of erosion, rather than stop completely.

  8. a Numerical Method for Turbulent Combustion Problems

    Science.gov (United States)

    Song, Yu.

    This dissertation presents a random numerical method which combines a random vortex method and a random choice method. With the assumption of incompressibility, the equations governing the fluid motion can be uncoupled from the equations governing the chemical reaction. A hybrid random vortex method is used for solving Navier -Stokes equation which governs the fluid motion. Combustion process is governed by reaction-diffusion system for the conservation of energy and the various chemical species participating in reaction. A random choice method is used for the modeling reaction-diffusion equations. The random choice method is tested and the numerical solutions are compared with the results by either the other numerical methods or exact solutions, good improvement and agreement have been obtained. For physical problem in two or more space dimensions, extension of the random choice method requires splitting the source terms into an x-sweep followed by a y-sweep. The splitting of the source term is also examined for an equation with an exact solution. The combustion model is applied to the problem of combustion in a circular cylinder with cylinder heated or kept cold. The flame profiles are obtained and effect of the turbulent is observed. The method is also applied to the ignition of a Bunsen burner. The correct modeling of mixing layer at the edge of the burner is found important in this application. Flame propagation profiles are obtained and have good agreement with experiments.

  9. Lagrangian numerical methods for ocean biogeochemical simulations

    Science.gov (United States)

    Paparella, Francesco; Popolizio, Marina

    2018-05-01

    We propose two closely-related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the Péclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection-reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects.

  10. Numerical methods and analysis of multiscale problems

    CERN Document Server

    Madureira, Alexandre L

    2017-01-01

    This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.

  11. Numerical calculation of the ground state of Helium atom using ...

    African Journals Online (AJOL)

    Hylleraas did the calculation of the ground state in 1926 using the variational parameter a. In this paper we trace Hylleraas historic calculation, the use of computer enables us to improve the approximation found by Hylleraas . The program was written in FORTRAN language, designed in such away that for a particular value ...

  12. Hybrid SN Laplace Transform Method For Slab Lattice Calculations

    International Nuclear Information System (INIS)

    Segatto, Cynthia F.; Vilhena, Marco T.; Zani, Jose H.; Barros, Ricardo C.

    2008-01-01

    In typical lattice cells where a highly absorbing, small fuel element is embedded in the moderator, a large weakly absorbing medium, high-order transport methods become unnecessary. In this paper we describe a hybrid discrete ordinates (S N ) method for slab lattice calculations. This hybrid S N method combines the convenience of a low-order S N method in the moderator with a high-order S N method in the fuel. We use special fuel-moderator interface conditions based on an approximate angular flux interpolation analytical method and the Laplace transform (LTS N ) numerical method to calculate the neutron flux distribution and the thermal disadvantage factor. We present numerical results for a range of typical model problems. (authors)

  13. Numerical methods for hyperbolic differential functional problems

    Directory of Open Access Journals (Sweden)

    Roman Ciarski

    2008-01-01

    Full Text Available The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.

  14. Numerical Methods through Open-Ended Projects

    Science.gov (United States)

    Cline, Kelly S.

    2005-01-01

    We present a design for a junior level numerical methods course that focuses on a series of five open-ended projects in applied mathematics. These projects were deliberately designed to present many of the ambiguities and complexities that appear any time we use mathematics in the real world, and so they offered the students a variety of possible…

  15. Numerical methods in nuclear engineering. Part 1

    International Nuclear Information System (INIS)

    Phillips, G.J.

    1983-08-01

    These proceedings, published in two parts contain the full text of 56 papers and summaries of six papers presented at the conference. They cover the use of numerical methods in thermal hydraulics, reactor physics, neutron diffusion, subchannel analysis, risk assessment, transport theory, and fuel behaviour

  16. Numerical methods in electron magnetic resonance

    International Nuclear Information System (INIS)

    Soernes, A.R.

    1998-01-01

    The focal point of the thesis is the development and use of numerical methods in the analysis, simulation and interpretation of Electron Magnetic Resonance experiments on free radicals in solids to uncover the structure, the dynamics and the environment of the system

  17. Numerical methods in electron magnetic resonance

    Energy Technology Data Exchange (ETDEWEB)

    Soernes, A.R

    1998-07-01

    The focal point of the thesis is the development and use of numerical methods in the analysis, simulation and interpretation of Electron Magnetic Resonance experiments on free radicals in solids to uncover the structure, the dynamics and the environment of the system.

  18. Comparison of Two Toric IOL Calculation Methods

    Directory of Open Access Journals (Sweden)

    C. Kern

    2018-01-01

    Full Text Available Purpose. To compare two calculators for toric intraocular lens (IOL calculation and to evaluate the prediction of refractive outcome. Methods. Sixty-four eyes of forty-five patients underwent cataract surgery followed by implantation of a toric intraocular lens (Zeiss Torbi 709 M calculated by a standard industry calculator using front keratometry values. Prediction error, median absolute error, and refractive astigmatism error were evaluated for the standard calculator. The predicted postoperative refraction and toric lens power values were evaluated and compared after postoperative recalculation using the Barrett calculator. Results. We observed a significant undercorrection in the spherical equivalent (0.19 D by using a standard calculator (p≤0.05. According to the Baylor nomogram and the refractive influence of posterior corneal astigmatism (PCA, undercorrection of the cylinder was lower for patients with WTR astigmatism, because of the tendency of overcorrection. An advantage of less residual postoperative SE, sphere, and cylinder for the Barrett calculator was observed when retrospectively comparing the calculated predicted postoperative refraction between calculators (p≤0.01. Conclusion. Consideration of only corneal front keratometric values for toric lens calculation may lead to postoperative undercorrection of astigmatism. The prediction of postoperative refractive outcome can be improved by using appropriate methods of adjustment in order to take PCA into account.

  19. Numerical calculation of particle collection efficiency in an ...

    Indian Academy of Sciences (India)

    The present numerical study involves the finding of the collection efficiency of an electrostatic precipitator (ESP) using a finite volume (ANUPRAVAHA) solver for the Navier–Stokes and continuity equations, along with the Poisson's equation for electric potential and current continuity. The particle movement is simulated ...

  20. Numeral Writing Skill and Elementary Arithmetic Mental Calculations

    Science.gov (United States)

    Johansson, Bo S.

    2005-01-01

    The paper reports three studies addressing the role of numeral writing for arithmetic performance. About 650 children in the age range 5-7 years participated in the studies. The results demonstrate a positive correlation between number of digits correctly written and number of arithmetic problems solved. The correlations between number of reversed…

  1. Numerical calculation of hemolysis levels in peripheral hemodialysis cannulas

    NARCIS (Netherlands)

    De Wachter, D; Verdonck, P

    Hemolysis in extracorporeal life support systems presents an underestimated problem. In this article, we investigate the hemolytic potential of peripheral hemodialysis cannulas numerically. An axisymmetrical finite element model of 3 cannula sizes was built (13G, 14G, and 16G) that was refined

  2. An introduction to numerical methods and analysis

    CERN Document Server

    Epperson, J F

    2007-01-01

    Praise for the First Edition "". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.""-Zentrablatt Math "". . . carefully structured with many detailed worked examples . . .""-The Mathematical Gazette "". . . an up-to-date and user-friendly account . . .""-Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or d

  3. Numerical methods for scientists and engineers

    CERN Document Server

    Antia, H M

    2012-01-01

    This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added.

  4. Numerical and analytical methods with Matlab

    CERN Document Server

    Bober, William; Masory, Oren

    2013-01-01

    Numerical and Analytical Methods with MATLAB® presents extensive coverage of the MATLAB programming language for engineers. It demonstrates how the built-in functions of MATLAB can be used to solve systems of linear equations, ODEs, roots of transcendental equations, statistical problems, optimization problems, control systems problems, and stress analysis problems. These built-in functions are essentially black boxes to students. By combining MATLAB with basic numerical and analytical techniques, the mystery of what these black boxes might contain is somewhat alleviated. This classroom-tested

  5. Calculation methods for determining dose equivalent

    International Nuclear Information System (INIS)

    Endres, G.W.R.; Tanner, J.E.; Scherpelz, R.I.; Hadlock, D.E.

    1988-01-01

    A series of calculations of neutron fluence as a function of energy in an anthropomorphic phantom was performed to develop a system for determining effective dose equivalent for external radiation sources. critical organ dose equivalents are calculated and effective dose equivalents are determined using ICRP-26 methods. Quality factors based on both present definitions and ICRP-40 definitions are used in the analysis. The results of these calculations are presented and discussed

  6. Calculating Resonance Positions and Widths Using the Siegert Approximation Method

    Science.gov (United States)

    Rapedius, Kevin

    2011-01-01

    Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…

  7. A method for calculating active feedback system to provide vertical ...

    Indian Academy of Sciences (India)

    the control of plasma vertical position with active feedback system. Calculation of feed- back control parameters is formulated as an optimization problem and an approximate method to solve the problem is suggested. Numerical simulations are performed with parameters of the T-15M tokamak in order to justify the ...

  8. Numerical Calculation of the Spectrum of the Severe (1%) Lighting Current and Its First Derivative

    Energy Technology Data Exchange (ETDEWEB)

    Brown, C G; Ong, M M; Perkins, M P; Speer, R D

    2010-02-12

    Recently, the direct-strike lighting environment for the stockpile-to-target sequence was updated [1]. In [1], the severe (1%) lightning current waveforms for first and subsequent return strokes are defined based on Heidler's waveform. This report presents numerical calculations of the spectra of those 1% lightning current waveforms and their first derivatives. First, the 1% lightning current models are repeated here for convenience. Then, the numerical method for calculating the spectra is presented and tested. The test uses a double-exponential waveform and its first derivative, which we fit to the previous 1% direct-strike lighting environment from [2]. Finally, the resulting spectra are given and are compared with those of the double-exponential waveform and its first derivative.

  9. Numerical calculations of an effective elasticity tensor and peak stresses for the large fusion magnets

    International Nuclear Information System (INIS)

    Iwanicki, T.; Maurer, W.; Heinz, W.

    1983-01-01

    For the calculation of mechanical properties of large magnet systems in 3-dimensional space, a very fine subdivision of the magnet structure is necessary. In the finite element programmes, this will lead to unacceptable long computing times and to the limits of computer-storage capacity. This limitation requires a simplification of the structure model. This problem can be solved by the numerical method, called ''numerical simulation'', by which an effective elasticity tensor will be obtained for a composite material. The structure has to perform a homogeneity condition, i.e. it must be possible to define a ''representative volume element'' (RVE). With the effective elasticity tensor, which can be found for such RVE, it is possible to calculate the average stress and with the interpolation of a surface displacement also the peak stresses in each point of the structure. A good agreement is found between experimental and theoretical moduli of elasticity. (author)

  10. Numerical calculation of mean intensity and radiative flux in plane-parallel stellar atmospheres

    Science.gov (United States)

    Nariai, K.; Yoshioka, K.

    The four-point Gaussian-quadrature formulas of Kegel (1962) for the evaluation of the intensity and flux (F) integrals is improved by using Bessel's interpolation technique and by subdividing the integral range. Steps in the analysis include the calculation of the Gaussian points of division and weightings for the interval (y, z), for a small (y, z), and for (O, z); determination of the precision of n-point formulas in calculating intensity and F; and the derivation of a four-point version of the two-point quadrature method of Cayrel (1960) and Norton (Mihalas, 1967). The numerical results are presented and compared with those of other models. The gray-model delta-F/F ratio calculated by this method is found to be less than 0.01 percent.

  11. Determination of Solution Accuracy of Numerical Schemes as Part of Code and Calculation Verification

    Energy Technology Data Exchange (ETDEWEB)

    Blottner, F.G.; Lopez, A.R.

    1998-10-01

    This investigation is concerned with the accuracy of numerical schemes for solving partial differential equations used in science and engineering simulation codes. Richardson extrapolation methods for steady and unsteady problems with structured meshes are presented as part of the verification procedure to determine code and calculation accuracy. The local truncation error de- termination of a numerical difference scheme is shown to be a significant component of the veri- fication procedure as it determines the consistency of the numerical scheme, the order of the numerical scheme, and the restrictions on the mesh variation with a non-uniform mesh. Genera- tion of a series of co-located, refined meshes with the appropriate variation of mesh cell size is in- vestigated and is another important component of the verification procedure. The importance of mesh refinement studies is shown to be more significant than just a procedure to determine solu- tion accuracy. It is suggested that mesh refinement techniques can be developed to determine con- sistency of numerical schemes and to determine if governing equations are well posed. The present investigation provides further insight into the conditions and procedures required to effec- tively use Richardson extrapolation with mesh refinement studies to achieve confidence that sim- ulation codes are producing accurate numerical solutions.

  12. Numerical methods and optimization a consumer guide

    CERN Document Server

    Walter, Éric

    2014-01-01

    Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods and Optimization – A Consumer Guide presents methods for dealing with them. Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to ·         discover how to escape the dictatorship of those particular cases that are simple enough to receive a closed-form solution, and thus gain the ability to solve complex, real-life problems; ·         understand the principles behind recognized algorithms used in state-of-the-art numerical software; ·         learn the advantag...

  13. Methods of bone marrow dose calculation

    International Nuclear Information System (INIS)

    Taboaco, R.C.

    1982-02-01

    Several methods of bone marrow dose calculation for photon irradiation were analised. After a critical analysis, the author proposes the adoption, by the Instituto de Radioprotecao e Dosimetria/CNEN, of Rosenstein's method for dose calculations in Radiodiagnostic examinations and Kramer's method in case of occupational irradiation. It was verified by Eckerman and Simpson that for monoenergetic gamma emitters uniformly distributed within the bone mineral of the skeleton the dose in the bone surface can be several times higher than dose in skeleton. In this way, is also proposed the Calculation of tissue-air ratios for bone surfaces in some irradiation geometries and photon energies to be included in the Rosenstein's method for organ dose calculation in Radiodiagnostic examinations. (Author) [pt

  14. Simple Calculation Programs for Biology Immunological Methods

    Indian Academy of Sciences (India)

    First page Back Continue Last page Overview Graphics. Simple Calculation Programs for Biology Immunological Methods. Computation of Ab/Ag Concentration from EISA data. Graphical Method; Raghava et al., 1992, J. Immuno. Methods 153: 263. Determination of affinity of Monoclonal Antibody. Using non-competitive ...

  15. Vector extrapolation methods. Applications and numerical comparison

    Science.gov (United States)

    Jbilou, K.; Sadok, H.

    2000-10-01

    The present paper is a survey of the most popular vector extrapolation methods such as the reduced rank extrapolation (RRE), the minimal polynomial extrapolation (MPE), the modified minimal polynomial extrapolation (MMPE), the vector [var epsilon]-algorithm (VEA) and the topological [var epsilon]-algorithm (TEA). Using projectors, we derive a different interpretation of these methods and give some theoretical results. The second aim of this work is to give a numerical comparison of the vector extrapolation methods above when they are used for practical large problems such as linear and nonlinear systems of equations.

  16. Partial differential equations with numerical methods

    CERN Document Server

    Larsson, Stig

    2003-01-01

    The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.

  17. Intelligent numerical methods applications to fractional calculus

    CERN Document Server

    Anastassiou, George A

    2016-01-01

    In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.

  18. A student's guide to numerical methods

    CERN Document Server

    Hutchinson, Ian H

    2015-01-01

    This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis of an accelerated introdu...

  19. A numerical method for free vibration analysis of beams

    Directory of Open Access Journals (Sweden)

    A. Prokić

    Full Text Available In this paper, a numerical method for solution of the free vibration of beams governed by a set of second-order ordinary differential equations of variable coefficients, with arbitrary boundary conditions, is presented. The method is based on numerical integration rather than the numerical differentiation since the highest derivatives of governing functions are chosen as the basic unknown quantities. The kernelsof integral equations turn out to be Green's function of corresponding equation with homogeneous boundary conditions. The accuracy of the proposed method is demonstrated by comparing the calculated results with those available in the literature. It is shown that good accuracy can be obtained even with a relatively small number of nodes.

  20. Hyperbolic conservation laws and numerical methods

    Science.gov (United States)

    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 Stochastic Computations A Spectral Method Approach

    CERN Document Server

    Xiu, Dongbin

    2010-01-01

    The first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC meth

  2. Numerical calculation of transient field effects in quenching superconducting magnets

    CERN Document Server

    Schwerg, Nikolai; Russenschuck, Stephan

    2009-01-01

    The maximum obtainable magnetic induction of accelerator magnets, relying on normal conducting cables and iron poles, is limited to around 2 T because of ohmic losses and iron saturation. Using superconducting cables, and employing permeable materials merely to reduce the fringe field, this limit can be exceeded and fields of more than 10 T can be obtained. A quench denotes the sudden transition from the superconducting to the normal conducting state. The drastic increase in electrical resistivity causes ohmic heating. The dissipated heat yields a temperature rise in the coil and causes the quench to propagate. The resulting high voltages and excessive temperatures can result in an irreversible damage of the magnet - to the extend of a cable melt-down. The quench behavior of a magnet depends on numerous factors, e.g. the magnet design, the applied magnet protection measures, the external electrical network, electrical and thermal material properties, and induced eddy current losses. The analysis and optimizat...

  3. Spectral methods in numerical plasma simulation

    International Nuclear Information System (INIS)

    Coutsias, E.A.; Hansen, F.R.; Huld, T.; Knorr, G.; Lynov, J.P.

    1989-01-01

    An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded in a two-dimensional Fourier series, while a Chebyshev-Fourier expansion is employed in the second case. A new, efficient algorithm for the solution of Poisson's equation on an annulus is introduced. Problems connected to aliasing and to short wavelength noise generated by gradient steepening are discussed. (orig.)

  4. Spectral Methods in Numerical Plasma Simulation

    DEFF Research Database (Denmark)

    Coutsias, E.A.; Hansen, F.R.; Huld, T.

    1989-01-01

    in a two-dimensional Fourier series, while a Chebyshev-Fourier expansion is employed in the second case. A new, efficient algorithm for the solution of Poisson's equation on an annulus is introduced. Problems connected to aliasing and to short wavelength noise generated by gradient steepening are discussed.......An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded...

  5. Numerical calculation of radiation pattern of plasma channel antenna

    International Nuclear Information System (INIS)

    Xia Xinren; Yin Chengyou

    2010-01-01

    The idea of plasma channel antenna (PCA) for high power microwave weapon is presented in this paper. The radiation pattern of PCA is calculated. The directivity functions of general antenna are derived. The near electromagnetic model of PCA is created based on physical circumstances. The electromagnetic fields of PCA and surrounding air in cylindrical coordinate are given. The dispersion equation of PCA is deduced by applying the boundary conditions of electromagnetic fields. The surface wave vector of PCA is achieved. The variations of radiation characteristic with plasma density, antenna length and antenna radius are emphatically discussed. The controllability of PCA's radiation patterns is confirmed. (authors)

  6. The Numerical Calculation and Experimental Measurement of the Inductance Parameters for Permanent Magnet Synchronous Motor in Electric Vehicle

    Science.gov (United States)

    Jiang, Chao; Qiao, Mingzhong; Zhu, Peng

    2017-12-01

    A permanent magnet synchronous motor with radial magnetic circuit and built-in permanent magnet is designed for the electric vehicle. Finite element numerical calculation and experimental measurement are adopted to obtain the direct axis and quadrature axis inductance parameters of the motor which are vital important for the motor control. The calculation method is simple, the measuring principle is clear, the results of numerical calculation and experimental measurement are mutual confirmation. A quick and effective method is provided to obtain the direct axis and quadrature axis inductance parameters of the motor, and then improve the design of motor or adjust the control parameters of the motor controller.

  7. Simple Calculation Programs for Biology Other Methods

    Indian Academy of Sciences (India)

    First page Back Continue Last page Overview Graphics. Simple Calculation Programs for Biology Other Methods. Hemolytic potency of drugs. Raghava et al., (1994) Biotechniques 17: 1148. FPMAP: methods for classification and identification of microorganisms 16SrRNA. graphical display of restriction and fragment map of ...

  8. RELAP-7 Numerical Stabilization: Entropy Viscosity Method

    Energy Technology Data Exchange (ETDEWEB)

    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.

  9. Numerical calculation of heat transfer by coexistence of forced and natural convections around a circular cylinder

    International Nuclear Information System (INIS)

    Kikuchi, Yoshihiro; Suzuki, Hiroshi

    1995-01-01

    In fast reactors, for removing decay heat after the reactors are shut off by natural circulation, various heat exchangers have been devised, but because the flow rate in this case is very small, the state of flow becomes the coexistence of forced and natural convections. In this research, by using numerical calculation technique, investigation was carried out on the heat transfer by coexisting forced and natural convections around a circular cylinder which is inserted perpendicularly in the flow in the channel between parallel plates in low Reynolds number region, and the flow characteristics. As for the techniques of numerical analysis, calculation domain, basic equations, grid, finite difference method, algorithm, initial conditions, boundary conditions and calculation conditions are explained. As the results of calculation, Nusselt number distribution and velocity distribution are reported. The mean Nusselt number of coexisting convections takes the same value as that of pure forced convection in low Rayleigh number region, and as Rayleigh number becomes higher, it decreases to the minimum value, and thereafter, increases rapidly, and approaches to the value of pure natural convection. (K.I.)

  10. Willow growing - Methods of calculation and profitability

    International Nuclear Information System (INIS)

    Rosenqvist, H.

    1997-01-01

    The calculation method presented here makes it possible to conduct profitability comparisons between annual and perennial crops and in addition take the planning situation into account. The method applied is a modified total step calculation. The difference between a traditional total step calculation and the modified version is the way in which payments and disbursements are taken into account over a period of several years. This is achieved by combining the present value method and the annuity method. The choice of interest rate has great bearing on the result in perennial calculations. The various components influencing the interest rate are analysed and factors relating to the establishment of the interest rate in different situations are described. The risk factor can be an important variable component of the interest rate calculation. Risk is also addressed from an approach in accordance with portfolio theory. The application of the methods sheds light on the profitability of Salix cultivation from the viewpoint of business economics, and also how different factors influence the profitability of Salix cultivation. Aspects studied are harvesting intervals, the importance of yield level, the competitiveness of Salix versus grain cultivation, the influence of income taxes on profitability etc. Methods for evaluation of activities concerning cultivation of a perennial crop are described and also involve the application of nitrogen fertilization to Salix cultivation. Studies have been performed using these methods to look into nitrogen fertilizer profitability in Salix cultivation during the first rotation period. Nitrogen fertilizer profitability has been investigated involving both production functions and cost calculations, taking the year fertilization into consideration. 72 refs., 2 figs., 52 tabs

  11. Highly parallel methods for numerical simulation in nonlinear structural mechanics

    OpenAIRE

    Negrello, Camille

    2017-01-01

    This thesis is aimed to contribute to the adoption of virtual testing, an industrial practice still embryonic which consists in optimizing and certifying by numerical simulations the dimensioning of critical industrial structures. The virtual testing will allow colossal savings in the design of mechanical parts and a greater respect for the environment, thanks to optimized designs. In order to achieve this goal, new calculation methods must be implemented, satisfying more requirements concern...

  12. Numerical perturbative methods in the quantum theory of physical systems

    International Nuclear Information System (INIS)

    Adam, G.

    1980-01-01

    During the last two decades, development of digital electronic computers has led to the deployment of new, distinct methods in theoretical physics. These methods, based on the advances of modern numerical analysis as well as on specific equations describing physical processes, enabled to perform precise calculations of high complexity which have completed and sometimes changed our image of many physical phenomena. Our efforts have concentrated on the development of numerical methods with such intrinsic performances as to allow a successful approach of some Key issues in present theoretical physics on smaller computation systems. The basic principle of such methods is to translate, in numerical analysis language, the theory of perturbations which is suited to numerical rather than to analytical computation. This idea has been illustrated by working out two problems which arise from the time independent Schroedinger equation in the non-relativistic approximation, within both quantum systems with a small number of particles and systems with a large number of particles, respectively. In the first case, we are led to the numerical solution of some quadratic ordinary differential equations (first section of the thesis) and in the second case, to the solution of some secular equations in the Brillouin area (second section). (author)

  13. Monte Carlo methods for shield design calculations

    International Nuclear Information System (INIS)

    Grimstone, M.J.

    1974-01-01

    A suite of Monte Carlo codes is being developed for use on a routine basis in commercial reactor shield design. The methods adopted for this purpose include the modular construction of codes, simplified geometries, automatic variance reduction techniques, continuous energy treatment of cross section data, and albedo methods for streaming. Descriptions are given of the implementation of these methods and of their use in practical calculations. 26 references. (U.S.)

  14. Numerical Methods for the Design and Analysis of Photonic Crystal Fibres

    DEFF Research Database (Denmark)

    Roberts, John

    2008-01-01

    The numerical methods available for calculating the electromagnetic mode properties of photonic crystal fibres are reviewed. The preferred schemes for analyzing TIR guiding and band gap guiding fibres are contrasted.......The numerical methods available for calculating the electromagnetic mode properties of photonic crystal fibres are reviewed. The preferred schemes for analyzing TIR guiding and band gap guiding fibres are contrasted....

  15. Numerical procedure for the calculation of nonsteady spherical shock fronts with radiation

    International Nuclear Information System (INIS)

    Winkler, K.H.

    The basis of the numerical method is an implicit difference scheme with time backward differences to a freely moving coordinate system. The coordinate system itself is determined simultaneously with the iterative solution of the physical equations as a function of the physical variables. Shock fronts, even nonsteady ones, are calculated as discontinuities according to the Rankine--Hugoniot equations. The radiation field is obtained from the two-dimensional, static, spherically symmetric transport equation in conjunction with the time-dependent one-dimensional moment equations. No artificial viscosity of any type is ever used. The applicability of the method developed is demonstrated by an example involving the calculation of protostar collapse. 11 figures

  16. [Magnetic field numerical calculation and analysis for magnetic coupling of centrifugal blood pump for extracorporeal circulation].

    Science.gov (United States)

    Hu, Zhaoyan; Lu, Lijun; Zhang, Tianyi; Chen, Zhenglong; Zhang, Tao

    2013-12-01

    This paper mainly studies the driving system of centrifugal blood pump for extracorporeal circulation, with the core being disc magnetic coupling. Structure parameters of disc magnetic coupling are related to the ability of transferring magnetic torque. Therefore, it is necessary to carry out disc magnetic coupling permanent magnet pole number (n), air gap length (L(g)), permanent magnet thickness (L(m)), permanent magnet body inside diameter (R(i)) and outside diameter (R(o)), etc. thoroughly. This paper adopts the three-dimensional static magnetic field edge element method of Ansys for numerical calculation, and analyses the relations of magnetic coupling each parameter to transmission magnetic torque. It provides a good theory basis and calculation method for further optimization of the disc magnetic coupling.

  17. Numerical methods for the Lévy LIBOR model

    DEFF Research Database (Denmark)

    Papapantoleon, Antonis; Skovmand, David

    2010-01-01

    but the methods are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure....... This enables simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.......The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the L\\'evy LIBOR model of Eberlein and \\"Ozkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates...

  18. Numerical Methods for the Lévy LIBOR Model

    DEFF Research Database (Denmark)

    Papapantoleon, Antonis; Skovmand, David

    are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure. This enables...... simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.......The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the Lévy LIBOR model of Eberlein and Özkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods...

  19. Numerical solution methods for viscoelastic orthotropic materials

    Science.gov (United States)

    Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

    1988-01-01

    Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

  20. Numerical Simulation of Shale Gas Production with Thermodynamic Calculations Incorporated

    KAUST Repository

    Urozayev, Dias

    2015-06-01

    In today’s energy sector, it has been observed a revolutionary increase in shale gas recovery induced by reservoir fracking. So-called unconventional reservoirs became profitable after introducing a well stimulation technique. Some of the analysts expect that shale gas is going to expand worldwide energy supply. However, there is still a lack of an efficient as well as accurate modeling techniques, which can provide a good recovery and production estimates. Gas transports in shale reservoir is a complex process, consisting of slippage effect, gas diffusion along the wall, viscous flow due to the pressure gradient. Conventional industrial simulators are unable to model the flow as the flow doesn’t follow Darcy’s formulation. It is significant to build a unified model considering all given mechanisms for shale reservoir production study and analyze the importance of each mechanism in varied conditions. In this work, a unified mathematical model is proposed for shale gas reservoirs. The proposed model was build based on the dual porosity continuum media model; mass conservation equations for both matrix and fracture systems were build using the dusty gas model. In the matrix, gas desorption, Knudsen diffusion and viscous flow were taken into account. The model was also developed by implementing thermodynamic calculations to correct for the gas compressibility, or to obtain accurate treatment of the multicomponent gas. Previously, the model was built on the idealization of the gas, considering every molecule identical without any interaction. Moreover, the compositional variety of shale gas requires to consider impurities in the gas due to very high variety. Peng-Robinson equation of state was used to com- pute and correct for the gas density to pressure relation by solving the cubic equation to improve the model. The results show that considering the compressibility of the gas will noticeably increase gas production under given reservoir conditions and slow down

  1. Comparison of accelerometry stride time calculation methods.

    Science.gov (United States)

    Norris, Michelle; Kenny, Ian C; Anderson, Ross

    2016-09-06

    Inertial sensors such as accelerometers and gyroscopes can provide a multitude of information on running gait. Running parameters such as stride time and ground contact time can all be identified within tibial accelerometry data. Within this, stride time is a popular parameter of interest, possibly due to its role in running economy. However, there are multiple methods utilised to derive stride time from tibial accelerometry data, some of which may offer complications when implemented on larger data files. Therefore, the purpose of this study was to compare previously utilised methods of stride time derivation to an original proposed method, utilising medio-lateral tibial acceleration data filtered at 2Hz, allowing for greater efficiency in stride time output. Tibial accelerometry data from six participants training for a half marathon were utilised. One right leg run was randomly selected for each participant, in which five consecutive running stride times were calculated. Four calculation methods were employed to derive stride time. A repeated measures analysis of variance (ANOVA) identified no significant difference in stride time between stride time calculation methods (p=1.00), whilst intra-class coefficient values (all >0.95) and coefficient of variance values (all method possibly offers a simplified technique for stride time output during running gait analysis. This method may be less influenced by "double peak" error and minor fluctuations within the data, allowing for accurate and efficient automated data output in both real time and post processing. Copyright © 2016 Elsevier Ltd. All rights reserved.

  2. Learning from numerical calculations of ion-atom collisions

    International Nuclear Information System (INIS)

    Reading, J.F.; Ford, A.L.; Martir, M.; Becker, R.L.

    1981-01-01

    Violent collision of two independent many-particle systems, victims, are discussed in the atomic sphere. The asymmetric region where the charge of the projectile Z/sub p/ is less than the target nuclear charge Z/sub n/ is now well understood though interesting details still need to be worked out. Negatively charged projectiles offer a new illustration of Fadeev re-arrangement collisions. Multi-electron coherence effects illustrate the richness of the field but a symmetric (Z/sub p/ approx. Z/sub n/) collision treatment is needed. A new one and a half center expansion method promises a solution to this problem. Future areas of interest are discussed

  3. Application of numerical methods to elasticity imaging.

    Science.gov (United States)

    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.

  4. A New Iterative Method to Calculate [pi

    Science.gov (United States)

    Dion, Peter; Ho, Anthony

    2012-01-01

    For at least 2000 years people have been trying to calculate the value of [pi], the ratio of the circumference to the diameter of a circle. People know that [pi] is an irrational number; its decimal representation goes on forever. Early methods were geometric, involving the use of inscribed and circumscribed polygons of a circle. However, real…

  5. Efficient pseudospectral methods for density functional calculations

    International Nuclear Information System (INIS)

    Murphy, R. B.; Cao, Y.; Beachy, M. D.; Ringnalda, M. N.; Friesner, R. A.

    2000-01-01

    Novel improvements of the pseudospectral method for assembling the Coulomb operator are discussed. These improvements consist of a fast atom centered multipole method and a variation of the Head-Gordan J-engine analytic integral evaluation. The details of the methodology are discussed and performance evaluations presented for larger molecules within the context of DFT energy and gradient calculations. (c) 2000 American Institute of Physics

  6. Three-dimensional space charge calculation method

    International Nuclear Information System (INIS)

    Lysenko, W.P.; Wadlinger, E.A.

    1981-01-01

    A method is presented for calculating space-charge forces suitable for use in a particle tracing code. Poisson's equation is solved in three dimensions with boundary conditions specified on an arbitrary surface by using a weighted residual method. Using a discrete particle distribution as our source input, examples are shown of off-axis, bunched beams of noncircular crosssection in radio-frequency quadrupole (RFQ) and drift-tube linac geometries

  7. Numerical calculation of spin echo amplitude in pulsed NMR: effects of quadrupole interaction

    International Nuclear Information System (INIS)

    Sobral, R.R.

    1986-01-01

    The spin echo obtained by nuclear magnetic resonance, in systems which atomic nuclei interact with magnetic fields and electric field gradients, present oscillations in function of the time interval between two excitations pulses. Using the density matrix formalism, the amplitudes of these echo is calculated, analytically. In this work, echo amplitudes obtained under different excitation conditions for nuclei of different nuclear spin values are calculated. The numerical results are compared with disposable analytical solutions. Applications of this method to the case of electric field gradient without axial symmetry were studied. Within the used approximation limits, an expression for attnuation of oscillatory behaviour of echo amplitude in function of the time interval between experimentally observed pulses was obtained. (M.C.K.) [pt

  8. Numerical Methods for Free Boundary Problems

    CERN Document Server

    1991-01-01

    About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990. The main purpose of this conference was to provide up-to-date information on important directions of research in the field of free boundary problems and their numerical solutions. The contributions contained in this volume cover the lectures given in the conference. The invited lectures were given by H.W. Alt, V. Barbu, K-H. Hoffmann, H. Mittelmann and V. Rivkind. In his lecture H.W. Alt considered a mathematical model and existence theory for non-isothermal phase separations in binary systems. The lecture of V. Barbu was on the approximate solvability of the inverse one phase Stefan problem. K-H. Hoff­ mann gave an up-to-date survey of several directions in free boundary problems and listed several applications, but the material of his lecture is not included in this proceedings. H.D. Mittelmann handled the stability of thermo capi...

  9. A new method for the automatic calculation of prosody

    International Nuclear Information System (INIS)

    GUIDINI, Annie

    1981-01-01

    An algorithm is presented for the calculation of the prosodic parameters for speech synthesis. It uses the melodic patterns, composed of rising and falling slopes, suggested by G. CAELEN, and rests on: 1. An analysis into units of meaning to determine a melodic pattern 2. the calculation of the numeric values for the prosodic variations of each syllable; 3. The use of a table of vocalic values for the three parameters for each vowel according to the consonantal environment and of a table of standard duration for consonants. This method was applied in the 'SARA' program of synthesis with satisfactory results. (author) [fr

  10. A generalized method for calculating wake potentials

    International Nuclear Information System (INIS)

    Napoly, O.; Chin, Y.H.; Zotter, B.

    1993-01-01

    The authors describe a generalized method to compute wake potentials created in axisymmetric structures. It relies on expressing the wake potentials, of any multipole order, as integrals over the e.m. fields along an arbitrary one-dimensional contour spanning the structure longitudinally. For perfectly conducting structures, the integration along the axis can then be replaced by choosing a contour beginning and ending on the beam tubes. Thus it generalizes the former method of calculating the wake potentials by integrating along a straight line at the beam tube radius. Its usefulness is illustrated with the computer code ABCI which permits calculation of wake potentials in structures extending to the inside of the beam tube radius, or having unequal beam tube radii at the two sides

  11. DEVELOPMENT OF CALCULATION METHOD OF SENSITIVITIES FOR LIGHT WATER REACTORS

    Directory of Open Access Journals (Sweden)

    TOSHIKAZU TAKEDA

    2013-11-01

    Full Text Available A new method of calculating sensitivity coefficients of core characteristics relative to infinite-dilution cross sections has been developed. Conventional sensitivity coefficients are evaluated for the changes of effective cross sections which are dependent on individual models of core and cell. Therefore a correction has been derived to the conventional sensitivity coefficients based on the perturbation theory. The accuracy of the present method has been verified by comparing numerical results of sensitivity coefficients with a reference Monte-Carlo method.

  12. Developing Teaching Material Software Assisted for Numerical Methods

    Science.gov (United States)

    Handayani, A. D.; Herman, T.; Fatimah, S.

    2017-09-01

    The NCTM vision shows the importance of two things in school mathematics, which is knowing the mathematics of the 21st century and the need to continue to improve mathematics education to answer the challenges of a changing world. One of the competencies associated with the great challenges of the 21st century is the use of help and tools (including IT), such as: knowing the existence of various tools for mathematical activity. One of the significant challenges in mathematical learning is how to teach students about abstract concepts. In this case, technology in the form of mathematics learning software can be used more widely to embed the abstract concept in mathematics. In mathematics learning, the use of mathematical software can make high level math activity become easier accepted by student. Technology can strengthen student learning by delivering numerical, graphic, and symbolic content without spending the time to calculate complex computing problems manually. The purpose of this research is to design and develop teaching materials software assisted for numerical method. The process of developing the teaching material starts from the defining step, the process of designing the learning material developed based on information obtained from the step of early analysis, learners, materials, tasks that support then done the design step or design, then the last step is the development step. The development of teaching materials software assisted for numerical methods is valid in content. While validator assessment for teaching material in numerical methods is good and can be used with little revision.

  13. Development of numerical methods for reactive transport

    International Nuclear Information System (INIS)

    Bouillard, N.

    2006-12-01

    When a radioactive waste is stored in deep geological disposals, it is expected that the waste package will be damaged under water action (concrete leaching, iron corrosion). Then, to understand these damaging processes, chemical reactions and solutes transport are modelled. Numerical simulations of reactive transport can be done sequentially by the coupling of several codes. This is the case of the software platform ALLIANCES which is developed jointly with CEA, ANDRA and EDF. Stiff reactions like precipitation-dissolution are crucial for the radioactive waste storage applications, but standard sequential iterative approaches like Picard's fail in solving rapidly reactive transport simulations with such stiff reactions. In the first part of this work, we focus on a simplified precipitation and dissolution process: a system made up with one solid species and two aqueous species moving by diffusion is studied mathematically. It is assumed that a precipitation dissolution reaction occurs in between them, and it is modelled by a discontinuous kinetics law of unknown sign. By using monotonicity properties, the convergence of a finite volume scheme on admissible mesh is proved. Existence of a weak solution is obtained as a by-product of the convergence of the scheme. The second part is dedicated to coupling algorithms which improve Picard's method and can be easily used in an existing coupling code. By extending previous works, we propose a general and adaptable framework to solve nonlinear systems. Indeed by selecting special options, we can either recover well known methods, like nonlinear conjugate gradient methods, or design specific method. This algorithm has two main steps, a preconditioning one and an acceleration one. This algorithm is tested on several examples, some of them being rather academical and others being more realistic. We test it on the 'three species model'' example. Other reactive transport simulations use an external chemical code CHESS. For a

  14. La résistance de vague des carènes. Calcul de la fonction de Green par intégration numérique et par une méthode asymptotique. 1° Partie Hull Resistance to Wave? Computing the Green Function by Numerical Integration and by an Asymptotic Method. Part One

    Directory of Open Access Journals (Sweden)

    Carou A.

    2006-11-01

    Full Text Available Le calcul de la résistance de vague d'une carène par éléments finis concentrés sur un ouvert borné nécessite la connaissance de la fonction de Green du problème à grande distance. Cette fonction est très difficile à calculer numériquement. On justifie dans ce travail une méthode asymptotique rapide, remplaçant avantageusement l'intégration numérique. Computing wave resistance -by finite elements concentrated on a bounded open set requires the prior knowledge of the Green function of the problem at a great distance. Computing this function is numerically very difficult. A fast asymptotic method is iustified in this article, and it can be used ta advantage as a replacemenf for numerical integration.

  15. Theoretical and applied aerodynamics and related numerical methods

    CERN Document Server

    Chattot, J J

    2015-01-01

    This book covers classical and modern aerodynamics, theories and related numerical methods, for senior and first-year graduate engineering students, including: -The classical potential (incompressible) flow theories for low speed aerodynamics of thin airfoils and high and low aspect ratio wings. - The linearized theories for compressible subsonic and supersonic aerodynamics. - The nonlinear transonic small disturbance potential flow theory, including supercritical wing sections, the extended transonic area rule with lift effect, transonic lifting line and swept or oblique wings to minimize wave drag. Unsteady flow is also briefly discussed. Numerical simulations based on relaxation mixed-finite difference methods are presented and explained. - Boundary layer theory for all Mach number regimes and viscous/inviscid interaction procedures used in practical aerodynamics calculations. There are also four chapters covering special topics, including wind turbines and propellers, airplane design, flow analogies and h...

  16. Efficient numerical method for district heating system hydraulics

    International Nuclear Information System (INIS)

    Stevanovic, Vladimir D.; Prica, Sanja; Maslovaric, Blazenka; Zivkovic, Branislav; Nikodijevic, Srdjan

    2007-01-01

    An efficient method for numerical simulation and analyses of the steady state hydraulics of complex pipeline networks is presented. It is based on the loop model of the network and the method of square roots for solving the system of linear equations. The procedure is presented in the comprehensive mathematical form that could be straightforwardly programmed into a computer code. An application of the method to energy efficiency analyses of a real complex district heating system is demonstrated. The obtained results show a potential for electricity savings in pumps operation. It is shown that the method is considerably more effective than the standard Hardy Cross method still widely used in engineering practice. Because of the ease of implementation and high efficiency, the method presented in this paper is recommended for hydraulic steady state calculations of complex networks

  17. Fast calculation technique for scattering in T-matrix method

    International Nuclear Information System (INIS)

    Yan Shaohui; Yao Baoli

    2008-01-01

    In scattering calculations using the T-matrix method, the calculation of the T-matrix involves multiplication and inversion of matrices. These two types of matrix operations are time-consuming, especially for the matrices with large size. Petrov et al. [D. Petrov, Y. Shkuratov, G. Videen, Opt. Lett. 32 (2007) 1168] proposed an optimized matrix inversion technique, which suggests the inversion of two matrices, each of which contains half the number of rows. This technique reduces time-consumption significantly. On the basis of this approach, we propose another fast calculation technique for scattering in the T-matrix method, which obtains the scattered fields through carrying out only the operations between matrices and the incident field coefficient. Numerical results show that this technique can decrease time-consumption by more than half that of the optimized matrix inversion technique by Petrov et al

  18. A numerical method for singular boundary value problem of ordinary differential equation

    International Nuclear Information System (INIS)

    He Qibing

    1992-12-01

    A numerical method, regularizing method, is suggested to treat the singular boundary problem of ordinary differential equation that is raised from controlled nuclear fusion science and other fields owing to their singular physical mechanism. This kind of singular boundary problem has been successfully solved by special treatment near the singular points and using difference method. This method overcomes difficulties in numerical calculation due to the singularity. The convergence results and numerical test are also given

  19. Criticality calculation method for mixer-settlers

    International Nuclear Information System (INIS)

    Gonda, Kozo; Aoyagi, Haruki; Nakano, Ko; Kamikawa, Hiroshi.

    1980-01-01

    A new criticality calculation code MACPEX has been developed to evaluate and manage the criticality of the process in the extractor of mixer-settler type. MACPEX can perform the combined calculation with the PUREX process calculation code MIXSET, to get the neutron flux and the effective multiplication constant in the mixer-settlers. MACPEX solves one-dimensional diffusion equation by the explicit difference method and the standard source-iteration technique. The characteristics of MACPEX are as follows. 1) Group constants of 4 energy groups for the 239 Pu-H 2 O solution, water, polyethylene and SUS 28 are provided. 2) The group constants of the 239 Pu-H 2 O solution are given by the functional formulae of the plutonium concentration, which is less than 50 g/l. 3) Two boundary conditions of the vacuum condition and the reflective condition are available in this code. 4) The geometrical bucklings can be calculated for a certain energy group and/or region by using the three dimentional neutron flux profiles obtained by CITATION. 5) The buckling correction search can be carried out in order to get a desired k sub(eff). (author)

  20. Acceleration methods and models in Sn calculations

    International Nuclear Information System (INIS)

    Sbaffoni, M.M.; Abbate, M.J.

    1984-01-01

    In some neutron transport problems solved by the discrete ordinate method, it is relatively common to observe some particularities as, for example, negative fluxes generation, slow and insecure convergences and solution instabilities. The commonly used models for neutron flux calculation and acceleration methods included in the most used codes were analyzed, in face of their use in problems characterized by a strong upscattering effect. Some special conclusions derived from this analysis are presented as well as a new method to perform the upscattering scaling for solving the before mentioned problems in this kind of cases. This method has been included in the DOT3.5 code (two dimensional discrete ordinates radiation transport code) generating a new version of wider application. (Author) [es

  1. Optimisation of sputnik distributor using numerical method

    Energy Technology Data Exchange (ETDEWEB)

    Guo, B.Y.; Dong, K.J.; Yu, A.B. [University of New South Wales, Sydney, NSW (Australia)

    2009-07-01

    A coal distributor is necessary to mix and split raw coal for subsequent processing in a parallel module coal preparation plant. The sputnik hydraulic distributor, a static device with two internal chambers and tangential water pipes, is widely employed for this purpose. We have recently developed a computational fluid dynamics (CFD) model which uses homogeneous two-phase flow method to solve the three-dimensional distribution of water flow and its volume fraction and a discrete element method (DEM) to describe the motion of coal particles in the distributor. In this article, extensive numerical experiments based on the CFD model are conducted and the detailed fluid flow pattern is analysed to understand the main causes for water maldistribution inside a 12-way coal distributor, aiming to identify the optimum operational condition and design for practice. Variables considered include water flow rate and velocity, layout of water inlets, size and position of the inserted table, geometry of orifice slots and outlet size. The initial momentum of tangential inlet jet is found to be most important to minimise biased mass flow rate among outlets. Three mechanisms, namely, geometric distribution, swirl distribution and gravity distribution, are found to be responsible for the water distribution. To test the outcomes, the flow of coal particles is also simulated using DEM. Several cases with different operational conditions are considered to clarify the influence of water flow on particle flow and the relationship between water distribution and particle flow distribution at the outlets.

  2. Enhanced Method for Cavity Impedance Calculations

    Energy Technology Data Exchange (ETDEWEB)

    Frank Marhauser, Robert Rimmer, Kai Tian, Haipeng Wang

    2009-05-01

    With the proposal of medium to high average current accelerator facilities the demand for cavities with extremely low Higher Order Mode (HOM) impedances is increasing. Modern numerical tools are still under development to more thoroughly predict impedances that need to take into account complex absorbing boundaries and lossy materials. With the usually large problem size it is preferable to utilize massive parallel computing when applicable and available. Apart from such computational issues, we have developed methods using available computer resources to enhance the information that can be extracted from a cavities? wakefield computed in time domain. In particular this is helpful for a careful assessment of the extracted RF power and the mitigation of potential beam break-up or emittance diluting effects, a figure of merit for the cavity performance. The method is described as well as an example of its implementation.

  3. Classical Methods and Calculation Algorithms for Determining Lime Requirements

    Directory of Open Access Journals (Sweden)

    André Guarçoni

    Full Text Available ABSTRACT The methods developed for determination of lime requirements (LR are based on widely accepted principles. However, the formulas used for calculation have evolved little over recent decades, and in some cases there are indications of their inadequacy. The aim of this study was to compare the lime requirements calculated by three classic formulas and three algorithms, defining those most appropriate for supplying Ca and Mg to coffee plants and the smaller possibility of causing overliming. The database used contained 600 soil samples, which were collected in coffee plantings. The LR was estimated by the methods of base saturation, neutralization of Al3+, and elevation of Ca2+ and Mg2+ contents (two formulas and by the three calculation algorithms. Averages of the lime requirements were compared, determining the frequency distribution of the 600 lime requirements (LR estimated through each calculation method. In soils with low cation exchange capacity at pH 7, the base saturation method may fail to adequately supply the plants with Ca and Mg in many situations, while the method of Al3+ neutralization and elevation of Ca2+ and Mg2+ contents can result in the calculation of application rates that will increase the pH above the suitable range. Among the methods studied for calculating lime requirements, the algorithm that predicts reaching a defined base saturation, with adequate Ca and Mg supply and the maximum application rate limited to the H+Al value, proved to be the most efficient calculation method, and it can be recommended for use in numerous crops conditions.

  4. Numerical methods for analyzing electromagnetic scattering

    Science.gov (United States)

    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.

  5. Methods for Calculating Empires in Quasicrystals

    Directory of Open Access Journals (Sweden)

    Fang Fang

    2017-10-01

    Full Text Available This paper reviews the empire problem for quasiperiodic tilings and the existing methods for generating the empires of the vertex configurations in quasicrystals, while introducing a new and more efficient method based on the cut-and-project technique. Using Penrose tiling as an example, this method finds the forced tiles with the restrictions in the high dimensional lattice (the mother lattice that can be cut-and-projected into the lower dimensional quasicrystal. We compare our method to the two existing methods, namely one method that uses the algorithm of the Fibonacci chain to force the Ammann bars in order to find the forced tiles of an empire and the method that follows the work of N.G. de Bruijn on constructing a Penrose tiling as the dual to a pentagrid. This new method is not only conceptually simple and clear, but it also allows us to calculate the empires of the vertex configurations in a defected quasicrystal by reversing the configuration of the quasicrystal to its higher dimensional lattice, where we then apply the restrictions. These advantages may provide a key guiding principle for phason dynamics and an important tool for self error-correction in quasicrystal growth.

  6. Numerical computation of FCT equilibria by inverse equilibrium method

    International Nuclear Information System (INIS)

    Tokuda, Shinji; Tsunematsu, Toshihide; Takeda, Tatsuoki

    1986-11-01

    FCT (Flux Conserving Tokamak) equilibria were obtained numerically by the inverse equilibrium method. The high-beta tokamak ordering was used to get the explicit boundary conditions for FCT equilibria. The partial differential equation was reduced to the simultaneous quasi-linear ordinary differential equations by using the moment method. The regularity conditions for solutions at the singular point of the equations can be expressed correctly by this reduction and the problem to be solved becomes a tractable boundary value problem on the quasi-linear ordinary differential equations. This boundary value problem was solved by the method of quasi-linearization, one of the shooting methods. Test calculations show that this method provides high-beta tokamak equilibria with sufficiently high accuracy for MHD stability analysis. (author)

  7. Group Contribution Methods for Phase Equilibrium Calculations.

    Science.gov (United States)

    Gmehling, Jürgen; Constantinescu, Dana; Schmid, Bastian

    2015-01-01

    The development and design of chemical processes are carried out by solving the balance equations of a mathematical model for sections of or the whole chemical plant with the help of process simulators. For process simulation, besides kinetic data for the chemical reaction, various pure component and mixture properties are required. Because of the great importance of separation processes for a chemical plant in particular, a reliable knowledge of the phase equilibrium behavior is required. The phase equilibrium behavior can be calculated with the help of modern equations of state or g(E)-models using only binary parameters. But unfortunately, only a very small part of the experimental data for fitting the required binary model parameters is available, so very often these models cannot be applied directly. To solve this problem, powerful predictive thermodynamic models have been developed. Group contribution methods allow the prediction of the required phase equilibrium data using only a limited number of group interaction parameters. A prerequisite for fitting the required group interaction parameters is a comprehensive database. That is why for the development of powerful group contribution methods almost all published pure component properties, phase equilibrium data, excess properties, etc., were stored in computerized form in the Dortmund Data Bank. In this review, the present status, weaknesses, advantages and disadvantages, possible applications, and typical results of the different group contribution methods for the calculation of phase equilibria are presented.

  8. Comparison of optimization methods for electronic-structure calculations

    International Nuclear Information System (INIS)

    Garner, J.; Das, S.G.; Min, B.I.; Woodward, C.; Benedek, R.

    1989-01-01

    The performance of several local-optimization methods for calculating electronic structure is compared. The fictitious first-order equation of motion proposed by Williams and Soler is integrated numerically by three procedures: simple finite-difference integration, approximate analytical integration (the Williams-Soler algorithm), and the Born perturbation series. These techniques are applied to a model problem for which exact solutions are known, the Mathieu equation. The Williams-Soler algorithm and the second Born approximation converge equally rapidly, but the former involves considerably less computational effort and gives a more accurate converged solution. Application of the method of conjugate gradients to the Mathieu equation is discussed

  9. An approach to first principles electronic structure calculation by symbolic-numeric computation

    Directory of Open Access Journals (Sweden)

    Akihito Kikuchi

    2013-04-01

    Full Text Available There is a wide variety of electronic structure calculation cooperating with symbolic computation. The main purpose of the latter is to play an auxiliary role (but not without importance to the former. In the field of quantum physics [1-9], researchers sometimes have to handle complicated mathematical expressions, whose derivation seems almost beyond human power. Thus one resorts to the intensive use of computers, namely, symbolic computation [10-16]. Examples of this can be seen in various topics: atomic energy levels, molecular dynamics, molecular energy and spectra, collision and scattering, lattice spin models and so on [16]. How to obtain molecular integrals analytically or how to manipulate complex formulas in many body interactions, is one such problem. In the former, when one uses special atomic basis for a specific purpose, to express the integrals by the combination of already known analytic functions, may sometimes be very difficult. In the latter, one must rearrange a number of creation and annihilation operators in a suitable order and calculate the analytical expectation value. It is usual that a quantitative and massive computation follows a symbolic one; for the convenience of the numerical computation, it is necessary to reduce a complicated analytic expression into a tractable and computable form. This is the main motive for the introduction of the symbolic computation as a forerunner of the numerical one and their collaboration has won considerable successes. The present work should be classified as one such trial. Meanwhile, the use of symbolic computation in the present work is not limited to indirect and auxiliary part to the numerical computation. The present work can be applicable to a direct and quantitative estimation of the electronic structure, skipping conventional computational methods.

  10. A keff calculation method by Monte Carlo

    International Nuclear Information System (INIS)

    Shen, H; Wang, K.

    2008-01-01

    The effective multiplication factor (k eff ) is defined as the ratio between the number of neutrons in successive generations, which definition is adopted by most Monte Carlo codes (e.g. MCNP). Also, it can be thought of as the ratio of the generation rate of neutrons by the sum of the leakage rate and the absorption rate, which should exclude the effect of the neutron reaction such as (n, 2n) and (n, 3n). This article discusses the Monte Carlo method for k eff calculation based on the second definition. A new code has been developed and the results are presented. (author)

  11. Testing the numerical method for one-dimensional shock treatment

    International Nuclear Information System (INIS)

    Horvat, A.

    1998-01-01

    In the early 80's the SMUP computer code was developed at the Jozef Stefan Institute for simulation of two-phase flow in steam generators. It was suitable only for steady-state problems and was unable to simulate transient behavior. In this paper, efforts are presented to find suitable numerical method to renew the old SMUP computer code. The obsolete numerical code has to be replaced with a more efficient one that would be able to treat time-dependent problems. It also has to ensure accurate solution during shock propagation. One-dimensional shock propagation in a tube were studied at zero viscosity. To simplify the equation of state the ideal gas was chosen as a working fluid. Stability margins in the form of transport matrix eigenvalues were calculated. Results were found to be close to those already published.(author)

  12. THE NUMERICAL ALGORITHM FOR CALCULATING TEMPERATURE FIELDS OF THE PNEUMATIC TIRES DURING VULCANIZATION

    Directory of Open Access Journals (Sweden)

    S. G. Tikhomirov

    2015-01-01

    Full Text Available In the article discussed the mathematical formulation and numerical algorithm for solving the problem of calculating the temperature field in the process vulcanizing of the product, whose the thermal characteristics are depended on the temperature. As a mathematical model considered the system of differential equations of heat conduction, taking into account the change in the coefficients of thermal conductivity and heat density in multilayer product of the temperature. The system of equations is solved for a given initial distribution of temperature and for a given (time-dependent temperatures on the border of the product to the press-mold and to the diaphragm. On the border of the contacts of adjacent layers are given the condition of continuity of temperature and heat flux. Change of the thermal conductivity from the time is approximated by linear functions. The activation energy of the vulcanization process is determined on the basis of experimental data obtained in the control test samples using a reometer. Considering the function representing the corresponding integrals of the thermal conductivity, the original system of differential equations is transformed to an equivalent system of differential equations convenient for constructing numerical algorithms for solving the problem. The resulting system of partial differential equations derived using the method of finite-difference approximation is replaced by a system of algebraic equations. Solution of the system of algebraic equations is carried out under the scheme explicit difference approximation. In the article calculated the temperature field for the tire at given initial and boundary conditions. Stability and accuracy of the numerical algorithm for solving the problem is demonstrated by the calculations performed with different sampling step along the time and space coordinates. Assessment of the degree of completion of the process is carried out by calculated equivalent time for

  13. Assessment of Soil Liquefaction Potential Based on Numerical Method

    DEFF Research Database (Denmark)

    Choobasti, A. Janalizadeh; Vahdatirad, Mohammad Javad; Torabi, M.

    2012-01-01

    simplified method have been developed over the years. Although simplified methods are available in calculating the liquefaction potential of a soil deposit and shear stresses induced at any point in the ground due to earthquake loading, these methods cannot be applied to all earthquakes with the same...... accuracy, also they lack the potential to predict the pore pressure developed in the soil. Therefore, it is necessary to carry out a ground response analysis to obtain pore pressures and shear stresses in the soil due to earthquake loading. Using soil historical, geological and compositional criteria......, a zone of the corridor of Tabriz urban railway line 2 susceptible to liquefaction was recognized. Then, using numerical analysis and cyclic stress method using QUAKE/W finite element code, soil liquefaction potential in susceptible zone was evaluated based on design earthquake....

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

    Science.gov (United States)

    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.

  15. Numerical methods in simulation of resistance welding

    DEFF Research Database (Denmark)

    Nielsen, Chris Valentin; Martins, Paulo A.F.; Zhang, Wenqi

    2015-01-01

    Finite element simulation of resistance welding requires coupling betweenmechanical, thermal and electrical models. This paper presents the numerical models and theircouplings that are utilized in the computer program SORPAS. A mechanical model based onthe irreducible flow formulation is utilized...... a resistance welding point of view, the most essential coupling between the above mentioned models is the heat generation by electrical current due to Joule heating. The interaction between multiple objects is anothercritical feature of the numerical simulation of resistance welding because it influences...

  16. Numerical Calculation of Coherent Synchrotron Radiation Effects Using TraFiC4

    International Nuclear Information System (INIS)

    Kabel, Andreas C.

    2000-01-01

    Coherent synchrotron radiation (CSR) occurs when short bunches travel on strongly bent trajectories. Its effects on high-quality beams can be severe and are well understood qualitatively. For quantitative results, however, one has to rely on numerical methods. There exist several simulation codes utilizing different approaches. The authors describe in some detail the code TraFiC 4 developed at DESY for design and analysis purposes, which approaches the problem from first principles and solves the equations of motion either perturbatively or self-consistently. They present some calculational results and comparison with experimental data. Also, they give examples of how the code can be used to design beamlines with minimal emittance growth due to CSR

  17. How to integrate divergent integrals: a pure numerical approach to complex loop calculations

    International Nuclear Information System (INIS)

    Caravaglios, F.

    2000-01-01

    Loop calculations involve the evaluation of divergent integrals. Usually [G. 't Hooft, M. Veltman, Nucl. Phys. B 44 (1972) 189] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers the Laurent expansion in powers of ε=n-4. In this paper we discuss a method to extract directly all coefficients of this expansion by means of concrete and well defined integrals in a five-dimensional space. We by-pass the formal and symbolic procedure of analytic continuation; instead we can numerically compute the integrals to extract directly both the coefficient of the pole 1/ε and the finite part

  18. A numerical simulation method for aircraft infrared imaging

    Science.gov (United States)

    Zhou, Yue; Wang, Qiang; Li, Ting; Hu, Haiyang

    2017-06-01

    Numerical simulation of infrared (IR) emission from aircraft is of great significance for military and civilian applications. In this paper, the narrow band k-distribution (NBK) model is used to calculate radiative properties of non-gray gases in the hot exhaust plume. With model parameters derived from the high resolution spectral database HITEMP 2010, the NBK model is validated by comparisons with exact line by line (LBL) results and experimental data. Based on the NBK model, a new finite volume and back ray tracing (FVBRT) method is proposed to solve the radiative transfer equations and produce IR imaging. Calculated results by the FVBRT method are compared with experimental data and available results in open references, which shows the FVBRT method can maintain good accuracy while producing IR images with better rendering effects. Finally, the NBK model and FVBRT method are integrated to calculate IR signature of an aircraft. The IR images and spatial distributions of radiative intensity are compared and analyzed in both 3 - 5 μm band and 8 - 12 μm band to provide references for engineering applications.

  19. Comparison of different approaches to the numerical calculation of the LMJ focal

    Directory of Open Access Journals (Sweden)

    Bourgeade A.

    2013-11-01

    Full Text Available The beam smoothing in the focal plane of high power lasers is of particular importance to laser-plasma interaction studies in order to minimize plasma parametric and hydrodynamic instabilities on the target. Here we investigate the focal spot structure in different geometrical configurations where standard paraxial hypotheses are no longer verified. We present numerical studies in the cases of single flat top square beam, LMJ quadruplet and complete ring of quads with large azimuth angle. Different calculations are made with Fresnel diffraction propagation model in the paraxial approximation and full vector Maxwell's equations. The first model is based on Fourier transform from near to far field method. The second model uses first spherical wave decomposition in plane waves with Fourier transform and propagates them to the focal spot. These two different approaches are compared with Miró [1] modeling results using paraxial or Feit and Fleck options. The methods presented here are generic for focal spot calculations. They can be used for other complex geometric configurations and various smoothing techniques. The results will be used as boundary conditions in plasma interaction computations.

  20. Comparison of different approaches to the numerical calculation of the LMJ focal

    Science.gov (United States)

    Bourgeade, A.; Coïc, H.; Goossens, J.-P.

    2013-11-01

    The beam smoothing in the focal plane of high power lasers is of particular importance to laser-plasma interaction studies in order to minimize plasma parametric and hydrodynamic instabilities on the target. Here we investigate the focal spot structure in different geometrical configurations where standard paraxial hypotheses are no longer verified. We present numerical studies in the cases of single flat top square beam, LMJ quadruplet and complete ring of quads with large azimuth angle. Different calculations are made with Fresnel diffraction propagation model in the paraxial approximation and full vector Maxwell's equations. The first model is based on Fourier transform from near to far field method. The second model uses first spherical wave decomposition in plane waves with Fourier transform and propagates them to the focal spot. These two different approaches are compared with Miró [1] modeling results using paraxial or Feit and Fleck options. The methods presented here are generic for focal spot calculations. They can be used for other complex geometric configurations and various smoothing techniques. The results will be used as boundary conditions in plasma interaction computations.

  1. Analytical and numerical calculations of resistive wall impedances for thin beam pipe structures at low frequencies

    Energy Technology Data Exchange (ETDEWEB)

    Niedermayer, U., E-mail: u.niedermayer@gsi.de [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder, Schlossgartenstrasse 8, 64289 Darmstadt (Germany); Boine-Frankenheim, O. [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder, Schlossgartenstrasse 8, 64289 Darmstadt (Germany)

    2012-09-21

    The resistive wall impedance is one of the main sources for beam instabilities in synchrotrons and storage rings. The fast ramped SIS18 synchrotron at GSI and the projected SIS100 synchrotron for FAIR both employ thin (0.3 mm) stainless steel beam pipes in order to reduce eddy current effects. The lowest betatron sidebands are at about 100 kHz, which demands accurate impedance predictions in the low frequency (LF) range where the beam pipe and possibly also the structures behind the pipe are the dominating impedance sources. The longitudinal and transverse resistive wall impedances of a circular multi-layer pipe are calculated analytically using the field matching technique. We compare the impedances obtained from a radial wave model, which corresponds to the setup used in bench measurements, with the axial wave model, which corresponds to an actual beam moving with relativistic velocity. For thin beam pipes the induced wall current and the corresponding shielding properties of the pipe are important. In both models the wall current is obtained analytically. The characteristic frequencies for the onset of the wall current are calculated from equivalent lumped element circuits corresponding to the radial model. For more complex structures, like the SIS100 beam pipe, we use a numerical method, in which the impedance is obtained from the total power loss. The method is validated by the analytic expressions for circular beam pipes.

  2. Simple method to calculate percolation, Ising and Potts clusters

    International Nuclear Information System (INIS)

    Tsallis, C.

    1981-01-01

    A procedure ('break-collapse method') is introduced which considerably simplifies the calculation of two - or multirooted clusters like those commonly appearing in real space renormalization group (RG) treatments of bond-percolation, and pure and random Ising and Potts problems. The method is illustrated through two applications for the q-state Potts ferromagnet. The first of them concerns a RG calculation of the critical exponent ν for the isotropic square lattice: numerical consistence is obtained (particularly for q→0) with den Nijs conjecture. The second application is a compact reformulation of the standard star-triangle and duality transformations which provide the exact critical temperature for the anisotropic triangular and honeycomb lattices. (Author) [pt

  3. Time Correlation Calculation Method Based on Delayed Coordinates

    Science.gov (United States)

    Morino, K.; Kobayashi, M. U.; Miyazaki, S.

    2009-06-01

    An approximate calculation method of time correlations by use of delayed coordinate is proposed. For a solvable piecewise linear hyperbolic chaotic map, this approximation is compared with the exact calculation, and an exponential convergence for the maximum time delay M is found. By use of this exponential convergence, the exact result for M &to ∞ is extrapolated from this approximation for the first few values of M. This extrapolation is shown to be much better than direct numerical simulations based on the definition of the time correlation function. As an application, the irregular dependence of diffusion coefficients similar to Takagi or Weierstrass functions is obtained from this approximation, which is indistinguishable from the exact result only at M = 2. The method is also applied to the dissipative Lozi and Hénon maps and the conservative standard map in order to show wide applicability.

  4. ANALYTICAL METHODS FOR CALCULATING FAN AERODYNAMICS

    Directory of Open Access Journals (Sweden)

    Jan Dostal

    2015-12-01

    Full Text Available This paper presents results obtained between 2010 and 2014 in the field of fan aerodynamics at the Department of Composite Technology at the VZLÚ aerospace research and experimental institute in Prague – Letnany. The need for rapid and accurate methods for the preliminary design of blade machinery led to the creation of a mathematical model based on the basic laws of turbomachine aerodynamics. The mathematical model, the derivation of which is briefly described below, has been encoded in a computer programme, which enables the theoretical characteristics of a fan of the designed geometry to be determined rapidly. The validity of the mathematical model is assessed continuously by measuring model fans in the measuring unit, which was developed and manufactured specifically for this purpose. The paper also presents a comparison between measured characteristics and characteristics determined by the mathematical model as the basis for a discussion on possible causes of measured deviations and calculation deviations.

  5. Optimization methods and silicon solar cell numerical models

    Science.gov (United States)

    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.

  6. New numerical methods for nuclear cross section processing

    International Nuclear Information System (INIS)

    Ferran, Ghislain

    2014-01-01

    Nuclear data allow to describe how a particle interacts with matter. These data are therefore at the basis of neutron transport and reactor physics calculations. Once measured and evaluated, they are given in libraries as a list of parameters. Before they can be used in neutron transport calculations, processing is required which includes taking into account several physical phenomena. This can be done by several softwares, such as NJOY, which all have the drawback to use old numerical methods derived from the same algorithms. For nuclear safety applications, it is important to rely on independent methods, to have a comparison point and to isolate the effects of the treatment on the final results. Moreover, it is important to properly master processing accuracy during its different steps. The objective of this PhD is then to develop independent numerical methods that can guarantee nuclear data processing within a given precision and to implement them practically, with the creation of the GAIA software. Our first step was the reconstruction of cross sections from the parameters given in libraries, with different approximations of the R-matrix theory. Reconstruction using the general formalism, without any approximation, has also been implemented, which has required the development of a new method to calculate the R-matrix. Tests have been performed on all existing formalisms, including the newest one. They have shown a good agreement between GAIA and NJOY. Reconstruction of angular differential cross sections directly from R-matrix parameters, using the Blatt-Biedenharn formula, has also been implemented and tested. The cross sections we have obtained at this point correspond to a target nucleus at absolute zero temperature. Because of thermal agitation, these cross sections are subject to a Doppler effect that is taken into account by integrating them with Solbrig's kernel. Our second step was then to calculate this integral. First, we have elaborated and

  7. Numerical Methods for Structured Matrices and Applications

    CERN Document Server

    Bini, Dario A; Olshevsky, Vadim; Tyrtsyhnikov, Eugene; van Barel, Marc

    2010-01-01

    This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to the topics where Georg Heinig had made outstanding achievements. In particular, this includes contributions from the fields of structured matrices, fast algorithms, operator theory, and applications to system theory and signal processing.

  8. CEMRACS 2010: Numerical methods for fusion

    International Nuclear Information System (INIS)

    2011-01-01

    This CEMRACS summer school is devoted to the mathematical and numerical modeling of plasma problems that occur in magnetic or inertial fusion. The main topics of this year are the following: -) asymptotic solutions for fluid models of plasma, -) the hydrodynamics of the implosion and the coupling with radiative transfer in inertial fusion, -) gyrokinetic simulations of magnetic fusion plasmas, and -) Landau damping.

  9. Handling Wavelet Expansions in numerical Methods

    NARCIS (Netherlands)

    Metselaar, Arend Aalberthus Roeland

    2002-01-01

    Wavelet expansions have drawn a lot of attention in recent decades. Wavelets originate from signal analysis, and one of the purposes is data compression. The ability to compress data can also be used to reduce the amount of computation work in a numerical simulation.A family of wavelets forms a

  10. Experiments in orbit determination using numerical methods

    NARCIS (Netherlands)

    Traas, C.R.

    1985-01-01

    The dynamics of the observed object is written as a system of integral equations. This system is solved numerically by representing the components of the force function as linear combinations of B-splines and by applying the multigrid technique. In an outer loop the orbit determination problem is

  11. Comparison of matrix exponential methods for fuel burnup calculations

    International Nuclear Information System (INIS)

    Oh, Hyung Suk; Yang, Won Sik

    1999-01-01

    Series expansion methods to compute the exponential of a matrix have been compared by applying them to fuel depletion calculations. Specifically, Taylor, Pade, Chebyshev, and rational Chebyshev approximations have been investigated by approximating the exponentials of bum matrices by truncated series of each method with the scaling and squaring algorithm. The accuracy and efficiency of these methods have been tested by performing various numerical tests using one thermal reactor and two fast reactor depletion problems. The results indicate that all the four series methods are accurate enough to be used for fuel depletion calculations although the rational Chebyshev approximation is relatively less accurate. They also show that the rational approximations are more efficient than the polynomial approximations. Considering the computational accuracy and efficiency, the Pade approximation appears to be better than the other methods. Its accuracy is better than the rational Chebyshev approximation, while being comparable to the polynomial approximations. On the other hand, its efficiency is better than the polynomial approximations and is similar to the rational Chebyshev approximation. In particular, for fast reactor depletion calculations, it is faster than the polynomial approximations by a factor of ∼ 1.7. (author). 11 refs., 4 figs., 2 tabs

  12. Thermal calculation for hydrocarbon vapor condensers by the Gloyer method. Its extrapolation to heat transfer calculation of two phase streams

    International Nuclear Information System (INIS)

    Grange, A.; Jamin, B.

    1974-01-01

    The report resumes the calculation basia given by Walter Gloyer in his different papers and adds certain improvements acquired by long experience in thermal calculation engineering. The following points, necessary for the calculations, are examined in detail: verification of the thermal balances; calculation of the average temperature difference between the vapour and liquid, taking into account the efficiency of the exchanger; pressure loss of the phase stream; calculation of the various thermal resistances; calculation of the exchange surface. The basis of calculation being thus defined, a numerical application of the cooler calculation for hydrocarbon vapour + liquid mixtures with partial condensation is treated and enables the general use of this method to be considered for transfer problems in two-phase streams [fr

  13. Real-space, mean-field algorithm to numerically calculate long-range interactions

    Science.gov (United States)

    Cadilhe, A.; Costa, B. V.

    2016-02-01

    Long-range interactions are known to be of difficult treatment in statistical mechanics models. There are some approaches that introduce a cutoff in the interactions or make use of reaction field approaches. However, those treatments suffer the illness of being of limited use, in particular close to phase transitions. The use of open boundary conditions allows the sum of the long-range interactions over the entire system to be done, however, this approach demands a sum over all degrees of freedom in the system, which makes a numerical treatment prohibitive. Techniques like the Ewald summation or fast multipole expansion account for the exact interactions but are still limited to a few thousands of particles. In this paper we introduce a novel mean-field approach to treat long-range interactions. The method is based in the division of the system in cells. In the inner cell, that contains the particle in sight, the 'local' interactions are computed exactly, the 'far' contributions are then computed as the average over the particles inside a given cell with the particle in sight for each of the remaining cells. Using this approach, the large and small cells limits are exact. At a fixed cell size, the method also becomes exact in the limit of large lattices. We have applied the procedure to the two-dimensional anisotropic dipolar Heisenberg model. A detailed comparison between our method, the exact calculation and the cutoff radius approximation were done. Our results show that the cutoff-cell approach outperforms any cutoff radius approach as it maintains the long-range memory present in these interactions, contrary to the cutoff radius approximation. Besides that, we calculated the critical temperature and the critical behavior of the specific heat of the anisotropic Heisenberg model using our method. The results are in excellent agreement with extensive Monte Carlo simulations using Ewald summation.

  14. Assessing numerical methods for molecular and particle simulation.

    Science.gov (United States)

    Shang, Xiaocheng; Kröger, Martin; Leimkuhler, Benedict

    2017-11-22

    We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss the characteristics of different algorithms, including their essential conservation properties, the convergence of averages, and the accuracy of numerical discretizations. Formulations of the equations of motion which are suited to both equilibrium and nonequilibrium simulation include Langevin dynamics, dissipative particle dynamics (DPD), and the more recently proposed "pairwise adaptive Langevin" (PAdL) method, which, like DPD but unlike Langevin dynamics, conserves momentum and better matches the relaxation rate of orientational degrees of freedom. PAdL is easy to code and suitable for a variety of problems in nonequilibrium soft matter modeling; our simulations of polymer melts indicate that this method can also provide dramatic improvements in computational efficiency. Moreover we show that PAdL gives excellent control of the relaxation rate to equilibrium. In the nonequilibrium setting, we further demonstrate that while PAdL allows the recovery of accurate shear viscosities at higher shear rates than are possible using the DPD method at identical timestep, it also outperforms Langevin dynamics in terms of stability and accuracy at higher shear rates.

  15. Research on Displacement Calculation of Dynamometer Card Based on Kaiman Filter and Discrete Numerical Integration

    Directory of Open Access Journals (Sweden)

    Yan Nan

    2017-01-01

    Full Text Available In order to calculate the dynamometer card of oil well using acceleration sensor, the algorithm which combined by Kalman filter and discrete numerical integration is proposed. It can be applied to calculate the displacement and precipitation displacement period of oil well dynamometer card. The Kalman filter not only filters out the noise of the acceleration signal, but also maintains the original shape feature. The accurate precipitation of the displacement period ensures the correctness of displacement. The discrete numerical integration algorithm can make the relative error of displacement measurement less than 1%, which meets the requirement for dynamometer card accuracy. It is suitable for different types of oil wells.

  16. Numerical calculation of hydrodynamic characteristics of tidal currents for submarine excavation engineering in coastal area

    Directory of Open Access Journals (Sweden)

    Jian-hua Li

    2016-04-01

    Full Text Available In coastal areas with complicated flow movement, deposition and scour readily occur in submarine excavation projects. In this study, a small-scale model, with a high resolution in the vertical direction, was used to simulate the tidal current around a submarine excavation project. The finite volume method was used to solve Navier-Stokes equations and the Reynolds stress transport equation, and the entire process of the tidal current was simulated with unstructured meshes, generated in the irregular shape area, and structured meshes, generated in other water areas. The meshes near the bottom and free surface were densified with a minimum layer thickness of 0.05 m. The volume of fluid method was used to track the free surface, the volume fraction of cells on the upstream boundary was obtained from the volume fraction of adjacent cells, and that on the downstream boundary was determined by the water level process. The numerical results agree with the observed data, and some conclusions can be drawn: after the foundation trench excavation, the flow velocity decreases quite a bit through the foundation trench, with reverse flow occurring on the lee slope in the foundation trench; the swirling flow impedes inflow, leading to the occurrence of dammed water above the foundation trench; the turbulent motion is stronger during ebbing than in other tidal stages, the range with the maximum value of turbulent viscosity, occurring on the south side of the foundation trench at maximum ebbing, is greater than those in other tidal stages in a tidal cycle, and the maximum value of Reynolds shear stress occurs on the south side of the foundation trench at maximum ebbing in a tidal cycle. The numerical calculation method shows a strong performance in simulation of the hydrodynamic characteristics of tidal currents in the foundation trench, providing a basis for submarine engineering construction in coastal areas.

  17. Comparison between measured and numerically calculated AC losses in second-generation high temperature superconductor pancake coils

    International Nuclear Information System (INIS)

    Zhao, Y.; Fang, J.; Zhang, W.; Zhao, J.; Sheng, L.

    2011-01-01

    The critical current and alternating current loss of HTS coil are not equal in different parts of HTS coil. AC loss inside the magnet forms a certain distribution which makes the winding loss calculation very complex. The analytical expressions are established based on Kim's model and the Clem model. The AC loss of HTS coil is measured by electrical method at 77 K and numerical calculation model is resolved by Matlab. The theoretical results and measurement data were compared and analyzed. As a high temperature superconductor (HTS) coil is a complex electromagnetic system, the critical current and alternating current loss are not equal in different parts of HTS coil. AC loss inside the magnet forms a certain distribution which makes the winding loss calculation very complex. The analytical expressions are established based on Kim's model and the Clem model. The AC loss of high-temperature superconductor pancake coil is generally obtained from experimental measurements and numerical calculations. The AC loss of high-temperature superconductor pancake coil is measured by electrical method at the temperature of liquid nitrogen. Numerical calculation model, which is set up and resolved by Matlab, was given as the theory equation in this study, where the theoretical results and measurement data were compared and analyzed.

  18. Computational methods in calculating superconducting current problems

    Science.gov (United States)

    Brown, David John, II

    Various computational problems in treating superconducting currents are examined. First, field inversion in spatial Fourier transform space is reviewed to obtain both one-dimensional transport currents flowing down a long thin tape, and a localized two-dimensional current. The problems associated with spatial high-frequency noise, created by finite resolution and experimental equipment, are presented, and resolved with a smooth Gaussian cutoff in spatial frequency space. Convergence of the Green's functions for the one-dimensional transport current densities is discussed, and particular attention is devoted to the negative effects of performing discrete Fourier transforms alone on fields asymptotically dropping like 1/r. Results of imaging simulated current densities are favorably compared to the original distributions after the resulting magnetic fields undergo the imaging procedure. The behavior of high-frequency spatial noise, and the behavior of the fields with a 1/r asymptote in the imaging procedure in our simulations is analyzed, and compared to the treatment of these phenomena in the published literature. Next, we examine calculation of Mathieu and spheroidal wave functions, solutions to the wave equation in elliptical cylindrical and oblate and prolate spheroidal coordinates, respectively. These functions are also solutions to Schrodinger's equations with certain potential wells, and are useful in solving time-varying superconducting problems. The Mathieu functions are Fourier expanded, and the spheroidal functions expanded in associated Legendre polynomials to convert the defining differential equations to recursion relations. The infinite number of linear recursion equations is converted to an infinite matrix, multiplied by a vector of expansion coefficients, thus becoming an eigenvalue problem. The eigenvalue problem is solved with root solvers, and the eigenvector problem is solved using a Jacobi-type iteration method, after preconditioning the

  19. An Implicit Numerical Method for the Simulation of Two-phase Flow

    Energy Technology Data Exchange (ETDEWEB)

    Yoon, Han Young; Lee, Seung-Jun [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Jeong, Jae Jun [Pusan National University, Busan (Korea, Republic of)

    2015-10-15

    An implicit numerical method is presented for the analysis of two-phase flows in PWRs. Numerical stability and efficiency are improved by decoupling energy equations from the pressure equation. All the convection and diffusion terms are calculated implicitly. The proposed numerical method is verified against conceptual two-phase flow problems. An implicit numerical method has been proposed for two-phase calculation where energy equations are decoupled from the pressure equation. Convection and diffusion terms are calculated implicitly. The calculation results are the same for PME-explicit, PM explicit, and PM-implicit. Large time step size has been tested with PM-implicit-c and the results are also the same.

  20. Distributed Sensor Network for meteorological observations and numerical weather Prediction Calculations

    Directory of Open Access Journals (Sweden)

    Á. Vas

    2013-06-01

    Full Text Available The prediction of weather generally means the solution of differential equations on the base of the measured initial conditions where the data of close and distant neighboring points are used for the calculations. It requires the maintenance of expensive weather stations and supercomputers. However, if weather stations are not only capable of measuring but can also communicate with each other, then these smart sensors can also be applied to run forecasting calculations. This applies the highest possible level of parallelization without the collection of measured data into one place. Furthermore, if more nodes are involved, the result becomes more accurate, but the computing power required from one node does not increase. Our Distributed Sensor Network for meteorological sensing and numerical weather Prediction Calculations (DSN-PC can be applied in several different areas where sensing and numerical calculations, even the solution of differential equations, are needed.

  1. Numerical calculation of primary slot leakage inductance of a Single-sided HTS linear induction motor used for linear metro

    Science.gov (United States)

    Li, Dong; Wen, Yinghong; Li, Weili; Fang, Jin; Cao, Junci; Zhang, Xiaochen; Lv, Gang

    2017-03-01

    In the paper, the numerical method calculating asymmetric primary slot leakage inductances of Single-sided High-Temperature Superconducting (HTS) Linear Induction Motor (HTS LIM) is presented. The mathematical and geometric models of three-dimensional nonlinear transient electromagnetic field are established and the boundary conditions are also given. The established model is solved by time-stepping Finite Element Method (FEM). Then, the three-phase asymmetric primary slot leakage inductances under different operation conditions are calculated by using the obtained electromagnetic field distribution. The influences of the special effects such as longitudinal end effects, transversal edge effects, etc. on the primary slot leakage inductance are investigated. The presented numerical method is validated by experiments carried out on a 3.5 kW prototype with copper wires which has the same structures with the HTS LIM.

  2. New Richardson's extrapolation spreadsheet calculator using VBA programming for numerical differentiations

    Science.gov (United States)

    Tay, Kim Gaik; Kek, Sie Long; Abdul-Kahar, Rosmila

    2015-05-01

    In this paper, we have further improved the limitations of our previous two Richardson's extrapolation spreadsheet calculators for computing differentiations numerically. The new feature in this new Richardson's extrapolation spreadsheet calculator is fully automated up to any level based on the stopping criteria using VBA programming. The new version is more flexible because it is controlled by programming. Furthermore, it reduces computational time and CPU memory.

  3. Novel Parallel Numerical Methods for Radiation and Neutron Transport

    International Nuclear Information System (INIS)

    Brown, P N

    2001-01-01

    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

  4. Survey of numerical methods for compressible fluids

    Energy Technology Data Exchange (ETDEWEB)

    Sod, G A

    1977-06-01

    The finite difference methods of Godunov, Hyman, Lax-Wendroff (two-step), MacCormack, Rusanov, the upwind scheme, the hybrid scheme of Harten and Zwas, the antidiffusion method of Boris and Book, and the artificial compression method of Harten are compared with the random choice known as Glimm's method. The methods are used to integrate the one-dimensional equations of gas dynamics for an inviscid fluid. The results are compared and demonstrate that Glimm's method has several advantages. 16 figs., 4 tables.

  5. Numerical Calculation for Whirling Motion of a Centrifugal Blood Pump with Conical Spiral Groove Bearings

    Science.gov (United States)

    Shigemaru, Daichi; Tsukamoto, Hiroshi

    2010-06-01

    Whirling motion of a pump impeller was calculated for the centrifugal blood pump with Conical Spiral Groove Bearings to get a criterion for the instability of impeller whirling motion. The motion of the centrifugal blood pump impeller was calculated based on a spring damping model, and unsteady flow in the pump was computed using the commercial CFD package ANSYS CFX. Also the whirling motion of rotating impeller was measured using two displacement sensors fixed to the blood pump casing. The numerical calculations were done for the blood pump impeller with conical spiral groove bearings, and impeller whirling motion was evaluated.

  6. Quantum dynamic imaging theoretical and numerical methods

    CERN Document Server

    Ivanov, Misha

    2011-01-01

    Studying and using light or "photons" to image and then to control and transmit molecular information is among the most challenging and significant research fields to emerge in recent years. One of the fastest growing areas involves research in the temporal imaging of quantum phenomena, ranging from molecular dynamics in the femto (10-15s) time regime for atomic motion to the atto (10-18s) time scale of electron motion. In fact, the attosecond "revolution" is now recognized as one of the most important recent breakthroughs and innovations in the science of the 21st century. A major participant in the development of ultrafast femto and attosecond temporal imaging of molecular quantum phenomena has been theory and numerical simulation of the nonlinear, non-perturbative response of atoms and molecules to ultrashort laser pulses. Therefore, imaging quantum dynamics is a new frontier of science requiring advanced mathematical approaches for analyzing and solving spatial and temporal multidimensional partial differ...

  7. Numerical methods in Markov chain modeling

    Science.gov (United States)

    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.

  8. A stable numerical solution method in-plane loading of nonlinear viscoelastic laminated orthotropic materials

    Science.gov (United States)

    Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

    1989-01-01

    In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.

  9. Transient voltage stress of 400 kV urban system evaluated by numerical calculations

    Energy Technology Data Exchange (ETDEWEB)

    Pack, S. [Institute for High Voltage Engineering and System Management, Graz University of Technology, 8010 Graz (Austria); Kornhuber, S. [Test Institution for High Voltage Engineering Graz Ltd., 8010 Graz (Austria); Reisinger, F. [NT3 Division of Wienstrom GmbH, 1020 Vienna (Austria)

    2009-03-15

    Overhead lines, high voltage cable systems and substations are important elements of the high voltage network. More and more close combinations of these elements are used in urban networks. This leads to new transient situations and a more complex transient behaviour in case of lightning or switching events. Additionally the requirements of a constant power supply ask for new efforts to predict impacts caused by interruptions. Based on this fact this paper deals with investigations to evaluate the transient behaviour of a close combined 400 kV urban system. Numerical tools are basically a modern method to estimate transient stresses, help to optimize the insulation coordination and can simulate various circuit states. Thus, temporary faults can be reduced or avoided at all. One of the major aspect of this work is the close connection of an overhead line, a cable section and a substation related to the 400 kV system. Additionally attention was paid to the transformers and the secondary side of the system, a 110-kV urban distribution network. A number of calculations were carried out to get an overview of the transient stress caused by lightning or switching in numerous network nodes of the substation. Of additional interest have been different circuit states at the 400 kV gas insulated substations (GIS) and the transient behaviour at the arrestors. Amplitudes and the energy consumption at the arrestors were taken into account. These actual investigations were carried out to get useful information's about the transient stress in this important Viennese 400 kV substation, which was officially put into operation in May 2006. As an output of these investigations the results influence the strategy in running the network. (author)

  10. Numerical methods for coupled fracture problems

    Science.gov (United States)

    Viesca, Robert C.; Garagash, Dmitry I.

    2018-04-01

    We consider numerical solutions in which the linear elastic response to an opening- or sliding-mode fracture couples with one or more processes. Classic examples of such problems include traction-free cracks leading to stress singularities or cracks with cohesive-zone strength requirements leading to non-singular stress distributions. These classical problems have characteristic square-root asymptotic behavior for stress, relative displacement, or their derivatives. Prior work has shown that such asymptotics lead to a natural quadrature of the singular integrals at roots of Chebyhsev polynomials of the first, second, third, or fourth kind. We show that such quadratures lead to convenient techniques for interpolation, differentiation, and integration, with the potential for spectral accuracy. We further show that these techniques, with slight amendment, may continue to be used for non-classical problems which lack the classical asymptotic behavior. We consider solutions to example problems of both the classical and non-classical variety (e.g., fluid-driven opening-mode fracture and fault shear rupture driven by thermal weakening), with comparisons to analytical solutions or asymptotes, where available.

  11. Numerical method for two-dimensional unsteady reacting flows

    International Nuclear Information System (INIS)

    Butler, T.D.; O'Rourke, P.J.

    1976-01-01

    A method that numerically solves the full two-dimensional, time-dependent Navier-Stokes equations with species transport, mixing, and chemical reaction between species is presented. The generality of the formulation permits the solution of flows in which deflagrations, detonations, or transitions from deflagration to detonation are found. The solution procedure is embodied in the RICE computer program. RICE is an Eulerian finite difference computer code that uses the Implicit Continuous-fluid Eulerian (ICE) technique to solve the governing equations. One first presents the differential equations of motion and the solution procedure of the Rice program. Next, a method is described for artificially thickening the combustion zone to dimensions resolvable by the computational mesh. This is done in such a way that the physical flame speed and jump conditions across the flame front are preserved. Finally, the results of two example calculations are presented. In the first, the artificial thickening technique is used to solve a one-dimensional laminar flame problem. In the second, the results of a full two-dimensional calculation of unsteady combustion in two connected chambers are detailed

  12. Hamiltonian lattice field theory: Computer calculations using variational methods

    International Nuclear Information System (INIS)

    Zako, R.L.

    1991-01-01

    I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. I show how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems

  13. Hamiltonian lattice field theory: Computer calculations using variational methods

    International Nuclear Information System (INIS)

    Zako, R.L.

    1991-01-01

    A variational method is developed for systematic numerical computation of physical quantities-bound state energies and scattering amplitudes-in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. An algorithm is presented for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. It is shown how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. It is shown how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. The author discusses the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, the author does not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. The method is applied to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. The author describes a computer implementation of the method and present numerical results for simple quantum mechanical systems

  14. A boundary integral equation method for the calculation of the effective permittivity of periodic composites

    OpenAIRE

    Sareni , Bruno; Krähenbühl , Laurent; Beroual , Abderrahmane; Nicolas , Alain; Brosseau , C.

    1997-01-01

    We present a numerical method based upon the resolution of boundary integral equations for the calculation of the effective permittivity of a lossless composite structure consisting of a two component mixture, each with its own dielectric anti shape characteristics. The topological arrangements considered are periodic lattices inhomogeneities. Our numerical simulations are compared to the effective medium approach and with results of previous works.

  15. Numerical path integration technique for the calculation of transport properties of proteins.

    Science.gov (United States)

    Kang, Eun-Hee; Mansfield, Marc L; Douglas, Jack F

    2004-03-01

    We present a new technique for the computation of both the translational diffusivity and the intrinsic viscosity of macromolecules, and apply it here to proteins. Traditional techniques employ finite element representations of the surface of the macromolecule, taking the surface to be a union of spheres or of polygons, and have computation times that are O(m(3)) where m is the number of finite elements. The new technique, a numerical path integration method, has computation times that are only O(m). We have applied the technique to approximately 1000 different protein structures. The computed translational diffusivities and intrinsic viscosities are, to lowest order, proportional respectively to N(-1/3)(R) and N(0)(R), where N(R) is the number of amino acid residues in the protein. Our calculations also show some correlation with the shape of the molecule, as represented by the ratio m(2)/m(3), where m(2) and m(3) are, respectively, the middle and the smallest of the three principal moments of inertia. Comparisons with a number of experimental results are also performed, with results generally consistent to within experimental error.

  16. Numerical Calculation and Exergy Equations of Spray Heat Exchanger Attached to a Main Fan Diffuser

    Science.gov (United States)

    Cui, H.; Wang, H.; Chen, S.

    2015-04-01

    In the present study, the energy depreciation rule of spray heat exchanger, which is attached to a main fan diffuser, is analyzed based on the second law of thermodynamics. Firstly, the exergy equations of the exchanger are deduced. The equations are numerically calculated by the fourth-order Runge-Kutta method, and the exergy destruction is quantitatively effected by the exchanger structure parameters, working fluid (polluted air, i.e., PA; sprayed water, i.e., SW) initial state parameters and the ambient reference parameters. The results are showed: (1) heat transfer is given priority to latent transfer at the bottom of the exchanger, and heat transfer of convection and is equivalent to that of condensation in the upper. (2) With the decrease of initial temperature of SW droplet, the decrease of PA velocity or the ambient reference temperature, and with the increase of a SW droplet size or initial PA temperature, exergy destruction both increase. (3) The exergy efficiency of the exchanger is 72.1 %. An approach to analyze the energy potential of the exchanger may be provided for engineering designs.

  17. Nonlinear ordinary differential equations analytical approximation and numerical methods

    CERN Document Server

    Hermann, Martin

    2016-01-01

    The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

  18. Deconstructing Calculation Methods, Part 3: Multiplication

    Science.gov (United States)

    Thompson, Ian

    2008-01-01

    In this third of a series of four articles, the author deconstructs the primary national strategy's approach to written multiplication. The approach to multiplication, as set out on pages 12 to 15 of the primary national strategy's "Guidance paper" "Calculation" (DfES, 2007), is divided into six stages: (1) mental…

  19. Development of CAD implementing the algorithm of boundary elements’ numerical analytical method

    Directory of Open Access Journals (Sweden)

    Yulia V. Korniyenko

    2015-03-01

    Full Text Available Up to recent days the algorithms for numerical-analytical boundary elements method had been implemented with programs written in MATLAB environment language. Each program had a local character, i.e. used to solve a particular problem: calculation of beam, frame, arch, etc. Constructing matrices in these programs was carried out “manually” therefore being time-consuming. The research was purposed onto a reasoned choice of programming language for new CAD development, allows to implement algorithm of numerical analytical boundary elements method and to create visualization tools for initial objects and calculation results. Research conducted shows that among wide variety of programming languages the most efficient one for CAD development, employing the numerical analytical boundary elements method algorithm, is the Java language. This language provides tools not only for development of calculating CAD part, but also to build the graphic interface for geometrical models construction and calculated results interpretation.

  20. Modelling asteroid brightness variations. I - Numerical methods

    Science.gov (United States)

    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.

  1. Numerical Methods Using B-Splines

    Science.gov (United States)

    Shariff, Karim; Merriam, Marshal (Technical Monitor)

    1997-01-01

    The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.

  2. Numerical methods for stochastic partial differential equations with white noise

    CERN Document Server

    Zhang, Zhongqiang

    2017-01-01

    This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...

  3. Fast Numerical Methods for Stochastic Partial Differential Equations

    Science.gov (United States)

    2016-04-15

    applicable SPDES with efficient numerical methods . This project is intended to address the numerical analysis as well as algorithm aspects of SPDES. Three...no. 1, 784–804. 10. Cao, Yanzhao; Wang, Peng; Wang, Xiaoshen Homotopy continuation methods for stochastic two-point boundary value problems driven by...convergence analysis of Quasi Monte Carlo based Particle Swarm Optimization (PSO) method ; ii) Efficient adaptive domain sparse grid method for SPDES; iii

  4. Numerical simulation of GEW equation using RBF collocation method

    Directory of Open Access Journals (Sweden)

    Hamid Panahipour

    2012-08-01

    Full Text Available The generalized equal width (GEW equation is solved numerically by a meshless method based on a global collocation with standard types of radial basis functions (RBFs. Test problems including propagation of single solitons, interaction of two and three solitons, development of the Maxwellian initial condition pulses, wave undulation and wave generation are used to indicate the efficiency and accuracy of the method. Comparisons are made between the results of the proposed method and some other published numerical methods.

  5. Numerical calculation of flashing from long pipes using a two-field model

    International Nuclear Information System (INIS)

    Rivard, W.C.; Torrey, M.D.

    1976-05-01

    A two-field model for two-phase flows, in which the vapor and liquid phases have different densities, velocities, and temperatures, has been used to calculate the flashing of water from long pipes. The IMF (Implicit Multifield) technique is used to numerically solve the transient equations that govern the dynamics of each phase. The flow physics is described with finite rate phase transitions, interfacial friction, heat transfer, pipe wall friction, and appropriate state equations. The results of the calculations are compared with measured histories of pressure, temperature, and void fraction. A parameter study indicates the relative sensitivity of the results to the various physical models that are used

  6. Numerical methods for hypersonic boundary layer stability

    Science.gov (United States)

    Malik, M. R.

    1990-01-01

    Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.

  7. Method for consequence calculations for severe accidents

    International Nuclear Information System (INIS)

    Nielsen, F.

    1988-01-01

    This report was commissioned by the Swedish State Power Board. The report contains a calculation of radiation doses in the surroundings caused by a theoretical core meltdown accident at Ringhals reactor No 3/4. The accident sequence chosen for the calcualtions was a release caused by total power failure. The calculations were made by means of the PLUCON4 code. A decontamination factor of 500 is used to account for the scrubber effect. Meteorological data for two years from the Ringhals meteorological tower were analysed to find representative weather situations. As typical weather, Pasquill D, was chosen with a wind speed of 10 m/s, and as extreme weather, Pasquill E, with a wind speed of 2 m/s. 19 refs. (author)

  8. First-Principles Calculation of Spin Transport in Magnetic Nanowire Using Green's Function Method with Localized Basis Set

    National Research Council Canada - National Science Library

    Kobayashi, Nobuhiko; Ozaki, Taisuke; Hirose, Kenji

    2006-01-01

    .... The electronic states are calculated using a numerical pseudo atomic orbital basis set in the frame work of the density functional theory, and the conductance is calculated using the Green's function method...

  9. COSTS CALCULATION OF TARGET COSTING METHOD

    OpenAIRE

    Sebastian UNGUREANU

    2014-01-01

    Cost information system plays an important role in every organization in the decision making process. An important task of management is ensuring control of the operations, processes, sectors, and not ultimately on costs. Although in achieving the objectives of an organization compete more control systems (production control, quality control, etc.), the cost information system is important because monitors results of the other. Detailed analysis of costs, production cost calculation, quantifi...

  10. Numerical Methods for Bayesian Inverse Problems

    KAUST Repository

    Ernst, Oliver

    2014-01-06

    We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.

  11. Quadratic String Method for Locating Instantons in Tunneling Splitting Calculations.

    Science.gov (United States)

    Cvitaš, Marko T

    2018-03-13

    The ring-polymer instanton (RPI) method is an efficient technique for calculating approximate tunneling splittings in high-dimensional molecular systems. In the RPI method, tunneling splitting is evaluated from the properties of the minimum action path (MAP) connecting the symmetric wells, whereby the extensive sampling of the full potential energy surface of the exact quantum-dynamics methods is avoided. Nevertheless, the search for the MAP is usually the most time-consuming step in the standard numerical procedures. Recently, nudged elastic band (NEB) and string methods, originaly developed for locating minimum energy paths (MEPs), were adapted for the purpose of MAP finding with great efficiency gains [ J. Chem. Theory Comput. 2016 , 12 , 787 ]. In this work, we develop a new quadratic string method for locating instantons. The Euclidean action is minimized by propagating the initial guess (a path connecting two wells) over the quadratic potential energy surface approximated by means of updated Hessians. This allows the algorithm to take many minimization steps between the potential/gradient calls with further reductions in the computational effort, exploiting the smoothness of potential energy surface. The approach is general, as it uses Cartesian coordinates, and widely applicable, with computational effort of finding the instanton usually lower than that of determining the MEP. It can be combined with expensive potential energy surfaces or on-the-fly electronic-structure methods to explore a wide variety of molecular systems.

  12. Soil structure interaction calculations: a comparison of methods

    International Nuclear Information System (INIS)

    Wight, L.; Zaslawsky, M.

    1976-01-01

    Two approaches for calculating soil structure interaction (SSI) are compared: finite element and lumped mass. Results indicate that the calculations with the lumped mass method are generally conservative compared to those obtained by the finite element method. They also suggest that a closer agreement between the two sets of calculations is possible, depending on the use of frequency-dependent soil springs and dashpots in the lumped mass calculations. There is a total lack of suitable guidelines for implementing the lumped mass method of calculating SSI, which leads to the conclusion that the finite element method is generally superior for calculative purposes

  13. Advanced Computational Methods for Monte Carlo Calculations

    Energy Technology Data Exchange (ETDEWEB)

    Brown, Forrest B. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2018-01-12

    This course is intended for graduate students who already have a basic understanding of Monte Carlo methods. It focuses on advanced topics that may be needed for thesis research, for developing new state-of-the-art methods, or for working with modern production Monte Carlo codes.

  14. The ion exchange and its connection the industry II.- Calculation methods for installations

    International Nuclear Information System (INIS)

    Uriarte Hueda, A.; Lopez Perez, B.; Gutierrez Jodra, L.

    1960-01-01

    An exposure is made of calculation methods for ion exchange installations based on kinetic considerations and similarity with other unitary operations. Factors to be experimentally obtained as well as difficulties which may occur in its determination are also given. Calculation procedures most commonly used in industry are enclosed and explained with numerical resolution of a problem of water demineralization. (Author) 22 refs

  15. Time domain numerical calculations of the short electron bunch wakefields in resistive structures

    International Nuclear Information System (INIS)

    Tsakanian, Andranik

    2010-10-01

    The acceleration of electron bunches with very small longitudinal and transverse phase space volume is one of the most actual challenges for the future International Linear Collider and high brightness X-Ray Free Electron Lasers. The exact knowledge on the wake fields generated by the ultra-short electron bunches during its interaction with surrounding structures is a very important issue to prevent the beam quality degradation and to optimize the facility performance. The high accuracy time domain numerical calculations play the decisive role in correct evaluation of the wake fields in advanced accelerators. The thesis is devoted to the development of a new longitudinally dispersion-free 3D hybrid numerical scheme in time domain for wake field calculation of ultra short bunches in structures with walls of finite conductivity. The basic approaches used in the thesis to solve the problem are the following. For materials with high but finite conductivity the model of the plane wave reflection from a conducting half-space is used. It is shown that in the conductive half-space the field components perpendicular to the interface can be neglected. The electric tangential component on the surface contributes to the tangential magnetic field in the lossless area just before the boundary layer. For high conducting media, the task is reduced to 1D electromagnetic problem in metal and the so-called 1D conducting line model can be applied instead of a full 3D space description. Further, a TE/TM (''transverse electric - transverse magnetic'') splitting implicit numerical scheme along with 1D conducting line model is applied to develop a new longitudinally dispersion-free hybrid numerical scheme in the time domain. The stability of the new hybrid numerical scheme in vacuum, conductor and bound cell is studied. The convergence of the new scheme is analyzed by comparison with the well-known analytical solutions. The wakefield calculations for a number of structures are performed

  16. Time domain numerical calculations of the short electron bunch wakefields in resistive structures

    Energy Technology Data Exchange (ETDEWEB)

    Tsakanian, Andranik

    2010-10-15

    The acceleration of electron bunches with very small longitudinal and transverse phase space volume is one of the most actual challenges for the future International Linear Collider and high brightness X-Ray Free Electron Lasers. The exact knowledge on the wake fields generated by the ultra-short electron bunches during its interaction with surrounding structures is a very important issue to prevent the beam quality degradation and to optimize the facility performance. The high accuracy time domain numerical calculations play the decisive role in correct evaluation of the wake fields in advanced accelerators. The thesis is devoted to the development of a new longitudinally dispersion-free 3D hybrid numerical scheme in time domain for wake field calculation of ultra short bunches in structures with walls of finite conductivity. The basic approaches used in the thesis to solve the problem are the following. For materials with high but finite conductivity the model of the plane wave reflection from a conducting half-space is used. It is shown that in the conductive half-space the field components perpendicular to the interface can be neglected. The electric tangential component on the surface contributes to the tangential magnetic field in the lossless area just before the boundary layer. For high conducting media, the task is reduced to 1D electromagnetic problem in metal and the so-called 1D conducting line model can be applied instead of a full 3D space description. Further, a TE/TM (''transverse electric - transverse magnetic'') splitting implicit numerical scheme along with 1D conducting line model is applied to develop a new longitudinally dispersion-free hybrid numerical scheme in the time domain. The stability of the new hybrid numerical scheme in vacuum, conductor and bound cell is studied. The convergence of the new scheme is analyzed by comparison with the well-known analytical solutions. The wakefield calculations for a number of

  17. COSTS CALCULATION OF TARGET COSTING METHOD

    Directory of Open Access Journals (Sweden)

    Sebastian UNGUREANU

    2014-06-01

    Full Text Available Cost information system plays an important role in every organization in the decision making process. An important task of management is ensuring control of the operations, processes, sectors, and not ultimately on costs. Although in achieving the objectives of an organization compete more control systems (production control, quality control, etc., the cost information system is important because monitors results of the other. Detailed analysis of costs, production cost calculation, quantification of losses, estimate the work efficiency provides a solid basis for financial control. Knowledge of the costs is a decisive factor in taking decisions and planning future activities. Managers are concerned about the costs that will appear in the future, their level underpinning the supply and production decisions as well as price policy. An important factor is the efficiency of cost information system in such a way that the information provided by it may be useful for decisions and planning of the work.

  18. A New subgroup method for resonance calculation

    International Nuclear Information System (INIS)

    Milosevic, M.

    1997-01-01

    In the current work, a generalization of the subgroup resonance treatment was derived to account for the space and energy dependence of the resonant absorption inside the fuel rod of a heterogenous lattice. This paper describes the basic principles and algorithms used in the proposed subgroup method. The method is validated for interference effects in a homogenous uranium-plutonium mixture, and for spatial resonance interference in a realistic fuel dissolver benchmark problem. (author)

  19. Numerical implementation of the loop-tree duality method

    Energy Technology Data Exchange (ETDEWEB)

    Buchta, Sebastian; Rodrigo, German [Universitat de Valencia-Consejo Superior de Investigaciones Cientificas, Parc Cientific, Instituto de Fisica Corpuscular, Valencia (Spain); Chachamis, Grigorios [Universidad Autonoma de Madrid, Instituto de Fisica Teorica UAM/CSIC, Madrid (Spain); Draggiotis, Petros [Institute of Nuclear and Particle Physics, NCSR ' ' Demokritos' ' , Agia Paraskevi (Greece)

    2017-05-15

    We present a first numerical implementation of the loop-tree duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable contour deformation in the loop three-momentum space to carry out the numerical integration. Then we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and we present explicit results for scalar and tensor integrals with up to eight external legs (octagons). The LTD method features an excellent performance independently of the number of external legs. (orig.)

  20. Fast Numerical Evaluation of Time-Derivative Nonadiabatic Couplings for Mixed Quantum-Classical Methods.

    Science.gov (United States)

    Ryabinkin, Ilya G; Nagesh, Jayashree; Izmaylov, Artur F

    2015-11-05

    We have developed a numerical differentiation scheme that eliminates evaluation of overlap determinants in calculating the time-derivative nonadiabatic couplings (TDNACs). Evaluation of these determinants was the bottleneck in previous implementations of mixed quantum-classical methods using numerical differentiation of electronic wave functions in the Slater determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals and then to apply a finite-difference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive several-order-of-magnitude speedups of the TDNAC calculation step for midsize molecules.

  1. Méthode numérique de calcul du mouvement d'un corps flottant soumis à l'influence d'une houle périodique en théorie linéaire Numerical Method for Calculating the Movement of a Floating Body Subjected to the Influence of Theoretically Linear Wave Action

    Directory of Open Access Journals (Sweden)

    Chenot J. -L.

    2006-11-01

    optimal quadratic-mean type cran also be used to connect the potential. The formulation adopted enables all the advantages of finiteelement methods to be maintained. Hence it is particularly well adopted for compiling a numerical model [6].

  2. Hybrid Monte-Carlo method for ICF calculations

    Energy Technology Data Exchange (ETDEWEB)

    Clouet, J.F.; Samba, G. [CEA Bruyeres-le-Chatel, 91 (France)

    2003-07-01

    ) conduction and ray-tracing for laser description. Radiation transport is usually solved by a Monte-Carlo method. In coupling diffusion approximation and transport description, the difficult part comes from the need for an implicit discretization of the emission-absorption terms: this problem was solved by using the symbolic Monte-Carlo method. This means that at each step of the simulation a matrix is computed by a Monte-Carlo method which accounts for the radiation energy exchange between the cells. Because of time step limitation by hydrodynamic motion, energy exchange is limited to a small number of cells and the matrix remains sparse. This matrix is added to usual diffusion matrix for thermal and radiative conductions: finally we arrive at a non-symmetric linear system to invert. A generalized Marshak condition describe the coupling between transport and diffusion. In this paper we will present the principles of the method and numerical simulation of an ICF hohlraum. We shall illustrate the benefits of the method by comparing the results with full implicit Monte-Carlo calculations. In particular we shall show how the spectral cut-off evolves during the propagation of the radiative front in the gold wall. Several issues are still to be addressed (robust algorithm for spectral cut- off calculation, coupling with ALE capabilities): we shall briefly discuss these problems. (authors)

  3. Hybrid Monte-Carlo method for ICF calculations

    International Nuclear Information System (INIS)

    Clouet, J.F.; Samba, G.

    2003-01-01

    ) conduction and ray-tracing for laser description. Radiation transport is usually solved by a Monte-Carlo method. In coupling diffusion approximation and transport description, the difficult part comes from the need for an implicit discretization of the emission-absorption terms: this problem was solved by using the symbolic Monte-Carlo method. This means that at each step of the simulation a matrix is computed by a Monte-Carlo method which accounts for the radiation energy exchange between the cells. Because of time step limitation by hydrodynamic motion, energy exchange is limited to a small number of cells and the matrix remains sparse. This matrix is added to usual diffusion matrix for thermal and radiative conductions: finally we arrive at a non-symmetric linear system to invert. A generalized Marshak condition describe the coupling between transport and diffusion. In this paper we will present the principles of the method and numerical simulation of an ICF hohlraum. We shall illustrate the benefits of the method by comparing the results with full implicit Monte-Carlo calculations. In particular we shall show how the spectral cut-off evolves during the propagation of the radiative front in the gold wall. Several issues are still to be addressed (robust algorithm for spectral cut- off calculation, coupling with ALE capabilities): we shall briefly discuss these problems. (authors)

  4. To the development of numerical methods in problems of radiation transport

    International Nuclear Information System (INIS)

    Germogenova, T.A.

    1990-01-01

    Review of studies on the development of numerical methods and the discrete ordinate method in particular, used for solution of radiation protection physics problems is given. Consideration is given to the problems, which arise when calculating fields of penetrating radiation and when studying processes of charged-particle transport and cascade processes, generated by high-energy primary radiation

  5. Classical and modern numerical analysis theory, methods and practice

    CERN Document Server

    Ackleh, Azmy S; Kearfott, R Baker; Seshaiyer, Padmanabhan

    2009-01-01

    Mathematical Review and Computer Arithmetic Mathematical Review Computer Arithmetic Interval ComputationsNumerical Solution of Nonlinear Equations of One Variable Introduction Bisection Method The Fixed Point Method Newton's Method (Newton-Raphson Method) The Univariate Interval Newton MethodSecant Method and Müller's Method Aitken Acceleration and Steffensen's Method Roots of Polynomials Additional Notes and SummaryNumerical Linear Algebra Basic Results from Linear Algebra Normed Linear Spaces Direct Methods for Solving Linear SystemsIterative Methods for Solving Linear SystemsThe Singular Value DecompositionApproximation TheoryIntroduction Norms, Projections, Inner Product Spaces, and Orthogonalization in Function SpacesPolynomial ApproximationPiecewise Polynomial ApproximationTrigonometric ApproximationRational ApproximationWavelet BasesLeast Squares Approximation on a Finite Point SetEigenvalue-Eigenvector Computation Basic Results from Linear Algebra The Power Method The Inverse Power Method Deflation T...

  6. Numerical solution of DGLAP equations using Laguerre polynomials expansion and Monte Carlo method.

    Science.gov (United States)

    Ghasempour Nesheli, A; Mirjalili, A; Yazdanpanah, M M

    2016-01-01

    We investigate the numerical solutions of the DGLAP evolution equations at the LO and NLO approximations, using the Laguerre polynomials expansion. The theoretical framework is based on Furmanski et al.'s articles. What makes the content of this paper different from other works, is that all calculations in the whole stages to extract the evolved parton distributions, are done numerically. The employed techniques to do the numerical solutions, based on Monte Carlo method, has this feature that all the results are obtained in a proper wall clock time by computer. The algorithms are implemented in FORTRAN and the employed coding ideas can be used in other numerical computations as well. Our results for the evolved parton densities are in good agreement with some phenomenological models. They also indicate better behavior with respect to the results of similar numerical calculations.

  7. Numerical calculation and experimental validation of safety valve flows at pressures up to 600 bar

    NARCIS (Netherlands)

    Beune, A.; Kuerten, Johannes G.M.; Schmidt, J.

    2011-01-01

    A numerical valve model has been validated to predict the discharge capacity in accordance to the requirements of valve sizing method EN ISO 4126-1 and the opening characteristic of high-pressure safety valves. The valve is modeled with computational fluid dynamics software ANSYS CFX, and the model

  8. Efficient Numerical Methods for Nonequilibrium Re-Entry Flows

    Science.gov (United States)

    2014-01-14

    numerical fluxes is to use a modified form of Steger -Warming flux-vector splitting.16 It should be noted that although we focus on this particular...numerical flux function, the approach is extensible to other upwind-biased flux methods. The modified Steger -Warming flux is based on the fact that the...1ΛX (8) where Λ is the diagonal eigenvalue matrix. The modified Steger -Warming flux-vector splitting method obtains the direction of the fluxes by

  9. General method for calculation of hydrogen-ion concentration in multicomponent acid-base mixtures.

    Science.gov (United States)

    Ventura, D A; Ando, H Y

    1980-08-01

    A generalized method for the rapid evaluation of complicated ionic equilibria in terms of the hydrogen-ion concentration was developed. The method was based on the derivation of a single general equation that could be used to evaluate any mixture. A tableau method also was developed which allowed calculation of the numerical solution to the general equation without computer analysis or graphical or intuitive approximations. Examples illustrating the utility of the method are presented. These examples include a mixture of barbital, citric acid, boric acid, monobasic sodium phosphate, and sodium hydroxide. Calculated hydrogen-ion concentrations showed good agreement with experimental values for simple and complex solutions. The major advantages of the method are its simplicity and the obtainment of numerical solutions without initial approximations in the calculations. However, activity corrections are not included in the calculations.

  10. Calculation-experimental method justifies the life of wagons

    Directory of Open Access Journals (Sweden)

    Валерія Сергіївна Воропай

    2015-11-01

    Full Text Available The article proposed a method to evaluate the technical state of tank wagons operating in chemical industry. An algorithm for evaluation the technical state of tank wagons was developed, that makes it possible on the basis of diagnosis and analysis of current condition to justify a further period of operation. The complex of works on testing the tanks and mathematical models for calculations of the design strength and reliability were proposed. The article is devoted to solving the problem of effective exploitation of the working fleet of tank wagons. Opportunities for further exploitation of cars, the complex of works on the assessment of their technical state and the calculation of the resources have been proposed in the article. Engineering research of the chemical industries park has reduced the shortage of the rolling stock for transportation of ammonia. The analysis of the chassis numerous faults and the main elements of tank wagons supporting structure after 20 years of exploitation was made. The algorithm of determining the residual life of the specialized tank wagons operating in an industrial plant has been proposed. The procedure for resource conservation of tank wagons carrying cargo under high pressure was first proposed. The improved procedure for identifying residual life proposed in the article has both theoretical and practical importance

  11. Numerical and adaptive grid methods for ideal magnetohydrodynamics

    Science.gov (United States)

    Loring, Burlen

    2008-02-01

    In this thesis numerical finite difference methods for ideal magnetohydrodynamics(MHD) are investigated. A review of the relevant physics, essential for interpreting the results of numerical solutions and constructing validation cases, is presented. This review includes a discusion of the propagation of small amplitude waves in the MHD system as well as a thorough discussion of MHD shocks, contacts and rarefactions and how they can be piece together to obtain a solutions to the MHD Riemann problem. Numerical issues relevant to the MHD system such as: the loss of nonlinear numerical stability in the presence of discontinuous solutions, the introduction of spurious forces due to the growth of the divergence of the magnetic flux density, the loss of pressure positivity, and the effects of non-conservative numerical methods are discussed, along with the practical approaches which can be used to remedy or minimize the negative consequences of each. The use of block structured adaptive mesh refinement is investigated in the context of a divergence free MHD code. A new method for conserving magnetic flux across AMR grid interfaces is developed and a detailed discussion of our implementation of this method using the CHOMBO AMR framework is given. A preliminary validation of the new method for conserving magnetic flux density across AMR grid interfaces illustrates that the method works. Finally a number of code validation cases are examined spurring a discussion of the strengths and weaknesses of the numerics employed.

  12. Methods of Calculation of Digital Signals Spectra

    Directory of Open Access Journals (Sweden)

    Gustav Cepciansky

    2011-01-01

    Full Text Available Modern telecommunication networks work on the transmission method of common data streams in which data bursts consisting of packets that further consist of particular bits are multiplexed from various traffic sources. The larger amount of data is transmitted through a transmission medium (optical fibre, the more frequently bursts occur, and the lower amount of data, the more rarely they follow. If it is required to monitor how large amount of data is being transmitted in a network branch in order to find out, to which measure this branch is occupied, it is not necessary to take each information unit (each packet or even each particular bit. It will do if information whether a data burst occurs in the transmission or does it not occur is taken in certain time intervals – with a certain sampling frequency. The paper deals with these sampling intervals.

  13. Molecular dynamics with deterministic and stochastic numerical methods

    CERN Document Server

    Leimkuhler, Ben

    2015-01-01

    This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications.  Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method...

  14. On the numerical stability analysis of pipelined Krylov subspace methods

    Czech Academy of Sciences Publication Activity Database

    Carson, E.T.; Rozložník, Miroslav; Strakoš, Z.; Tichý, P.; Tůma, M.

    submitted 2017 (2018) R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : Krylov subspace methods * the conjugate gradient method * numerical stability * inexact computations * delay of convergence * maximal attainable accuracy * pipelined Krylov subspace methods * exascale computations

  15. Two numerical methods for mean-field games

    KAUST Repository

    Gomes, Diogo A.

    2016-01-09

    Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.

  16. Numerical Calculation of the Correlation Moments of the Sound Field Scattered by a Rough Surface

    Science.gov (United States)

    Baranov, V. F.; Gulin, É. P.

    2000-05-01

    Numerically calculated two-dimensional correlation moments of the surface-scattered sound field are presented in the form of correlation surfaces and analyzed. The models of three-dimensional anisotropic and two-dimensional quasi-harmonic surface waves are considered. Data are presented on the angular dependence of the space-time correlation domains of the scattered sound field for receivers spaced across the propagation path in both horizontal and vertical directions, as well as on the shapes of the time-frequency and space-frequency correlation domains.

  17. Stochastic numerical methods an introduction for students and scientists

    CERN Document Server

    Toral, Raul

    2014-01-01

    Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability ConceptsMonte Carlo IntegrationGeneration of Uniform and Non-uniformRandom Numbers: Non-correlated ValuesDynamical MethodsApplications to Statistical MechanicsIn...

  18. A numerical method for predicting Rayleigh surface wave velocity in anisotropic crystals

    Science.gov (United States)

    Cherry, Matthew R.; Sathish, Shamachary; Grandhi, Ramana

    2017-12-01

    A numerical method was developed for calculating the Rayleigh Surface Wave (RSW) velocity in arbitrarily oriented single crystals in 360 degrees of propagation. This method relies on the results from modern analysis of RSW behavior with the Stroh formalism to restrict the domain in which to search for velocities by first calculating the limiting velocity. This extension of existing numerical methods also leads to a natural way of determining both the existence of the RSW as well as the possibility of encountering a pseudo-surface wave. Furthermore, the algorithm is applied to the calculation of elastic properties from measurement of the surface wave velocity in multiple different directions on a single crystal sample. The algorithm was tested with crystal symmetries and single crystal elastic moduli from literature. It was found to be very robust and efficient in calculating RSW velocity curves in all cases.

  19. Comparison between Two Methods to Calculate the Transition Matrix of Orbit Motion

    Directory of Open Access Journals (Sweden)

    Ana Paula Marins Chiaradia

    2012-01-01

    Full Text Available Two methods to evaluate the state transition matrix are implemented and analyzed to verify the computational cost and the accuracy of both methods. This evaluation represents one of the highest computational costs on the artificial satellite orbit determination task. The first method is an approximation of the Keplerian motion, providing an analytical solution which is then calculated numerically by solving Kepler's equation. The second one is a local numerical approximation that includes the effect of 2. The analysis is performed comparing these two methods with a reference generated by a numerical integrator. For small intervals of time (1 to 10 s and when one needs more accuracy, it is recommended to use the second method, since the CPU time does not excessively overload the computer during the orbit determination procedure. For larger intervals of time and when one expects more stability on the calculation, it is recommended to use the first method.

  20. A contribution to the numerical calculation of static electromagnetic fields in unbounded domains

    International Nuclear Information System (INIS)

    Krawczyk, F.

    1990-11-01

    The numerical calculation of static electromagnetic fields for arbitrarily shaped three-dimensional structures, especially in unbounded domains, is very memory and cpu-time consuming. In this thesis several schemes that reduce memory and cpu-time consumption have been developed or introduced. The memory needed can be reduced by a special simulation of boundaries towards open space and by the use of a scalar potential for the field description. Known disadvantages of the use of such a potential are avoided by an improved formulation of the used algorithms. The cpu-time for the calculations can be reduced remarkably in many cases by using a multigrid solution scheme including a defect-correction. A computer code has been written that uses these algorithms. With the help of this program it has been demonstrated that using these algorithms, distinct improvements in terms of computer memory, cpu-time consumption and accuracy can be achieved. (orig.) [de

  1. Asymptotic-induced numerical methods for conservation laws. Final report

    International Nuclear Information System (INIS)

    Garbey, M.; Scroggs, J.S.

    1990-12-01

    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

  2. Asymptotic-induced numerical methods for conservation laws

    Science.gov (United States)

    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.

  3. Numerical methods for semiconductor heterostructures with band nonparabolicity

    International Nuclear Information System (INIS)

    Wang Weichung; Hwang Tsungmin; Lin Wenwei; Liu Jinnliang

    2003-01-01

    This article presents numerical methods for computing bound state energies and associated wave functions of three-dimensional semiconductor heterostructures with special interest in the numerical treatment of the effect of band nonparabolicity. A nonuniform finite difference method is presented to approximate a model of a cylindrical-shaped semiconductor quantum dot embedded in another semiconductor matrix. A matrix reduction method is then proposed to dramatically reduce huge eigenvalue systems to relatively very small subsystems. Moreover, the nonparabolic band structure results in a cubic type of nonlinear eigenvalue problems for which a cubic Jacobi-Davidson method with an explicit nonequivalence deflation method are proposed to compute all the desired eigenpairs. Numerical results are given to illustrate the spectrum of energy levels and the corresponding wave functions in rather detail

  4. Three dimensional internal electromagnetic pulse calculated by particle source method

    International Nuclear Information System (INIS)

    Wang Yuzhi; Wang Taichun

    1986-01-01

    The numerical results of the primary electric current and the internal electromagnetic pulse were obtained by particle method in the rectanglar cavity. The results obtained from this method is compared with three dimensional Euler-method. It is shown that two methods are in good agreement if the conditions are the same

  5. A First Course in Numerical Methods with "Mathematica"

    OpenAIRE

    Andrei A. Kolyshkin

    2008-01-01

    In the present paper some recommendations for the use of software package "Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail.

  6. Numerical methods of mathematical optimization with Algol and Fortran programs

    CERN Document Server

    Künzi, Hans P; Zehnder, C A; Rheinboldt, Werner

    1971-01-01

    Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs reviews the theory and the practical application of the numerical methods of mathematical optimization. An ALGOL and a FORTRAN program was developed for each one of the algorithms described in the theoretical section. This should result in easy access to the application of the different optimization methods.Comprised of four chapters, this volume begins with a discussion on the theory of linear and nonlinear optimization, with the main stress on an easily understood, mathematically precise presentation. In addition

  7. Numerical methods for plasma physics in collisional regimes

    OpenAIRE

    Dimarco, Giacomo; Li, Qin; Pareschi, Lorenzo; Yan, Bokai

    2015-01-01

    International audience; We consider the development of accurate and efficient numerical methods for the solution of the Vlasov-Landau equation describing a collisional plasma. The methods combine a Lagrangian approach for the Vlasov solver with a fast spectral method for the solution of the Landau operator. To this goal new modified spectral methods for the Landau integral which are capable to capture correctly the Maxwellian steady state are introduced. A particular care is devoted to the co...

  8. Numerical methods for modeling photonic-crystal VCSELs

    DEFF Research Database (Denmark)

    Dems, Maciej; Chung, Il-Sug; Nyakas, Peter

    2010-01-01

    We show comparison of four different numerical methods for simulating Photonic-Crystal (PC) VCSELs. We present the theoretical basis behind each method and analyze the differences by studying a benchmark VCSEL structure, where the PC structure penetrates all VCSEL layers, the entire top-mirror DBR...... to the effective index method. The simulation results elucidate the strength and weaknesses of the analyzed methods; and outline the limits of applicability of the different models....

  9. Transport and Storage Cask Safety Assessment - Drop Tests and Numerical Calculations -

    International Nuclear Information System (INIS)

    Voelzke, H.; Wille, F.; Wieser, G.; Quercetti, Th.

    2006-01-01

    BAM (the German Federal Institute for Materials Research and Testing) has been performing cask design testing for more than 30 years with a large number of prototype casks of original dimensions and of 1:2 or 1:3 scales. In 2004 a brand new drop test facility was built at the new BAM test facility at Horstwalde about 80 km to the south of Berlin. In September 2004 first demonstration tests with 2 different cask designs were performed in connection with the PATRAM 2004 conference held in Berlin. The dropped prototype casks had gross masses of 141 and 181 metric tons. Since that time BAM has been performing a lot of more drop tests with new cask designs developed by different international cask manufacturers for getting German Type B(U) transport licenses. Current safety assessments especially for mechanical accident scenarios require a combination of experimental and analytical/numerical proofs commonly, because both methods offer specific options and advantages with respect to more and more detailed structural analyses. That again is a consequence of the permanent cask design optimisation for commercial reasons leading to higher stress levels in general. For that reason BAM also improves its numerical analyses capacities including the operation of different software codes. A general BAM guideline describing basic requirements for numerical safety assessment reports gives a good orientation for both applicants and inspectors. But different details of any cask design and safety assessment have to be taken into account and lead to specific questions, investigations and experiences. This paper gives an overview about the new BAM drop test facility and the ongoing drop testing there and it presents current experiences and results of numerical cask analyses and the specific methods developed and used by BAM. In this context special attention is turned to the correlation between experimental and numerical results and an outlook to future developments is given. (authors)

  10. A numerical method for solving singular De`s

    Energy Technology Data Exchange (ETDEWEB)

    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.

  11. A numerical test of the collective coordinate method

    International Nuclear Information System (INIS)

    Dobrowolski, T.; Tatrocki, P.

    2008-01-01

    The purpose of this Letter is to compare the dynamics of the kink interacting with the imperfection which follows from the collective coordinate method with the numerical results obtained on the ground of the field theoretical model. We showed that for weekly interacting kinks the collective coordinate method works similarly well for low and extremely large speeds

  12. Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance

    KAUST Repository

    Happola, Juho

    2017-09-19

    Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.

  13. Investigating Convergence Patterns for Numerical Methods Using Data Analysis

    Science.gov (United States)

    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…

  14. Application of numerical analysis methods to thermoluminescence dosimetry

    International Nuclear Information System (INIS)

    Gomez Ros, J. M.; Delgado, A.

    1989-01-01

    This report presents the application of numerical methods to thermoluminescence dosimetry (TLD), showing the advantages obtained over conventional evaluation systems. Different configurations of the analysis method are presented to operate in specific dosimetric applications of TLD, such as environmental monitoring and mailed dosimetry systems for quality assurance in radiotherapy facilities. (Author) 10 refs

  15. Core burn-up calculation method of JRR-3

    International Nuclear Information System (INIS)

    Kato, Tomoaki; Yamashita, Kiyonobu

    2007-01-01

    SRAC code system is utilized for core burn-up calculation of JRR-3. SRAC code system includes calculation modules such as PIJ, PIJBURN, ANISN and CITATION for making effective cross section and calculation modules such as COREBN and HIST for core burn-up calculation. As for calculation method for JRR-3, PIJBURN (Cell burn-up calculation module) is used for making effective cross section of fuel region at each burn-up step. PIJ, ANISN and CITATION are used for making effective cross section of non-fuel region. COREBN and HIST is used for core burn-up calculation and fuel management. This paper presents details of NRR-3 core burn-up calculation. FNCA Participating countries are expected to carry out core burn-up calculation of domestic research reactor by SRAC code system by utilizing the information of this paper. (author)

  16. Comparison of different dose calculation methods for irregular photon fields

    International Nuclear Information System (INIS)

    Zakaria, G.A.; Schuette, W.

    2000-01-01

    In this work, 4 calculation methods (Wrede method, Clarskon method of sector integration, beam-zone method of Quast and pencil-beam method of Ahnesjoe) are introduced to calculate point doses in different irregular photon fields. The calculations cover a typical mantle field, an inverted Y-field and different blocked fields for 4 and 10 MV photon energies. The results are compared to those of measurements in a water phantom. The Clarkson and the pencil-beam method have been proved to be the methods of equal standard in relation to accuracy. Both of these methods are being distinguished by minimum deviations and applied in our clinical routine work. The Wrede and beam-zone methods deliver useful results to central beam and yet provide larger deviations in calculating points beyond the central axis. (orig.) [de

  17. Numerical Calculation of Electric Fields in Housing Spaces Due to Electromagnetic Radiation from Antennas for Mobile Communication

    Directory of Open Access Journals (Sweden)

    H.-P. Geromiller

    2003-01-01

    Full Text Available The influence of electromagnetic radiation from mobile antennas on humans is under discussion in va'rious groups ofscientists, This paper deals with the impact ofelectromagnetic radiation in a housing space. The space is assumedto be bordered by 5 walls of ferroconcrete and a door-window combination on the 6th side, the latter to be electromagnetically transparent. The transparent side of the housing is exposed to an electromagnetic wave. As the source ofradiation is considered to be far away from the housing, the radiation is regarded to be from a plane wave. Due to the high signal frequency and ferroconcrete walls, 5 sides ofthe housing space are considered to be perfect conductors. The electric field inside the housing is calculated numerically by the method of finite differences for different angles of incidence of the radiated electromagnetic wave. The maximum value of the calculated electric field is outlined in a diagram.

  18. Numerical Calculation of Electric Fields in Housing Spaces due to Electromagnetic Radiation from Antennas for Mobile Communication

    Directory of Open Access Journals (Sweden)

    H.-P. Geromiller

    2004-01-01

    Full Text Available The influence of electromagnetic radiation from mobile antennas on humans is under discussion in various group of scientists. This paper deals with the impact of electromagnetic radiation in housing spaces. The space is assumed to be bordered by 5 walls of ferroconcrete and a door-window combination on the 6th side, the latter to be electromagnetic transparent. The transparent side of the housing is exposed to an electromagnetic wave. As the source of radiation is considered to be far away from the housing, the radiation is regarded as a plane wave. Due to the high signal frequency and the ferroconcrete walls, 5 sides of the housing space are considered to be perfect conductors. The electric field inside the housing is calculated numerically by the method of finite differences for different angles of incidence of the radiated electromagnetic wave. The maximum value of the calculated electric field is outlined in a diagram.

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

    Science.gov (United States)

    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. Numerical methods for Bayesian inference in the face of aging

    International Nuclear Information System (INIS)

    Clarotti, C.A.; Villain, B.; Procaccia, H.

    1996-01-01

    In recent years, much attention has been paid to Bayesian methods for Risk Assessment. Until now, these methods have been studied from a theoretical point of view. Researchers have been mainly interested in: studying the effectiveness of Bayesian methods in handling rare events; debating about the problem of priors and other philosophical issues. An aspect central to the Bayesian approach is numerical computation because any safety/reliability problem, in a Bayesian frame, ends with a problem of numerical integration. This aspect has been neglected until now because most Risk studies assumed the Exponential model as the basic probabilistic model. The existence of conjugate priors makes numerical integration unnecessary in this case. If aging is to be taken into account, no conjugate family is available and the use of numerical integration becomes compulsory. EDF (National Board of Electricity, of France) and ENEA (National Committee for Energy, New Technologies and Environment, of Italy) jointly carried out a research program aimed at developing quadrature methods suitable for Bayesian Interference with underlying Weibull or gamma distributions. The paper will illustrate the main results achieved during the above research program and will discuss, via some sample cases, the performances of the numerical algorithms which on the appearance of stress corrosion cracking in the tubes of Steam Generators of PWR French power plants. (authors)

  1. Evolution of calculation methods taking into account severe accidents

    International Nuclear Information System (INIS)

    L'Homme, A.; Courtaud, J.M.

    1990-12-01

    During the first decade of PWRs operation in France the calculation methods used for design and operation have improved very much. This paper gives a general analysis of the calculation methods evolution in parallel with the evolution of safety approach concerning PWRs. Then a comprehensive presentation of principal calculation tools is presented as applied during the past decade. An effort is done to predict the improvements in near future

  2. Current trends in methods for neutron diffusion calculations

    International Nuclear Information System (INIS)

    Adams, C.H.

    1977-01-01

    Current work and trends in the application of neutron diffusion theory to reactor design and analysis are reviewed. Specific topics covered include finite-difference methods, synthesis methods, nodal calculations, finite-elements and perturbation theory

  3. On numerical solution of Burgers' equation by homotopy analysis method

    International Nuclear Information System (INIS)

    Inc, Mustafa

    2008-01-01

    In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions

  4. Interdisciplinary Study of Numerical Methods and Power Plants Engineering

    Directory of Open Access Journals (Sweden)

    Ioana OPRIS

    2014-08-01

    Full Text Available The development of technology, electronics and computing opened the way for a cross-disciplinary research that brings benefits by combining the achievements of different fields. To prepare the students for their future interdisciplinary approach,aninterdisciplinary teaching is adopted. This ensures their progress in knowledge, understanding and ability to navigate through different fields. Aiming these results, the Universities introduce new interdisciplinary courses which explore complex problems by studying subjects from different domains. The paper presents a problem encountered in designingpower plants. The method of solvingthe problem isused to explain the numerical methods and to exercise programming.The goal of understanding a numerical algorithm that solves a linear system of equations is achieved by using the knowledge of heat transfer to design the regenerative circuit of a thermal power plant. In this way, the outcomes from the prior courses (mathematics and physics are used to explain a new subject (numerical methods and to advance future ones (power plants.

  5. Application of the photoelastic experimental hybrid method with new numerical method to the high stress distribution

    International Nuclear Information System (INIS)

    Hawong, Jai Sug; Lee, Dong Hun; Lee, Dong Ha; Tche, Konstantin

    2004-01-01

    In this research, the photoelastic experimental hybrid method with Hook-Jeeves numerical method has been developed: This method is more precise and stable than the photoelastic experimental hybrid method with Newton-Rapson numerical method with Gaussian elimination method. Using the photoelastic experimental hybrid method with Hook-Jeeves numerical method, we can separate stress components from isochromatics only and stress intensity factors and stress concentration factors can be determined. The photoelastic experimental hybrid method with Hook-Jeeves had better be used in the full field experiment than the photoelastic experimental hybrid method with Newton-Rapson with Gaussian elimination method

  6. Neutrons and numerical methods. A new look at rotational tunneling

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, M.R.; Kearley, G.J. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)

    1997-04-01

    Molecular modelling techniques are easily adapted to calculate rotational potentials in crystals of simple molecular compounds. A comparison with the potentials obtained from the tunnelling spectra provides a stringent means for validating current methods of calculating Van der Waals, Coulomb and covalent terms. (author). 5 refs.

  7. An analytical-numerical comprehensive method for optimizing the fringing magnetic field

    International Nuclear Information System (INIS)

    Xiao Meiqin; Mao Naifeng

    1991-01-01

    The criterion of optimizing the fringing magnetic field is discussed, and an analytical-numerical comprehensive method for realizing the optimization is introduced. The method mentioned above consists of two parts, the analytical part calculates the field of the shims, which corrects the fringing magnetic field by using uniform magnetizing method; the numerical part fulfils the whole calculation of the field distribution by solving the equation of magnetic vector potential A within the region covered by arbitrary triangular meshes with the aid of finite difference method and successive over relaxation method. On the basis of the method, the optimization of the fringing magnetic field for a large-scale electromagnetic isotope separator is finished

  8. Status and future prospects of using numerical methods to study complex flows at High Reynolds numbers

    Science.gov (United States)

    Maccormack, R. W.

    1978-01-01

    The calculation of flow fields past aircraft configuration at flight Reynolds numbers is considered. Progress in devising accurate and efficient numerical methods, in understanding and modeling the physics of turbulence, and in developing reliable and powerful computer hardware is discussed. Emphasis is placed on efficient solutions to the Navier-Stokes equations.

  9. Fourier Bessel transform method for efficiently calculating the magnetic field of solenoids

    International Nuclear Information System (INIS)

    Nachamkin, J.; Maggiore, C.J.

    1980-01-01

    A numerical procedure for calculating the magnetic field of a selenoid is derived. Based on the properties of Bessel functions, the procedure is shown to be convergent everywhere, including within the windings of the solenoid. The most critical part of the procedure is detailed in the main text. A simple method is used to ensure numerical significance while allowing economical computational times. In the appendix the procedure is generalized to universal convergence by appropriate partitioning of the solenoid windings

  10. Numerical Calculation of Transport Based on the Drift Kinetic Equation for plasmas in General Toroidal Magnetic Geometry

    International Nuclear Information System (INIS)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-01-01

    This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs

  11. A numerical method for acoustic oscillations in tubes

    Science.gov (United States)

    Gary, John M.

    1988-01-01

    A numerical method to obtain the neutral curve for the onset of acoustic oscillations in a helium-filled tube is described. Such oscillations can cause a serious heat loss in the plumbing associated with liquid helium dewars. The problem is modelled by a second-order, ordinary differential eigenvalue problem for the pressure perturbation. The numerical method to find the eigenvalues and track the resulting points along the neutral curve is tailored to this problem. The results show that a tube with a uniform temperature gradient along it is much more stable than one where the temperature suddenly jumps from the cold to the hot value in the middle of the tube.

  12. Numerical method of entangled state selection in association of molecules

    Science.gov (United States)

    Arakelov, K. S.; Ozhigov, Yu. I.

    2008-03-01

    We represent the economy method of separation of the entangled states of GHZ and W types which arise in the process of association of a single molecule. It makes possible to separate these types of quantum states in the simulation of real processes like the association of molecular ion of hydrogen by means of existing computers with the strictly limited memory. Numerical realization of this method is in process; we represent the semiclassical part of it, that is based on Landau-Ziner description of the association of molecules. Results of statistical processing of the row of numerical experiments are shown.

  13. Iterative acceleration methods for Monte Carlo and deterministic criticality calculations

    Energy Technology Data Exchange (ETDEWEB)

    Urbatsch, T.J.

    1995-11-01

    If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors.

  14. Comment on "Numerical methods for stochastic differential equations".

    Science.gov (United States)

    Burrage, Kevin; Burrage, Pamela; Higham, Desmond J; Kloeden, Peter E; Platen, Eckhard

    2006-12-01

    Wilkie [Phys. Rev. E 70, 017701 (2004)] used a heuristic approach to derive Runge-Kutta-based numerical methods for stochastic differential equations based on methods used for solving ordinary differential equations. The aim was to follow solution paths with high order. We point out that this approach is invalid in the general case and does not lead to high order methods. We warn readers against the inappropriate use of deterministic calculus in a stochastic setting.

  15. Krylov subspace method for evaluating the self-energy matrices in electron transport calculations

    DEFF Research Database (Denmark)

    Sørensen, Hans Henrik Brandenborg; Hansen, Per Christian; Petersen, D. E.

    2008-01-01

    We present a Krylov subspace method for evaluating the self-energy matrices used in the Green's function formulation of electron transport in nanoscale devices. A procedure based on the Arnoldi method is employed to obtain solutions of the quadratic eigenvalue problem associated with the infinite...... calculations. Numerical tests within a density functional theory framework are provided to validate the accuracy and robustness of the proposed method, which in most cases is an order of magnitude faster than conventional methods....

  16. Numerical computation methods for magnet design of spectrometer, accelerator and beam transport systems

    International Nuclear Information System (INIS)

    Fan Mingwu; Maio Yixin

    1986-01-01

    High calculation accuracy is expected in the design of spectrometer, accelerator or beam transport systems. Three dimensional electromagnetic field computation is needed in some cases. In solving these problems, numerical computation methods have been dominating in the area. Advantages and disadvantages among the methods are discussed and errors between computed and measured values are analysised. The application of making full use of these methods is discussed based on some practical models

  17. A numerical scheme to calculate temperature and salinity dependent air-water transfer velocities for any gas

    Science.gov (United States)

    Johnson, M. T.

    2010-02-01

    The transfer velocity determines the rate of exchange of a gas across the air-water interface for a given deviation from Henry's law equilibrium between the two phases. In the thin film model of gas exchange, which is commonly used for calculating gas exchange rates from measured concentrations of trace gases in the atmosphere and ocean/freshwaters, the overall transfer is controlled by diffusion-mediated films on either side of the air-water interface. Calculating the total transfer velocity (i.e. including the influence from both molecular layers) requires the Henry's law constant and the Schmidt number of the gas in question, the latter being the ratio of the viscosity of the medium and the molecular diffusivity of the gas in the medium. All of these properties are both temperature and (on the water side) salinity dependent and extensive calculation is required to estimate these properties where not otherwise available. The aim of this work is to standardize the application of the thin film approach to flux calculation from measured and modelled data, to improve comparability, and to provide a numerical framework into which future parameter improvements can be integrated. A detailed numerical scheme is presented for the calculation of the gas and liquid phase transfer velocities (ka and kw respectively) and the total transfer velocity, K. The scheme requires only basic physical chemistry data for any gas of interest and calculates K over the full range of temperatures, salinities and wind-speeds observed in and over the ocean. Improved relationships for the wind-speed dependence of ka and for the salinity-dependence of the gas solubility (Henry's law) are derived. Comparison with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general but significant improvements under certain conditions. The scheme is provided as a downloadable program in the supplementary material, along with input files containing molecular

  18. A (Slightly Less Brutal) Method for Numerically Evaluating Structure Functions

    CERN Document Server

    Fasching, D

    1996-01-01

    A fast numerical algorithm for the evolution of parton distributions in x space is described. The method is close in spirit to `brute' force techniques. The necessary integrals are performed by summing the approximate contributions from small steps of the integration region. Because it is a numerical evaluation it shares the advantage with brute force numerical integration that there are no restrictions placed on the functional form of the distributions to be evolved. However, an improvement in the approximation technique results in a significant reduction in the number of integration steps and a savings in time on the order of three hundred fifty. The method has been implemented for the structure functions F_2 and g_1 at next-to-leading order.

  19. The power series method in the effectiveness factor calculations

    OpenAIRE

    Filipich, C. P.; Villa, L. T.; Grossi, Ricardo Oscar

    2017-01-01

    In the present paper, exact analytical solutions are obtained for nonlinear ordinary differential equations which appear in complex diffusionreaction processes. A technique based on the power series method is used. Numerical results were computed for a number of cases which correspond to boundary value problems available in the literature. Additionally, new numerical results were generated for several important cases. Fil: Filipich, C. P.. Universidad Tecnológica Nacional. Facultad Regiona...

  20. An efficient numerical method for solving nonlinear foam drainage equation

    Science.gov (United States)

    Parand, Kourosh; Delkhosh, Mehdi

    2018-02-01

    In this paper, the nonlinear foam drainage equation, which is a famous nonlinear partial differential equation, is solved by using a hybrid numerical method based on the quasilinearization method and the bivariate generalized fractional order of the Chebyshev functions (B-GFCF) collocation method. First, using the quasilinearization method, the equation is converted into a sequence of linear partial differential equations (LPD), and then these LPDs are solved using the B-GFCF collocation method. A very good approximation of solutions is obtained, and comparisons show that the obtained results are more accurate than the results of other researchers.

  1. Acceleration methods for assembly-level transport calculations

    International Nuclear Information System (INIS)

    Adams, Marvin L.; Ramone, Gilles

    1995-01-01

    A family acceleration methods for the iterations that arise in assembly-level transport calculations is presented. A single iteration in these schemes consists of a transport sweep followed by a low-order calculation which is itself a simplified transport problem. It is shown that a previously-proposed method fitting this description is unstable in two and three dimensions. It is presented a family of methods and shown that some members are unconditionally stable. (author). 8 refs, 4 figs, 4 tabs

  2. A finite element method for SSI time history calculations

    International Nuclear Information System (INIS)

    Ni, X.M.; Gantenbein, F.; Petit, M.

    1989-01-01

    The method which is proposed is based on a finite element modelisation for the soil and the structure and a time history calculation. It has been developed for plane and axisymmetric geometries. The principle of this method will be presented, then applications will be given, first to a linear calculation for which results will be compared to those obtained by standard methods. Then results for a non linear behavior will be described

  3. Study on grain growth of fine grained WC-Co hardmetal by numerical calculation

    Energy Technology Data Exchange (ETDEWEB)

    Matsuoka, N. [Kobe Steel, Ltd., Kobe (Japan); Hayashi, K. [The University of Tokyo, Tokyo (Japan). Institute of industrial Science

    2000-12-15

    This paper reviews our simulation study by numerical calculation based on two-, three- and multi-grain-size models on WC grain growth in fine grained WC-Co hardmetal doped with VC. The study aimed to presume or predict the following: (1) the cause and conditions for the abnormal grain growth which occurs in some cases in the fine grained hardmetal prepared from fine WC powders with mean grain size below about 0.2{mu}m, and (2) how the mean grain size of the hardmetal varies with decreasing mean grain size of the WC starting powder to 0.1 pm or nano-meter size. The calculation results by these three kinds of models suggested the following, respectively: (1) the occurrence of the abnormal grain growth is generally substantial for WC starting powder with bimodal size-distribution and mean gram size below 0.1 - 0.2{mu}m, and not due to the non-uniform distribution of the grain growth inhibitor, (2) the introduction of middle grains caused the disappearance of small (fine) grains during sintering, leading to abruptly increase of the mean grain size of alloy, and (3) the mean grain size of alloy becomes so large as about 0.3 - 0.4{mu}m, even when the WC starting powders with nano-size as well as 0.1 {mu}m are used. (author)

  4. Numerical simulation methods of fires in nuclear power plants

    International Nuclear Information System (INIS)

    Keski-Rahkonen, O.; Bjoerkman, J.; Heikkilae, L.

    1992-01-01

    Fire is a significant hazard to the safety of nuclear power plants (NPP). Fire may be serious accident as such, but even small fire at a critical point in a NPP may cause an accident much more serious than fire itself. According to risk assessments a fire may be an initial cause or a contributing factor in a large part of reactor accidents. At the Fire Technology and the the Nuclear Engineering Laboratory of the Technical Research Centre of Finland (VTT) fire safety research for NPPs has been carried out in a large extent since 1985. During years 1988-92 a project Advanced Numerical Modelling in Nuclear Power Plants (PALOME) was carried out. In the project the level of numerical modelling for fire research in Finland was improved by acquiring, preparing for use and developing numerical fire simulation programs. Large scale test data of the German experimental program (PHDR Sicherheitsprogramm in Kernforschungscentral Karlsruhe) has been as reference. The large scale tests were simulated by numerical codes and results were compared to calculations carried out by others. Scientific interaction with outstanding foreign laboratories and scientists has been an important part of the project. This report describes the work of PALOME-project carried out at the Fire Technology Laboratory only. A report on the work at the Nuclear Engineering Laboratory will be published separatively. (au)

  5. High accuracy mantle convection simulation through modern numerical methods

    KAUST Repository

    Kronbichler, Martin

    2012-08-21

    Numerical simulation of the processes in the Earth\\'s mantle is a key piece in understanding its dynamics, composition, history and interaction with the lithosphere and the Earth\\'s core. However, doing so presents many practical difficulties related to the numerical methods that can accurately represent these processes at relevant scales. This paper presents an overview of the state of the art in algorithms for high-Rayleigh number flows such as those in the Earth\\'s mantle, and discusses their implementation in the Open Source code Aspect (Advanced Solver for Problems in Earth\\'s ConvecTion). Specifically, we show how an interconnected set of methods for adaptive mesh refinement (AMR), higher order spatial and temporal discretizations, advection stabilization and efficient linear solvers can provide high accuracy at a numerical cost unachievable with traditional methods, and how these methods can be designed in a way so that they scale to large numbers of processors on compute clusters. Aspect relies on the numerical software packages deal.II and Trilinos, enabling us to focus on high level code and keeping our implementation compact. We present results from validation tests using widely used benchmarks for our code, as well as scaling results from parallel runs. © 2012 The Authors Geophysical Journal International © 2012 RAS.

  6. Combination methods for numerical inclusion of the zeros of a ...

    African Journals Online (AJOL)

    In the numerical inclusion and isolation of the zeros of a polynomial in an interval on the plane, hybrid combination methods have been found quite useful for their virtue of easy construction and reduced computational cost with respect to interval arithmetic operations, while still providing restrictive inclusion for the respective ...

  7. Kinetic calculations for miniature neutron source reactor using analytical and numerical techniques

    International Nuclear Information System (INIS)

    Ampomah-Amoako, E.

    2008-06-01

    The analytical methods, step change in reactivity and ramp change in reactivity as well as numerical methods, fixed point iteration and Runge Kutta-gill were used to simulate the initial build up of neutrons in a miniature neutron source reactor with and without temperature feedback effect. The methods were modified to include photo neutron concentration. PARET 7.3 was used to simulate the transients behaviour of Ghana Research Reactor-1. The PARET code was capable of simulating the transients for 2.1 mk and 4 mk insertions of reactivity with peak powers of 49.87 kW and 92.34 kW, respectively. PARET code however failed to simulate 6.71 mk of reactivity which was predicted by Akaho et al through TEMPFED. (au)

  8. Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems

    Energy Technology Data Exchange (ETDEWEB)

    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.

  9. Numerical models for calculating hydrologic processes in river and lake-river systems

    Science.gov (United States)

    Nikiforovskaya, V. S.; Voevodin, A. F.

    2017-10-01

    We use one-dimensional (1D) and two-dimensional (2D) longitudinal-vertical mathematical models and their 2D+1D combination as well as numerical methods to study unsteady processes in the complex open channel systems under the influence of water management measures. The analysis shows the economic feasibility and efficiency of using the developed mathematical models to study hydrological process in water bodies. The study of the physical processes in complex water body, consisting of significantly different components, based on the use of only one chosen mathematical model, is uneconomical and inefficient from the viewpoint of computational expense.

  10. Field calculations. Part I: Choice of variables and methods

    International Nuclear Information System (INIS)

    Turner, L.R.

    1981-01-01

    Magnetostatic calculations can involve (in order of increasing complexity) conductors only, material with constant or infinite permeability, or material with variable permeability. We consider here only the most general case, calculations involving ferritic material with variable permeability. Variables suitable for magnetostatic calculations are the magnetic field, the magnetic vector potential, and the magnetic scalar potential. For two-dimensional calculations the potentials, which each have only one component, have advantages over the field, which has two components. Because it is a single-valued variable, the vector potential is perhaps the best variable for two-dimensional calculations. In three dimensions, both the field and the vector potential have three components; the scalar potential, with only one component,provides a much smaller system of equations to be solved. However the scalar potential is not single-valued. To circumvent this problem, a calculation with two scalar potentials can be performed. The scalar potential whose source is the conductors can be calculated directly by the Biot-Savart law, and the scalar potential whose source is the magnetized material is single valued. However in some situations, the fields from the two potentials nearly cancel; and the numerical accuracy is lost. The 3-D magnetostatic program TOSCA employs a single total scalar potential; the program GFUN uses the magnetic field as its variable

  11. Analytic method for calculating properties of random walks on networks

    Science.gov (United States)

    Goldhirsch, I.; Gefen, Y.

    1986-01-01

    A method for calculating the properties of discrete random walks on networks is presented. The method divides complex networks into simpler units whose contribution to the mean first-passage time is calculated. The simplified network is then further iterated. The method is demonstrated by calculating mean first-passage times on a segment, a segment with a single dangling bond, a segment with many dangling bonds, and a looplike structure. The results are analyzed and related to the applicability of the Einstein relation between conductance and diffusion.

  12. New numerical method for solving the solute transport equation

    International Nuclear Information System (INIS)

    Ross, B.; Koplik, C.M.

    1978-01-01

    The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste

  13. Numerical methods and computers used in elastohydrodynamic lubrication

    Science.gov (United States)

    Hamrock, B. J.; Tripp, J. H.

    1982-01-01

    Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.

  14. The development and validation of control rod calculation methods

    International Nuclear Information System (INIS)

    Rowlands, J.L.; Sweet, D.W.; Franklin, B.M.

    1979-01-01

    Fission rate distributions have been measured in the zero power critical facility, ZEBRA, for a series of eight different arrays of boron carbide control rods. Diffusion theory calculations have been compared with these measurements. The normalised fission rates differ by up to about 30% in some regions, between the different arrays, and these differences are well predicted by the calculations. A development has been made to a method used to produce homogenised cross sections for lattice regions containing control rods. Calculations show that the method also reproduces the reaction rate within the rod and the fission rate dip at the surface of the rod in satisfactory agreement with the more accurate calculations which represent the fine structure of the rod. A comparison between diffusion theory and transport theory calculations of control rod reactivity worths in the CDFR shows that for the standard design method the finite mesh approximation and the difference between diffusion theory and transport theory (the transport correction) tend to cancel and result in corrections to be applied to the standard mesh diffusion theory calculations of about +- 2% or less. This result applies for mesh centred finite difference diffusion theory codes and for the arrays of natural boron carbide control rods for which the calculations were made. Improvements have also been made to the effective diffusion coefficients used in diffusion theory calculations for control rod followers and these give satisfactory agreement with transport theory calculations. (U.K.)

  15. Numerical Methods for Plate Forming by Line Heating

    DEFF Research Database (Denmark)

    Clausen, Henrik Bisgaard

    2000-01-01

    Few researchers have addressed so far the topic Line Heating in the search for better control of the process. Various methods to help understanding the mechanics have been used, including beam analysis approximation, equivalent force calculation and three-dimensional finite element analysis. I...... consider here finite element methods to model the behaviour and to predict the heating paths....

  16. Dynamical Systems Method and Applications Theoretical Developments and Numerical Examples

    CERN Document Server

    Ramm, Alexander G

    2012-01-01

    Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and

  17. Simple numerical method for predicting steady compressible flows

    Science.gov (United States)

    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.

  18. Singularity Preserving Numerical Methods for Boundary Integral Equations

    Science.gov (United States)

    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.

  19. Finite difference method and algebraic polynomial interpolation for numerically solving Poisson's equation over arbitrary domains

    Directory of Open Access Journals (Sweden)

    Tsugio Fukuchi

    2014-06-01

    Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.

  20. Numerical optimization methods for controlled systems with parameters

    Science.gov (United States)

    Tyatyushkin, A. I.

    2017-10-01

    First- and second-order numerical methods for optimizing controlled dynamical systems with parameters are discussed. In unconstrained-parameter problems, the control parameters are optimized by applying the conjugate gradient method. A more accurate numerical solution in these problems is produced by Newton's method based on a second-order functional increment formula. Next, a general optimal control problem with state constraints and parameters involved on the righthand sides of the controlled system and in the initial conditions is considered. This complicated problem is reduced to a mathematical programming one, followed by the search for optimal parameter values and control functions by applying a multimethod algorithm. The performance of the proposed technique is demonstrated by solving application problems.

  1. Numerical method for the nonlinear Fokker-Planck equation

    International Nuclear Information System (INIS)

    Zhang, D.S.; Wei, G.W.; Kouri, D.J.; Hoffman, D.K.

    1997-01-01

    A practical method based on distributed approximating functionals (DAFs) is proposed for numerically solving a general class of nonlinear time-dependent Fokker-Planck equations. The method relies on a numerical scheme that couples the usual path-integral concept to the DAF idea. The high accuracy and reliability of the method are illustrated by applying it to an exactly solvable nonlinear Fokker-Planck equation, and the method is compared with the accurate K-point Stirling interpolation formula finite-difference method. The approach is also used successfully to solve a nonlinear self-consistent dynamic mean-field problem for which both the cumulant expansion and scaling theory have been found by Drozdov and Morillo [Phys. Rev. E 54, 931 (1996)] to be inadequate to describe the occurrence of a long-lived transient bimodality. The standard interpretation of the transient bimodality in terms of the flat region in the kinetic potential fails for the present case. An alternative analysis based on the effective potential of the Schroedinger-like Fokker-Planck equation is suggested. Our analysis of the transient bimodality is strongly supported by two examples that are numerically much more challenging than other examples that have been previously reported for this problem. copyright 1997 The American Physical Society

  2. CEA data and methods for control rod calculations

    International Nuclear Information System (INIS)

    Salvatores, M.

    1988-01-01

    Methods and data used at CEA for LMFBR control rod calculations are presented. The performances of both the design methods and of the refined methods for the SUPER PHENIX start-up experiments are given. New developments for future core design and operation are also reported, together with the role of integral experiments to validate them. (author). 15 refs, 4 figs, 11 tabs

  3. A calculation method of cracking moment for the high strength ...

    Indian Academy of Sciences (India)

    In this study, a method is given to calculate cracking moments of high strength reinforced concrete beams under the effect of pure torsion. To determine the method, both elastic and plastic theories were used. In this method, dimensions of beam cross-section were considered besides stirrup and longitudinal reinforcements.

  4. Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method

    International Nuclear Information System (INIS)

    Lima E Silva, A.L.F.; Silveira-Neto, A.; Damasceno, J.J.R.

    2003-01-01

    In this work, a virtual boundary method is applied to the numerical simulation of a uniform flow over a cylinder. The force source term, added to the two-dimensional Navier-Stokes equations, guarantees the imposition of the no-slip boundary condition over the body-fluid interface. These equations are discretized, using the finite differences method. The immersed boundary is represented with a finite number of Lagrangian points, distributed over the solid-fluid interface. A Cartesian grid is used to solve the fluid flow equations. The key idea is to propose a method to calculate the interfacial force without ad hoc constants that should usually be adjusted for the type of flow and the type of the numerical method, when this kind of model is used. In the present work, this force is calculated using the Navier-Stokes equations applied to the Lagrangian points and then distributed over the Eulerian grid. The main advantage of this approach is that it enables calculation of this force field, even if the interface is moving or deforming. It is unnecessary to locate the Eulerian grid points near this immersed boundary. The lift and drag coefficients and the Strouhal number, calculated for an immersed cylinder, are compared with previous experimental and numerical results, for different Reynolds numbers

  5. Methods for tornado frequency calculation of nuclear power plant

    International Nuclear Information System (INIS)

    Liu Haibin; Li Lin

    2012-01-01

    In order to take probabilistic safety assessment of nuclear power plant tornado attack event, a method to calculate tornado frequency of nuclear power plant is introduced based on HAD 101/10 and NUREG/CR-4839 references. This method can consider history tornado frequency of the plant area, construction dimension, intensity various along with tornado path and area distribution and so on and calculate the frequency of different scale tornado. (authors)

  6. 3D electric field calculation with surface charge method

    International Nuclear Information System (INIS)

    Yamada, S.

    1992-01-01

    This paper describes an outline and some examples of three dimensional electric field calculations with a computer code developed at NIRS. In the code, a surface charge method is adopted because of it's simplicity in the mesh establishing procedure. The charge density in a triangular mesh is assumed to distribute with a linear function of the position. The electric field distribution is calculated for a pair of drift tubes with the focusing fingers on the opposing surfaces. The field distribution in an acceleration gap is analyzed with a Fourier-Bessel series expansion method. The calculated results excellently reproduces the measured data with a magnetic model. (author)

  7. A numerical scheme to calculate temperature and salinity dependent air-water transfer velocities for any gas

    Science.gov (United States)

    Johnson, M. T.

    2010-10-01

    The ocean-atmosphere flux of a gas can be calculated from its measured or estimated concentration gradient across the air-sea interface and the transfer velocity (a term representing the conductivity of the layers either side of the interface with respect to the gas of interest). Traditionally the transfer velocity has been estimated from empirical relationships with wind speed, and then scaled by the Schmidt number of the gas being transferred. Complex, physically based models of transfer velocity (based on more physical forcings than wind speed alone), such as the NOAA COARE algorithm, have more recently been applied to well-studied gases such as carbon dioxide and DMS (although many studies still use the simpler approach for these gases), but there is a lack of validation of such schemes for other, more poorly studied gases. The aim of this paper is to provide a flexible numerical scheme which will allow the estimation of transfer velocity for any gas as a function of wind speed, temperature and salinity, given data on the solubility and liquid molar volume of the particular gas. New and existing parameterizations (including a novel empirical parameterization of the salinity-dependence of Henry's law solubility) are brought together into a scheme implemented as a modular, extensible program in the R computing environment which is available in the supplementary online material accompanying this paper; along with input files containing solubility and structural data for ~90 gases of general interest, enabling the calculation of their total transfer velocities and component parameters. Comparison of the scheme presented here with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general. It is intended that the various components of this numerical scheme should be applied only in the absence of experimental data providing robust values for parameters for a particular gas of interest.

  8. A numerical scheme to calculate temperature and salinity dependent air-water transfer velocities for any gas

    Directory of Open Access Journals (Sweden)

    M. T. Johnson

    2010-10-01

    Full Text Available The ocean-atmosphere flux of a gas can be calculated from its measured or estimated concentration gradient across the air-sea interface and the transfer velocity (a term representing the conductivity of the layers either side of the interface with respect to the gas of interest. Traditionally the transfer velocity has been estimated from empirical relationships with wind speed, and then scaled by the Schmidt number of the gas being transferred. Complex, physically based models of transfer velocity (based on more physical forcings than wind speed alone, such as the NOAA COARE algorithm, have more recently been applied to well-studied gases such as carbon dioxide and DMS (although many studies still use the simpler approach for these gases, but there is a lack of validation of such schemes for other, more poorly studied gases. The aim of this paper is to provide a flexible numerical scheme which will allow the estimation of transfer velocity for any gas as a function of wind speed, temperature and salinity, given data on the solubility and liquid molar volume of the particular gas. New and existing parameterizations (including a novel empirical parameterization of the salinity-dependence of Henry's law solubility are brought together into a scheme implemented as a modular, extensible program in the R computing environment which is available in the supplementary online material accompanying this paper; along with input files containing solubility and structural data for ~90 gases of general interest, enabling the calculation of their total transfer velocities and component parameters. Comparison of the scheme presented here with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general. It is intended that the various components of this numerical scheme should be applied only in the absence of experimental data providing robust values for parameters for a particular gas of interest.

  9. Numerical analysis of jet breakup behavior using particle method

    International Nuclear Information System (INIS)

    Shibata, Kazuya; Koshizuka, Seiichi; Oka, Yoshiaki

    2002-01-01

    A continuous jet changes to droplets where jet breakup occurs. In this study, two-dimensional numerical analysis of jet breakup is performed using the MPS method (Moving Particle Semi-implicit Method) which is a particle method for incompressible flows. The continuous fluid surrounding the jet is neglected. Dependencies of the jet breakup length on the Weber number and the Froude number agree with the experiment. The size distribution of droplets is in agreement with the Nukiyama-Tanasawa distribution which has been widely used as an experimental correlation. Effects of the Weber number and the Froude number on the size distribution are also obtained. (author)

  10. Projected discrete ordinates methods for numerical transport problems

    Energy Technology Data Exchange (ETDEWEB)

    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.

  11. Comparison of several numerical methods for internal transonic flow problems

    Energy Technology Data Exchange (ETDEWEB)

    Dobes, J.; Fort, J.; Fuerst, J.; Halama, J.; Kozel, K. [Karlova Univ., Prague (Czech Republic). Dept. of Technical Mathematics

    2001-07-01

    This contribution summarizes results of several numerical methods developed at our department. Presented methods are based on central TVD schemes, upwind TVD schemes with or without Riemann solver, ENO schemes and Lax-Wendroff type schemes. The results of 2D methods, computed on either structured quadrilateral grids or unstructured grids composed of triangles and quadrilaterals, are compared on 2D axial and radial turbine cascade and 2D axial compressor cascade. A comparison of results, obtained on structured hexahedral grids, is shown for 3D axial turbine cascade of Skoda Pilsen enterprise. (orig.)

  12. Study on numerical methods for transient flow induced by speed-changing impeller of fluid machinery

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Dazhuan; Chen, Tao; Wang, Leqin [Zhejiang University, Hangzhou (China); Cheng, Wentao [Research Institute of Product Quality and Standard of Ministry of Water Recourse, Hangzhou (China); Sun, Youbo [Zhejiang Academy of Safety Science and Technology, Hangzhou (China)

    2013-06-15

    In order to establish a reliable numerical method for solving the transient rotating flow induced by a speed-changing impeller, two numerical methods based on finite volume method (FVM) were presented and analyzed in this study. Two-dimensional numerical simulations of incompressible transient unsteady flow induced by an impeller during starting process were carried out respectively by using DM and DSR methods. The accuracy and adaptability of the two methods were evaluated by comprehensively comparing the calculation results. Moreover, an intensive study on the application of DSR method was conducted subsequently. The results showed that transient flow structure evolution and transient characteristics of the starting impeller are obviously affected by the starting process. The transient flow can be captured by both two methods, and the DSR method shows a higher computational efficiency. As an application example, the starting process of a mixed-flow pump was simulated by using DSR method. The calculation results were analyzed by comparing with the experiment data.

  13. Study on numerical methods for transient flow induced by speed-changing impeller of fluid machinery

    International Nuclear Information System (INIS)

    Wu, Dazhuan; Chen, Tao; Wang, Leqin; Cheng, Wentao; Sun, Youbo

    2013-01-01

    In order to establish a reliable numerical method for solving the transient rotating flow induced by a speed-changing impeller, two numerical methods based on finite volume method (FVM) were presented and analyzed in this study. Two-dimensional numerical simulations of incompressible transient unsteady flow induced by an impeller during starting process were carried out respectively by using DM and DSR methods. The accuracy and adaptability of the two methods were evaluated by comprehensively comparing the calculation results. Moreover, an intensive study on the application of DSR method was conducted subsequently. The results showed that transient flow structure evolution and transient characteristics of the starting impeller are obviously affected by the starting process. The transient flow can be captured by both two methods, and the DSR method shows a higher computational efficiency. As an application example, the starting process of a mixed-flow pump was simulated by using DSR method. The calculation results were analyzed by comparing with the experiment data.

  14. Comparison of MCNPX and Albedo method in criticality calculation

    International Nuclear Information System (INIS)

    Cunha, Victor L. Lassance; Rebello, Wilson F.; Cabral, Ronaldo G.; Melo, Fernando da S.; Silva, Ademir X. da

    2009-01-01

    This study aims to conduct a computer simulation that will calculate the reactivity of a homogeneous reactor and compare the results with the calculations made by the albedo method. The simulation will be developed using the MCNPX. The study compared the results calculated for a hypothetical reactor by the albedo method for four groups of energy with those obtained by the MCNPX simulation. The design of the reactor is spherical and homogeneous with a reflector of finite thickness. The value obtained for the neutron effective multiplication factor - k eff will be compared. Different situations were simulated in order to obtain results closer to the compared method and reality. The was Good consistency could be noticed between the calculated results. (author)

  15. Multiregion, multigroup collision probability method with white boundary condition for light water reactor thermalization calculations

    International Nuclear Information System (INIS)

    Ozgener, B.; Ozgener, H.A.

    2005-01-01

    A multiregion, multigroup collision probability method with white boundary condition is developed for thermalization calculations of light water moderated reactors. Hydrogen scatterings are treated by Nelkin's kernel while scatterings from other nuclei are assumed to obey the free-gas scattering kernel. The isotropic return (white) boundary condition is applied directly by using the appropriate collision probabilities. Comparisons with alternate numerical methods show the validity of the present formulation. Comparisons with some experimental results indicate that the present formulation is capable of calculating disadvantage factors which are closer to the experimental results than alternative methods

  16. Multiband method for resonance self-shielding calculation of fuel assembly in arbitrary geometries

    International Nuclear Information System (INIS)

    Huang Weibin; Wu Hongchun; Cao Liangzhi; Yang Weiyan

    2009-01-01

    A formula to calculate the multiband parameters is derived based on the multiband method. Adopting the method combining two-band and three-band, and based on the WIMSD4-69 library, a code named RESCAL is developed. The validation shows that the results of RESCAL code are well in accordance with MCNP's, and the numerical errors meet the practical requirement. Due to the limitation of WIMSD4 69-group library and the method adopted to calculate multiband parameters, the precision of RESCAL code is highly affected by the ratio of water to uranium. (authors)

  17. The effective atomic numbers of some biomolecules calculated by two methods: A comparative study

    DEFF Research Database (Denmark)

    Manohara, S.R.; Hanagodimath, S.M.; Gerward, Leif

    2009-01-01

    The effective atomic numbers Z(eff) of some fatty acids and amino acids have been calculated by two numerical methods, a direct method and an interpolation method, in the energy range of 1 keV-20 MeV. The notion of Z(eff) is given a new meaning by using a modern database of photon interaction cross...... constant and equal to the mean atomic number of the material. Wherever possible, the calculated values of Z(eff) are compared with experimental data....

  18. Mixed layer depth calculation in deep convection regions in ocean numerical models

    Science.gov (United States)

    Courtois, Peggy; Hu, Xianmin; Pennelly, Clark; Spence, Paul; Myers, Paul G.

    2017-12-01

    Mixed Layer Depths (MLDs) diagnosed by conventional numerical models are generally based on a density difference with the surface (e.g., 0.01 kg.m-3). However, the temperature-salinity compensation and the lack of vertical resolution contribute to over-estimated MLD, especially in regions of deep convection. In the present work, we examined the diagnostic MLD, associated with the deep convection of the Labrador Sea Water (LSW), calculated with a simple density difference criterion. The over-estimated MLD led us to develop a new tool, based on an observational approach, to recalculate MLD from model output. We used an eddy-permitting, 1/12° regional configuration of the Nucleus for European Modelling of the Ocean (NEMO) to test and discuss our newly defined MLD. We compared our new MLD with that from observations, and we showed a major improvement with our new algorithm. To show the new MLD is not dependent on a single model and its horizontal resolution, we extended our analysis to include 1/4° eddy-permitting simulations, and simulations using the Modular Ocean Model (MOM) model.

  19. Numerical calculation of a sea water heta exchanger using Simulink softwear

    Science.gov (United States)

    Preda, A.; Popescu, L. L.; Popescu, R. S.

    2017-08-01

    To highlight the heat exchange taking place between seawater as primary agent and the working fluid (water, glycol or Freon) as secondary agent, I have used the Simulink softwear in order to creat a new sequence for numerical calculation of heat exchanging. For optimum heat transfer we opted for a counter movement. The model developed to view the dynamic behavior of the exchanger consists of four interconnected levelsess. In the simulations was found that a finer mesh of the whole exchanger lead to results much closer to reality. There have been various models meshing, starting from a single cell and then advancing noticed an improvement in resultsSimulations were made in both the summer and the winter, using as a secondary agent process water and glycol solution. Studying heat transfer that occurs in the primary exchanger of a heat pump, having the primary fluid sea water with this program, we get the data plausible and worthy of consideration. Inserting into the program, the seasonal water temperatures of Black Sea water layers, we get a encouraging picture about storage capacity and heat transfer of sea water.

  20. Rigid inclusions-Comparison between analytical and numerical methods

    International Nuclear Information System (INIS)

    Gomez Perez, R.; Melentijevic, S.

    2014-01-01

    This paper compares different analytical methods for analysis of rigid inclusions with finite element modeling. First of all, the load transfer in the distribution layer is analyzed for its different thicknesses and different inclusion grids to define the range between results obtained by analytical and numerical methods. The interaction between the soft soil and the inclusion in the estimation of settlements is studied as well. Considering different stiffness of the soft soil, settlements obtained analytical and numerically are compared. The influence of the soft soil modulus of elasticity on the neutral point depth was also performed by finite elements. This depth has a great importance for the definition of the total length of rigid inclusion. (Author)

  1. Second GAMM-conference on numerical methods in fluid mechanics

    International Nuclear Information System (INIS)

    Hirschel, E.H.; Geller, W.

    1977-01-01

    Proceedings of the Second GAMM-Conference on Numerical Methods in Fluid Mechanics held at the DFVLR, Koeln, October 11 to 13, 1977. The conference was attended by approximately 100 participants from 13 European countries representing quite different fields ranging from Aerodynamics to Nuclear Energy. At the meeting 34 papers were presented, many of them concerned with basic problems in the field. It was well demonstrated that Numerical Methods in Fluid Mechanics do not only serve as means for the computation of flow fields but also as tools in the analysis of fluid mechanical phenomena, a role of large future importance if one considers the complexity especially of three-dimensional flows. (orig./RW) [de

  2. Numerical method for solving stochastic differential equations with dichotomous noise.

    Science.gov (United States)

    Kim, Changho; Lee, Eok Kyun; Talkner, Peter

    2006-02-01

    We propose a numerical method for solving stochastic differential equations with dichotomous Markov noise. The numerical scheme is formulated such that (i) the stochastic formula used follows the Stratonovich-Taylor form over the entire range of noise correlation times, including the Gaussian white noise limit; and (ii) the method is readily applicable to dynamical systems driven by arbitrary types of noise, provided there exists a way to describe the random increment of the stochastic process expressed in the Stratonovich-Taylor form. We further propose a simplified Taylor scheme that significantly reduces the computation time, while still satisfying the moment properties up to the required order. The accuracies and efficiencies of the proposed algorithms are validated by applying the schemes to two prototypical model systems that possess analytical solutions.

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

    International Nuclear Information System (INIS)

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

    2015-01-01

    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. (paper)

  4. A New Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method

    Directory of Open Access Journals (Sweden)

    Marco Gonzalez

    Full Text Available Abstract The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs. The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has become very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacement-based methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes.

  5. Numerical solution of the problem of selecting the optimum method of operating oil wells

    Energy Technology Data Exchange (ETDEWEB)

    Skryago, A.M.; Chirikov, L.I.; Fridman, G.Sh.; Kolokolov, A.A.; Panteleyev, G.V.; Terent' yev, S.A.; Zabudskiy, G.G.

    1981-01-01

    A mathematical model is studied for selecting the optimum method of operating the wells of an oil field, which is a linear Boolean programming problem. It is shown that this problem is equivalent to the generalized packet problem and a single product variant model of sectoral planning. Numerical calculations on the computer using as the initial problem the modified method of E. Balash, for the generalized packet problem the method of M.F. Kazakovaya, and the single product variant problem of sectoral planning the method of A. Ye. Bakhtin, show the greatest effectiveness for the problem studied of A. Ye. Bakhtin's method.

  6. On Some Recent Developments in Numerical Methods for Relativistic MHD

    CERN Document Server

    Komissarov, S S

    2006-01-01

    In recent years we have witnessed the rapid development of new numerical methods for Relativistic Magnetohydrodynamics. It is not going to be long before they become standard computational tools available to any keen researcher interested in relativistic astrophysics. In this paper I provide a very broad and yet brief review that is intended to help those who are not yet expert in the field, but who wish to become one in the future.

  7. Numerical simulation of boundary layers. Part 1: Weak formulation and numerical method

    Science.gov (United States)

    Spalart, P. R.

    1986-01-01

    A numerical method designed to solve the time-dependent, three-dimensional, incompressible Navier-Stokes equations in boundary layers is presented. The fluid domain is the half-space over a flat plate, and periodic conditions are applied in the horizontal directions. The discretization is spectral. The basis functions are divergence-free and a weak formulation of the momentum equation is used, which eliminates the pressure term. An exponential mapping and Jacobi polynomials are used in the semi-infinite direction, with the irrotational component receiving special treatment. Issues related to the accuracy, stability and efficiency of the method are discussed. Very fast convergence is demonstrated on some model problems with smooth solutions. The method has also been shown to accurately resolve the fine scales of transitional and turbulent boundary layers.

  8. Design and Numerical Calculation of Variable Test Section for Small Supersonic Wind Tunnel

    Directory of Open Access Journals (Sweden)

    Václav DVOŘÁK

    2010-12-01

    Full Text Available The paper is concerned with numerical modelling of transition in a separated boundary layer. The model of laminar/turbulent transition is based on the combination of empirical terms determining position of the transition and averaged Navier – Stokes equations closed by the k – ω SST turbulence model. The model of transition is applied in computation of 2D flow past NACA63A421 airfoil. Computation is performed using the commercial code ANSYS Fluent 6.3.26, in which the transition method is implemented as a User-Defined-Function. Computed distributions of Cp along the airfoil are verified by comparison with experimental data, which were obtained by measurements in a closed circuit wind tunnel at the constant Reynolds number and several angles of attack. Comparisons prove applicability of the implemented transitional model.

  9. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

    Science.gov (United States)

    Khoromskaia, Venera; Khoromskij, Boris N

    2015-12-21

    We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

  10. Calculation method for gamma dose rates from Gaussian puffs

    International Nuclear Information System (INIS)

    Thykier-Nielsen, S.; Deme, S.; Lang, E.

    1995-06-01

    The Lagrangian puff models are widely used for calculation of the dispersion of releases to the atmosphere. Basic output from such models is concentration of material in the air and on the ground. The most simple method for calculation of the gamma dose from the concentration of airborne activity is based on the semi-infinite cloud model. This method is however only applicable for puffs with large dispersion parameters, i.e. for receptors far away from the release point. The exact calculation of the cloud dose using volume integral requires large computer time usually exceeding what is available for real time calculations. The volume integral for gamma doses could be approximated by using the semi-infinite cloud model combined with correction factors. This type of calculation procedure is very fast, but usually the accuracy is poor because only a few of the relevant parameters are considered. A multi-parameter method for calculation of gamma doses is described here. This method uses precalculated values of the gamma dose rates as a function of E γ , σ y , the asymmetry factor - σ y /σ z , the height of puff center - H and the distance from puff center R xy . To accelerate the calculations the release energy, for each significant radionuclide in each energy group, has been calculated and tabulated. Based on the precalculated values and suitable interpolation procedure the calculation of gamma doses needs only short computing time and it is almost independent of the number of radionuclides considered. (au) 2 tabs., 15 ills., 12 refs

  11. Comparison of electrical conductivity calculation methods for natural waters

    Science.gov (United States)

    McCleskey, R. Blaine; Nordstrom, D. Kirk; Ryan, Joseph N.

    2012-01-01

    The capability of eleven methods to calculate the electrical conductivity of a wide range of natural waters from their chemical composition was investigated. A brief summary of each method is presented including equations to calculate the conductivities of individual ions, the ions incorporated, and the method's limitations. The ability of each method to reliably predict the conductivity depends on the ions included, effective accounting of ion pairing, and the accuracy of the equation used to estimate the ionic conductivities. The performances of the methods were evaluated by calculating the conductivity of 33 environmentally important electrolyte solutions, 41 U.S. Geological Survey standard reference water samples, and 1593 natural water samples. The natural waters tested include acid mine waters, geothermal waters, seawater, dilute mountain waters, and river water impacted by municipal waste water. The three most recent conductivity methods predict the conductivity of natural waters better than other methods. Two of the recent methods can be used to reliably calculate the conductivity for samples with pH values greater than about 3 and temperatures between 0 and 40°C. One method is applicable to a variety of natural water types with a range of pH from 1 to 10, temperature from 0 to 95°C, and ionic strength up to 1 m.

  12. Prediction of Deepwater FPSO responses using different numerical analysis methods

    Science.gov (United States)

    Guan, Matthew; Osman, Montasir; Ng, Cheng Yee

    2018-03-01

    The limitations of existing wave basins present a significant challenge when modelling offshore deepwater systems, particularly due to the basin's relatively shallow depth. Numerical simulation thus becomes valuable in predicting its behaviour during operation at sea. The coupled dynamic analysis is preferred over the traditional quasi-static method, as the former enables the inclusion of damping and added mass properties of the complete mooring line system, which becomes increasingly prominent at greater water depths. This paper investigates the motions and mooring line tensions of a turret moored Floating Production Storage Offloading (FPSO) platform using three numerical models, i.e. a dynamic system, quasi-static system and linear spring system subjected to unidirectional random wave condition. Analysis is carried out using a commercial software AQWA. The first two numerical models utilise a complete system of the same setup and configuration, while the linear spring system substitutes the mooring lines with equivalent linear springs and attempts to match the total mooring line restoring forces with that of the coupled dynamic analysis. The study demonstrates the significance of coupled dynamic analysis on the responses of an FPSO in deepwater. The numerical model of the FPSO is validated against the results of a published work.

  13. METHOD FOR NUMERICAL MODELING OF UNSTEADY SEPARATED FLOW AROUND AIRFOILS MOVING CLOSE TO FLAT SCREEN

    Directory of Open Access Journals (Sweden)

    V. Pogrebnaya Tamara

    2017-01-01

    Full Text Available In this article an attempt is made to explain the nature of differences in measurements of forces and moments, which influence an aircraft at take-off and landing when testing on different types of stands. An algorithm for numerical simulation of unsteady separated flow around airfoil is given. The algorithm is based on the combination of discrete vortex method and turbulent boundary layer equations. An unsteady flow separation modeling has been used. At each interval vortex method was used to calculate the potential flow around airfoils located near a screen. Calculated pressures and velocities were then used in boundary layer calculations to determine flow separation points and separated vortex in- tensities. After that calculation were made to determine free vortex positions to next time step and the process was fulfilled for next time step. The proposed algorithm allows using numeric visualization to understand physical picture of flow around airfoil moving close to screen. Three different ways of flow modeling (mirror method, fixed or movable screens were tested. In each case the flow separation process, which determines pressure distribution over airfoil surface and influ- ences aerodynamic performance, was viewed. The results of the calculations showed that at low atitudes of airfoil over screen mirror method over predicts lift force compared with movable screen, while fixed screen under predicts it. The data obtained can be used when designing equipment for testing in wind tunnels.

  14. An analytical transport theory method for calculating flux distribution in slab cells

    International Nuclear Information System (INIS)

    Abdel Krim, M.S.

    2001-01-01

    A transport theory method for calculating flux distributions in slab fuel cell is described. Two coupled integral equations for flux in fuel and moderator are obtained; assuming partial reflection at moderator external boundaries. Galerkin technique is used to solve these equations. Numerical results for average fluxes in fuel and moderator and the disadvantage factor are given. Comparison with exact numerical methods, that is for total reflection moderator outer boundaries, show that the Galerkin technique gives accurate results for the disadvantage factor and average fluxes. (orig.)

  15. A numerical method for acoustic normal modes for shear flows

    Science.gov (United States)

    Porter, M. B.; Reiss, E. L.

    1985-05-01

    The normal modes and their propagation numbers for acoustic propagation in wave guides with flow are the eigenvectors and eigenvalues of a boundary value problem for a non-standard Sturm-Liouville problem. It is non-standard because it depends non-linearly on the eigenvalue parameter. (In the classical problem for ducts with no flow, the problem depends linearly on the eigenvalue parameter). In this paper a method is presented for the fast numerical solution of this problem. It is a generalization of a method that was developed for the classical problem. A finite difference method is employed that combines well known numerical techniques and a generalization of the Sturm sequence method to solve the resulting algebraic eigenvalue problem. Then a modified Richardson extrapolation method is used that dramatically increases the accuracy of the computed eigenvalues. The method is then applied to two problems. They correspond to acoustic propagation in the ocean in the presence of a current, and to acoustic propagation in shear layers over flat plates.

  16. Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

    Science.gov (United States)

    Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing

    2016-10-01

    The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.

  17. Calculation method for gamma-dose rates from spherical puffs

    International Nuclear Information System (INIS)

    Thykier-Nielsen, S.; Deme, S.; Lang, E.

    1993-05-01

    The Lagrangian puff-models are widely used for calculation of the dispersion of atmospheric releases. Basic output from such models are concentrations of material in the air and on the ground. The most simple method for calculation of the gamma dose from the concentration of airborne activity is based on semi-infinite cloud model. This method is however only applicable for points far away from the release point. The exact calculation of the cloud dose using the volume integral requires significant computer time. The volume integral for the gamma dose could be approximated by using the semi-infinite cloud model combined with correction factors. This type of calculation procedure is very fast, but usually the accuracy is poor due to the fact that the same correction factors are used for all isotopes. The authors describe a more elaborate correction method. This method uses precalculated values of the gamma-dose rate as a function of the puff dispersion parameter (δ p ) and the distance from the puff centre for four energy groups. The release of energy for each radionuclide in each energy group has been calculated and tabulated. Based on these tables and a suitable interpolation procedure the calculation of gamma doses takes very short time and is almost independent of the number of radionuclides. (au) (7 tabs., 7 ills., 12 refs.)

  18. Numerical Calculation of Transient Thermal Characteristics in Gas-Insulated Transmission Lines

    Directory of Open Access Journals (Sweden)

    Hongtao Li

    2013-11-01

    Full Text Available For further knowledge of the thermal characteristics in gas-insulated transmission lines (GILs installed above ground, a finite-element model coupling fluid field and thermal field is established, in which the corresponding assumptions and boundary conditions are given.  Transient temperature rise processes of the GIL under the conditions of variable ambient temperature, wind velocity and solar radiation are respectively investigated. Equivalent surface convective heat transfer coefficient and heat flux boundary conditions are updated in the analysis process. Unlike the traditional finite element methods (FEM, the variability of the thermal properties with temperature is considered. The calculation results are validated by the tests results reported in the literature. The conclusion provides method and theory basis for the knowledge of transient temperature rise characteristics of GILs in open environment.

  19. Application of nonparametric statistic method for DNBR limit calculation

    International Nuclear Information System (INIS)

    Dong Bo; Kuang Bo; Zhu Xuenong

    2013-01-01

    Background: Nonparametric statistical method is a kind of statistical inference method not depending on a certain distribution; it calculates the tolerance limits under certain probability level and confidence through sampling methods. The DNBR margin is one important parameter of NPP design, which presents the safety level of NPP. Purpose and Methods: This paper uses nonparametric statistical method basing on Wilks formula and VIPER-01 subchannel analysis code to calculate the DNBR design limits (DL) of 300 MW NPP (Nuclear Power Plant) during the complete loss of flow accident, simultaneously compared with the DL of DNBR through means of ITDP to get certain DNBR margin. Results: The results indicate that this method can gain 2.96% DNBR margin more than that obtained by ITDP methodology. Conclusions: Because of the reduction of the conservation during analysis process, the nonparametric statistical method can provide greater DNBR margin and the increase of DNBR margin is benefited for the upgrading of core refuel scheme. (authors)

  20. Numerical experiment on finite element method for matching data

    International Nuclear Information System (INIS)

    Tokuda, Shinji; Kumakura, Toshimasa; Yoshimura, Koichi.

    1993-03-01

    Numerical experiments are presented on the finite element method by Pletzer-Dewar for matching data of an ordinary differential equation with regular singular points by using model equation. Matching data play an important role in nonideal MHD stability analysis of a magnetically confined plasma. In the Pletzer-Dewar method, the Frobenius series for the 'big solution', the fundamental solution which is not square-integrable at the regular singular point, is prescribed. The experiments include studies of the convergence rate of the matching data obtained by the finite element method and of the effect on the results of computation by truncating the Frobenius series at finite terms. It is shown from the present study that the finite element method is an effective method for obtaining the matching data with high accuracy. (author)

  1. Meshless Methods for Numerical Solution of Partial Differential Equations

    Science.gov (United States)

    Li, Gang; Jin, Xiaozhong; Alum, N. R.

    A popular research topic in numerical methods recently has been the development of meshless methods as alternatives to the traditional finite element, finite volume, and finite difference methods. The traditional methods all require some connectivity knowledge a priori, such as the generation of a mesh, whereas the aim of meshless methods is to sprinkle only a set of points or nodes covering the computational domain, with no connectivity information required among the set of points. Multiphysics and multiscale analysis, which is a common requirement for microsystem technologies such as MEMS and Bio-MEMS, is radically simplified by meshless techniques as we deal with only nodes or points instead of a mesh. Meshless techniques are also appealing because of their potential in adaptive techniques, where a user can simply add more points in a particular region to obtain more accurate results.

  2. Linear augmented plane wave method for self-consistent calculations

    International Nuclear Information System (INIS)

    Takeda, T.; Kuebler, J.

    1979-01-01

    O.K. Andersen has recently introduced a linear augmented plane wave method (LAPW) for the calculation of electronic structure that was shown to be computationally fast. A more general formulation of an LAPW method is presented here. It makes use of a freely disposable number of eigenfunctions of the radial Schroedinger equation. These eigenfunctions can be selected in a self-consistent way. The present formulation also results in a computationally fast method. It is shown that Andersen's LAPW is obtained in a special limit from the present formulation. Self-consistent test calculations for copper show the present method to be remarkably accurate. As an application, scalar-relativistic self-consistent calculations are presented for the band structure of FCC lanthanum. (author)

  3. Optimization method for quantitative calculation of clay minerals in soil

    Indian Academy of Sciences (India)

    Therefore, we rec- ommend employing Matlab to solve equations of the kind discussed here. In conclusion, using optimization methods to calculate the clay mineral contents in soil is viable based on the chemical analysis data. Further stud- ies combining this method with X-ray diffraction, differential thermal, and infrared ...

  4. Use of the Local Variation Methods for Nuclear Design Calculations

    International Nuclear Information System (INIS)

    Zhukov, A.I.

    2006-01-01

    A new problem-solving method for steady-state equations, which describe neutron diffusion, is presented. The method bases on a variation principal for steady-state diffusion equations and direct search the minimum of a corresponding functional. Benchmark problem calculation for power of fuel assemblies show ∼ 2% relative accuracy

  5. Optimization method for quantitative calculation of clay minerals in soil

    Indian Academy of Sciences (India)

    In this study, an attempt was made to propose an optimization method for the quantitative determination of clay minerals in soil based on bulk chemical composition data. The fundamental principles and processes of the calculation are elucidated. Some samples were used for reliability verification of the method and the ...

  6. Efficient Calculation of Near Fields in the FDTD Method

    DEFF Research Database (Denmark)

    Franek, Ondrej

    2011-01-01

    When calculating frequency-domain near fields by the FDTD method, almost 50 % reduction in memory and CPU operations can be achieved if only E-fields are stored during the main time-stepping loop and H-fields computed later. An improved method of obtaining the H-fields from Faraday's Law...

  7. Approximating Sievert Integrals to Monte Carlo Methods to calculate ...

    African Journals Online (AJOL)

    Radiation dose rates along the transverse axis of a miniature P192PIr source were calculated using Sievert Integral (considered simple and inaccurate), and by the sophisticated and accurate Monte Carlo method. Using data obt-ained by the Monte Carlo method as benchmark and applying least squares regression curve ...

  8. A new method for the calculation of Sommerfeld screening ...

    Indian Academy of Sciences (India)

    A new method for the calculation of Sommerfeld screening parameter 1 in x-ray spectra. U D Misra S Chaturvedi. Research Articles ... earlier by Gokhale and Misra. The method brings out the constancy of 1(23)-1(1) in a natural way and may thus be regarded as providing theoretical explanation of the Hertz law.

  9. Ion cyclotron emission calculations using a 2D full wave numerical code

    International Nuclear Information System (INIS)

    Batchelor, D.B.; Jaeger, E.F.; Colestock, P.L.

    1987-01-01

    Measurement of radiation in the HF band due to cyclotron emission by energetic ions produced by fusion reactions or neutral beam injection promises to be a useful diagnostic on large devices which are entering the reactor regime of operation. A number of complications make the modelling and interpretation of such measurements difficult using conventional geometrical optics methods. In particular the long wavelength and lack of high directivity of antennas in this frequency regime make observation of a single path across the plasma into a viewing dump impractical. Pickup antennas effectively see the whole plasma and wall reflection effects are important. We have modified our 2D full wave ICRH code 2 to calculate wave fields due to a distribution of energetic ions in tokamak geometry. The radiation is modeled as due to an ensemble of localized source currents distributed in space. The spatial structure of the coherent wave field is then calculated including cyclotron harmonic damping as compared to the usual procedure of incoherently summing powers of individual radiators. This method has the advantage that phase information from localized radiating currents is globally retained so the directivity of the pickup antennas is correctly represented. Also standing waves and wall reflections are automatically included

  10. Investigation of CFD calculation method of a centrifugal pump with unshrouded impeller

    Science.gov (United States)

    Wu, Dazhuan; Yang, Shuai; Xu, Binjie; Liu, Qiaoling; Wu, Peng; Wang, Leqin

    2014-03-01

    Currently, relatively large errors are found in numerical results in some low-specific-speed centrifugal pumps with unshrouded impeller because the effect of clearances and holes are not accurately modeled. Establishing an accurate analytical model to improve performance prediction accuracy is therefore necessary. In this paper, a three-dimensional numerical simulation is conducted to predict the performance of a low-specific-speed centrifugal pump, and the modeling, numerical scheme, and turbulent selection methods are discussed. The pump performance is tested in a model pump test bench, and flow rate, head, power and efficiency of the pump are obtained. The effect of taking into consideration the back-out vane passage, clearance, and balance holes is analyzed by comparing it with experimental results, and the performance prediction methods are validated by experiments. The analysis results show that the pump performance can be accurately predicted by the improved method. Ignoring the back-out vane passage in the calculation model of unshrouded impeller is found to generate better numerical results. Further, the calculation model with the clearances and balance holes can obviously enhance the numerical accuracy. The application of disconnect interface can reduce meshing difficulty but increase the calculation error at the off-design operating point at the same time. Compared with the standard k-ɛ, renormalization group k-ɛ, and Spalart-Allmars models, the Realizable k-ɛ model demonstrates the fastest convergent speed and the highest precision for the unshrouded impeller flow simulation. The proposed modeling and numerical simulation methods can improve the performance prediction accuracy of the low-specific-speed centrifugal pumps, and the modeling method is especially suitable for the centrifugal pump with unshrouded impeller.

  11. New numerical method to study phase transitions and its applications

    International Nuclear Information System (INIS)

    Lee, Jooyoung; Kosterlitz, J.M.

    1991-11-01

    We present a powerful method of identifying the nature of transitions by numerical simulation of finite systems. By studying the finite size scaling properties of free energy barrier between competing states, we can identify unambiguously a weak first order transition even when accessible system sizes are L/ξ < 0.05 as in the five state Potts model in two dimensions. When studying a continuous phase transition we obtain quite accurate estimates of critical exponents by treating it as a field driven first order transition. The method has been successfully applied to various systems

  12. Integrated numerical methods for hypersonic aircraft cooling systems analysis

    Science.gov (United States)

    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.

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

    Energy Technology Data Exchange (ETDEWEB)

    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.

  14. A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method

    Directory of Open Access Journals (Sweden)

    Changqing Yang

    2012-01-01

    Full Text Available A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

  15. On the resolvents methods in quantum perturbation calculations

    International Nuclear Information System (INIS)

    Burzynski, A.

    1979-01-01

    This paper gives a systematic review of resolvent methods in quantum perturbation calculations. The case of discrete spectrum of hamiltonian is considered specially (in the literature this is the fewest considered case). The topics of calculations of quantum transitions by using of the resolvent formalism, quantum transitions between states from particular subspaces, the shifts of energy levels, are shown. The main ideas of stationary perturbation theory developed by Lippmann and Schwinger are considered too. (author)

  16. Method for dose calculation in intracavitary irradiation of endometrical carcinoma

    International Nuclear Information System (INIS)

    Zevrieva, I.F.; Ivashchenko, N.T.; Musapirova, N.A.; Fel'dman, S.Z.; Sajbekov, T.S.

    1979-01-01

    A method for dose calculation for the conditions of intracavitary gamma therapy of endometrial carcinoma using spherical and linear 60 Co sources was elaborated. Calculations of dose rates for different amount and orientation of spherical radiation sources and for different planes were made with the aid of BEhSM-4M computer. Dosimet were made with the aid of BEhSM-4M computer. Dosimetric study of dose fields was made using a phantom imitating the real conditions of irradiation. Discrepancies between experimental and calculated values are within the limits of the experiment accuracy

  17. Analytic-numerical method of determining the freezing front location

    Directory of Open Access Journals (Sweden)

    R. Grzymkowski

    2011-07-01

    Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic boundary problems with the moving boundary. Solution of such defined problem requires, most often, to use sophisticated numerical techniques and far advanced mathematical tools. Excellent illustration of the complexity of considered problems, as well as of the variety of approaches used for finding their solutions, gives the papers [1-4]. In the current paper, the authors present the, especially attractive from the engineer point of view, analytic-numerical method for finding the approximate solution of selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of the sought function describing the temperature field into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of the function defining the location of freezing front with the broken line, parameters of which are numerically determined.

  18. Sensitivity of solutions computed through the Asymptotic Numerical Method

    Science.gov (United States)

    Charpentier, Isabelle

    2008-10-01

    The Asymptotic Numerical Method (ANM) allows one to compute solution branches of sufficiently smooth non-linear PDE problems using truncated Taylor expansions. The Diamant approach of the ANM has been proposed for hiding definitively the differentiation aspects to the user. In this Note, this significant improvement in terms of genericity is exploited to compute the sensitivity of ANM solutions with respect to modelling parameters. The differentiation in the parameters is discussed at both the equation and code level to highlight the Automatic Differentiation (AD) purposes. A numerical example proves the interest of such techniques for a generic and efficient implementation of sensitivity computations. To cite this article: I. Charpentier, C. R. Mecanique 336 (2008).

  19. Numerical investigation of floating breakwater movement using SPH method

    Directory of Open Access Journals (Sweden)

    A. Najafi-Jilani

    2011-06-01

    Full Text Available In this work, the movement pattern of a floating breakwater is numerically analyzed using Smoothed Particle Hydrodynamic (SPH method as a Lagrangian scheme. At the seaside, the regular incident waves with varying height and period were considered as the dynamic free surface boundary conditions. The smooth and impermeable beach slope was defined as the bottom boundary condition. The effects of various boundary conditions such as incident wave characteristics, beach slope, and water depth on the movement of the floating body were studied. The numerical results are in good agreement with the available experimental data in the literature The results of the movement of the floating body were used to determine the transmitted wave height at the corresponding boundary conditions

  20. Application of a primitive variable Newton's method for the calculation of an axisymmetric laminar diffusion flame

    International Nuclear Information System (INIS)

    Xu, Yuenong; Smooke, M.D.

    1993-01-01

    In this paper we present a primitive variable Newton-based solution method with a block-line linear equation solver for the calculation of reacting flows. The present approach is compared with the stream function-vorticity Newton's method and the SIMPLER algorithm on the calculation of a system of fully elliptic equations governing an axisymmetric methane-air laminar diffusion flame. The chemical reaction is modeled by the flame sheet approximation. The numerical solution agrees well with experimental data in the major chemical species. The comparison of three sets of numerical results indicates that the stream function-vorticity solution using the approximate boundary conditions reported in the previous calculations predicts a longer flame length and a broader flame shape. With a new set of modified vorticity boundary conditions, we obtain agreement between the primitive variable and stream function-vorticity solutions. The primitive variable Newton's method converges much faster than the other two methods. Because of much less computer memory required for the block-line tridiagonal solver compared to a direct solver, the present approach makes it possible to calculate multidimensional flames with detailed reaction mechanisms. The SIMPLER algorithm shows a slow convergence rate compared to the other two methods in the present calculation

  1. The numerical calculation of hydrological processes in the coastal zone of the Black Sea region in the city of Poti

    Science.gov (United States)

    Saghinadze, Ivane; Pkhakadze, Manana

    2016-04-01

    (The article was published with support of the Sh. Rustaveli National Science Foundation) The serious environmental problems started in Poti after transfer of the main flow of the river Rioni to the north. As a result the flooding of the city stopped, but the reduction of water consumption in the city channel, caused a decrease of the sediments carried away by the river, what leads to coastal erosion. The coast changes are connected with the movement of the waves and currents in the coastal part of the sea. In the paper, the three-dimensional mathematical model of sediment transport and coastal zone lithodynamics is developed. The finite element formulations for the problems of wave modes, coastal currents, sediment transport and evolution of the coastal zone of the sea, are given. The numerical algorithms, implemented in the form of software. Programs are allowing to bring the solutions of the tasks to numerical results. The numerical modeling was developed in three stages. In the first stage the topography of the coast and the initial geometry of the structures are considered as an input parameters. Then, coastal wave field is calculated for the conditions prescribed in the initial wave. In the second stage, the calculated wave field is used to estimate the spatial distribution of the radiation stresses near-bottom orbital velocity. In the third stage the coastal wave fields and flow fields are used in the sub-models of sediment transport and changes in the topography of the coast. In the numerical solution of basic equations of motion of the waves, coastal currents and changes in sea bottom topography we use: finite element, finite difference methods and the method of upper relaxation, Crank-Nicolson scheme. As an example, we are giving the results of research of the wave regime in the coastal area of the city of Poti (700X600m) adjacent to the port of Poti. The bottom profile, in this area is rather complicated. During the calculations of the average rise of

  2. Transmission calculation by empirical numerical model and Monte Carlo simulation in high energy proton radiography of thick objects

    Science.gov (United States)

    Zheng, Na; Xu, Hai-Bo

    2015-10-01

    An empirical numerical model that includes nuclear absorption, multiple Coulomb scattering and energy loss is presented for the calculation of transmission through thick objects in high energy proton radiography. In this numerical model the angular distributions are treated as Gaussians in the laboratory frame. A Monte Carlo program based on the Geant4 toolkit was developed and used for high energy proton radiography experiment simulations and verification of the empirical numerical model. The two models are used to calculate the transmission fraction of carbon and lead step-wedges in proton radiography at 24 GeV/c, and to calculate radial transmission of the French Test Object in proton radiography at 24 GeV/c with different angular cuts. It is shown that the results of the two models agree with each other, and an analysis of the slight differences is given. Supported by NSAF (11176001) and Science and Technology Developing Foundation of China Academy of Engineering Physics (2012A0202006)

  3. Intercomparison of extremal wave analysis methods using numerically simulated data

    Energy Technology Data Exchange (ETDEWEB)

    Goda, Y.; Hawkes, P.; Mansard, E.; Martin, M.J.; Mathiesen, M.; Peltier, E.; Thompson, E.; Vledder, G. van.

    1993-07-01

    Several methods of extreme wave analysis were applied to 1000 samples of numerically simulated data for evaluation of their performance in the estimation of return wave heights. The Weibull distribution with the shape parameter k=1.4 was selected as the parent population, and the FT-I, FT-II and Weibull distributions were fitted to the samples by the Methods of Moments, Least Squares, and Maximum Likelihood. The mean value of the estimated return wave heights was almost the same as the true value, but their statistical deviations were large owing to the sampling variability. For uncensored samples, the Maximum Likelihood Method performed well, but its performance for censored samples was not much different from the other methods. 11 refs., 2 figs., 2 tabs.

  4. Numerical methods for optimal control problems with state constraints

    CERN Document Server

    Pytlak, Radosław

    1999-01-01

    While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.

  5. Numerical method for gas dynamics combining characteristic and conservation concepts

    Science.gov (United States)

    Coakley, T. J.

    1981-01-01

    An efficient implicit numerical method that solves the compressible Navier-Stokes equations in arbitrary curvilinear coordinates by the finite-volume technique is presented. An intrinsically dissipative difference scheme and a fully implicit treatment of boundary conditions, based on characteristic and conservation concepts, are used to improve stability and accuracy. Efficiency is achieved by using a diagonal form of the implicit algorithm and spatially varying time-steps. Comparisons of various schemes and methods are presented for one- and two-dimensional flows, including transonic separated flow past a thick circular-arc airfoil in a channel. The new method is equal to or better than a version of MacCormack's hybrid method in accuracy and it converges to a steady state up to an order of magnitude faster.

  6. METHOD OF CALCULATING THE OPTIMAL HEAT EMISSION GEOTHERMAL WELLS

    Directory of Open Access Journals (Sweden)

    A. I. Akaev

    2015-01-01

    Full Text Available This paper presents a simplified method of calculating the optimal regimes of the fountain and the pumping exploitation of geothermal wells, reducing scaling and corrosion during operation. Comparative characteristics to quantify the heat of formation for these methods of operation under the same pressure at the wellhead. The problem is solved graphic-analytical method based on a balance of pressure in the well with the heat pump. 

  7. Advanced numerical methods in mesh generation and mesh adaptation

    Energy Technology Data Exchange (ETDEWEB)

    Lipnikov, Konstantine [Los Alamos National Laboratory; Danilov, A [MOSCOW, RUSSIA; Vassilevski, Y [MOSCOW, RUSSIA; Agonzal, A [UNIV OF LYON

    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

  8. Comparison of different methods of calculating CT radiation effective dose in children.

    Science.gov (United States)

    Newman, Beverley; Ganguly, Arundhuti; Kim, Jee-Eun; Robinson, Terry

    2012-08-01

    CT radiation dose is a subject of intense interest and concern, especially in children. Effective dose, a summation of whole-body exposure weighted by specific organ sensitivities, is most often used to compute and compare radiation dose; however, there is little standardization, and there are numerous different methods of calculating effective dose. This study compares five such methods in a group of children undergoing routine chest CT and explores their advantages and pitfalls. Patient data from 120 pediatric chest CT examinations were retrospectively used to calculate effective dose: two scanner dose-length product (DLP) methods using published sets of conversion factors by Shrimpton and Deak, the imaging performance and assessment of CT (ImPact) calculator method, the Alessio online calculator, and the Huda method. The Huda method mean effective dose (4.4 ± 2.2 mSv) and Alessio online calculator (5.2 ± 2.8 mSv) yielded higher mean numbers for effective dose than both DLP calculations (Shrimpton, 3.65 ± 1.8 mSv, and Deak, 3.2 ± 1.5 mSv) as well as the ImPact calculator effective dose (3.4 ± 1.7 mSv). Mean differences ranged from 10.2% ± 10.1% lower to 28% ± 37.3% higher than the Shrimpton method (used as the standard for comparison). Differences were more marked at 120 kVp than at 80 or 100 kVp and varied at different ages. Concordance coefficients relative to the Shrimpton DLP method were Deak DLP, 0.907; Alessio online calculator, 0.735; ImPact calculator, 0.926; and Huda, 0.777. Different methods of computing effective dose for pediatric CT produce varying results. The method used must be clearly described to allay confusion about documenting and communicating dose for archiving as well as comparative research purposes.

  9. Efficient methods for time-absorption (α) eigenvalue calculations

    International Nuclear Information System (INIS)

    Hill, T.R.

    1983-01-01

    The time-absorption eigenvalue (α) calculation is one of the options found in most discrete-ordinates transport codes. Several methods have been developed at Los Alamos to improve the efficiency of this calculation. Two procedures, based on coarse-mesh rebalance, to accelerate the α eigenvalue search are derived. A hybrid scheme to automatically choose the more-effective rebalance method is described. The α rebalance scheme permits some simple modifications to the iteration strategy that eliminates many unnecessary calculations required in the standard search procedure. For several fast supercritical test problems, these methods resulted in convergence with one-fifth the number of iterations required for the conventional eigenvalue search procedure

  10. Nuclear Structure Calculations with Coupled Cluster Methods from Quantum Chemistry

    CERN Document Server

    Dean, D.J.; Hagen, G.; Hjorth-Jensen, M.; Kowalski, K.; Papenbrock, T.; Piecuch, P.; Wloch, M.

    2005-01-01

    We present several coupled-cluster calculations of ground and excited states of 4He and 16O employing methods from quantum chemistry. A comparison of coupled cluster results with the results of exact diagonalization of the hamiltonian in the same model space and other truncated shell-model calculations shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei, with much less computational effort than traditional large-scale shell-model approaches. Unless truncations are made, for nuclei like 16O, full-fledged shell-model calculations with four or more major shells are not possible. However, these and even larger systems can be studied with the coupled cluster methods due to the polynomial rather than factorial scaling inherent in standard shell-model studies. This makes the coupled cluster approaches, developed in quantum chemistry, viable methods for describing weakly bound systems of interest for future nuclear facilities...

  11. Comparison between ASHRAE and ISO thermal transmittance calculation methods

    DEFF Research Database (Denmark)

    Blanusa, Petar; Goss, William P.; Roth, Hartwig

    2007-01-01

    . The fenestration thermal transmittance calculations analyses presented in this paper show that small differences exist between the calculated thermal transmittance values produced by the ISO and ASHRAE methods. The results also show that the overall thermal transmittance difference between the two methodologies...... decreases as the total window area (glazing plus frame) increases. Thus, the resulting difference in thermal transmittance values for the two methods is negligible for larger windows. This paper also shows algebraically that the differences between the ISO and ASHRAE methods turn out to be due to the way......The intent of this paper is to describe and compare the two different two-dimensional frame/spacer heat transfer calculation methodologies used in North America (FRAME [EEL. The FRAMEplus Toolkit for Heat Transfer Assessment of Building Components, Version 3.0, Enermodal Engineering, Kichener...

  12. RCS Leak Rate Calculation with High Order Least Squares Method

    International Nuclear Information System (INIS)

    Lee, Jeong Hun; Kang, Young Kyu; Kim, Yang Ki

    2010-01-01

    As a part of action items for Application of Leak before Break(LBB), RCS Leak Rate Calculation Program is upgraded in Kori unit 3 and 4. For real time monitoring of operators, periodic calculation is needed and corresponding noise reduction scheme is used. This kind of study was issued in Korea, so there have upgraded and used real time RCS Leak Rate Calculation Program in UCN unit 3 and 4 and YGN unit 1 and 2. For reduction of the noise in signals, Linear Regression Method was used in those programs. Linear Regression Method is powerful method for noise reduction. But the system is not static with some alternative flow paths and this makes mixed trend patterns of input signal values. In this condition, the trend of signal and average of Linear Regression are not entirely same pattern. In this study, high order Least squares Method is used to follow the trend of signal and the order of calculation is rearranged. The result of calculation makes reasonable trend and the procedure is physically consistence

  13. Multi-scale calculation based on dual domain material point method combined with molecular dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Dhakal, Tilak Raj [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-02-27

    This dissertation combines the dual domain material point method (DDMP) with molecular dynamics (MD) in an attempt to create a multi-scale numerical method to simulate materials undergoing large deformations with high strain rates. In these types of problems, the material is often in a thermodynamically non-equilibrium state, and conventional constitutive relations are often not available. In this method, the closure quantities, such as stress, at each material point are calculated from a MD simulation of a group of atoms surrounding the material point. Rather than restricting the multi-scale simulation in a small spatial region, such as phase interfaces, or crack tips, this multi-scale method can be used to consider non-equilibrium thermodynamic e ects in a macroscopic domain. This method takes advantage that the material points only communicate with mesh nodes, not among themselves; therefore MD simulations for material points can be performed independently in parallel. First, using a one-dimensional shock problem as an example, the numerical properties of the original material point method (MPM), the generalized interpolation material point (GIMP) method, the convected particle domain interpolation (CPDI) method, and the DDMP method are investigated. Among these methods, only the DDMP method converges as the number of particles increases, but the large number of particles needed for convergence makes the method very expensive especially in our multi-scale method where we calculate stress in each material point using MD simulation. To improve DDMP, the sub-point method is introduced in this dissertation, which provides high quality numerical solutions with a very small number of particles. The multi-scale method based on DDMP with sub-points is successfully implemented for a one dimensional problem of shock wave propagation in a cerium crystal. The MD simulation to calculate stress in each material point is performed in GPU using CUDA to accelerate the

  14. The new high resolution method of Godunov`s type for 3D viscous flow calculations

    Energy Technology Data Exchange (ETDEWEB)

    Yershov, S.V.; Rusanov, A.V. [Ukranian National Academy of Sciences, Kahrkov (Ukraine)

    1996-12-31

    The numerical method is suggested for the calculations of the 3D viscous compressible flows described by the thin-layer Reynolds-averaged Navier-Stokes equations. The method is based on the Godunov`s finite-difference scheme and it uses the ENO reconstruction suggested by Harten to achieve the uniformly high-order accuracy. The computational efficiency is provided with the simplified multi grid approach and the implicit step written in {delta} -form. The turbulent effects are simulated with the Baldwin - Lomax turbulence model. The application package FlowER is developed to calculate the 3D turbulent flows within complex-shape channels. The numerical results for the 3D flow around a cylinder and through the complex-shaped channels show the accuracy and the reliability of the suggested method. (author)

  15. Calculation of foundation response to spatially varying ground motion by finite element method

    International Nuclear Information System (INIS)

    Wang, F.; Gantenbein, F.

    1995-01-01

    This paper presents a general method to compute the response of a rigid foundation of arbitrary shape resting on a homogeneous or multilayered elastic soil when subjected to a spatially varying ground motion. The foundation response is calculated from the free-field ground motion and the contact tractions between the foundation and the soil. The spatial variation of ground motion in this study is introduced by a coherence function and the contact tractions are obtained numerically using the Finite Element Method in the process of calculating the dynamic compliance of the foundation. Applications of this method to a massless rigid disc supported on an elastic half space and to that founded on an elastic medium consisting of a layer of constant thickness supported on an elastic half space are described. The numerical results obtained are in very good agreement with analytical solutions published in the literature. (authors). 5 refs., 8 figs

  16. Applying multi-resolution numerical methods to geodynamics

    Science.gov (United States)

    Davies, David Rhodri

    Computational models yield inaccurate results if the underlying numerical grid fails to provide the necessary resolution to capture a simulation's important features. For the large-scale problems regularly encountered in geodynamics, inadequate grid resolution is a major concern. The majority of models involve multi-scale dynamics, being characterized by fine-scale upwelling and downwelling activity in a more passive, large-scale background flow. Such configurations, when coupled to the complex geometries involved, present a serious challenge for computational methods. Current techniques are unable to resolve localized features and, hence, such models cannot be solved efficiently. This thesis demonstrates, through a series of papers and closely-coupled appendices, how multi-resolution finite-element methods from the forefront of computational engineering can provide a means to address these issues. The problems examined achieve multi-resolution through one of two methods. In two-dimensions (2-D), automatic, unstructured mesh refinement procedures are utilized. Such methods improve the solution quality of convection dominated problems by adapting the grid automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. Thermal and thermo-chemical validation tests illustrate that the technique is robust and highly successful, improving solution accuracy whilst increasing computational efficiency. These points are reinforced when the technique is applied to geophysical simulations of mid-ocean ridge and subduction zone magmatism. To date, successful goal-orientated/error-guided grid adaptation techniques have not been utilized within the field of geodynamics. The work included herein is therefore the first geodynamical application of such methods. In view of the existing three-dimensional (3-D) spherical mantle dynamics codes, which are built upon a quasi-uniform discretization of the sphere and closely coupled

  17. Introduction to quantum calculation methods in high resolution NMR; Introduction aux methodes quantiques de calcul en RMN de haute resolution

    Energy Technology Data Exchange (ETDEWEB)

    Goldman, M

    1996-12-31

    New techniques as for instance the polarization transfer, the coherence with several quanta and the double Fourier transformation have appeared fifteen years ago. These techniques constitute a considerable advance in NMR. Indeed, they allow to study more complex molecules than it was before possible. But with these advances, the classical description of the NMR is not enough to understand precisely the physical phenomena induced by these methods. It is then necessary to resort to quantum calculation methods. The aim of this work is to present these calculation methods. After some recalls of quantum mechanics, the author describes the NMR with the density matrix, reviews the main methods of double Fourier transformation and then gives the principle of the relaxation times calculation. (O.M.)

  18. Theoretical description and numerical calculations of significant three-dimensional magnetic field configurations

    Energy Technology Data Exchange (ETDEWEB)

    Mierau, Anna; Weiland, Thomas [Technische Universitaet Darmstadt (DE). Institut fuer Theorie Elektromagnetischer Felder (TEMF); Schnizer, Pierre; Fischer, Egbert [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany); Akishin, Pavel [JINR, Dubna (Russian Federation)

    2010-07-01

    The heavy ion synchrotron SIS100, the core component of the Facility of Antiproton and Ion Research will accelerate high current ion beams of up to U{sup 27+}. For operating such a machine the static and transient magnetic field quality must be fully understood. This is also necessary to keep the beam losses well below acceptable limits and to prepare a sound strategy for high resolution magnetic measurements and data analysis. Challenging preconditions to perform such work are to find a proper description for the non. Cartesian symmetry of the magnets, most important for curved dipoles with elliptical apertures. We describe the parameterisation methods using elliptic and toroidal multipoles and summarise comparing the calculated to the measured field quality.

  19. A new family of time integration methods for heat conduction problems using numerical green's functions

    Science.gov (United States)

    Loureiro, F. S.; Mansur, Webe Joao

    2009-09-01

    This paper is concerned with the formulation and numerical implementation of a new class of time integration schemes applied to linear heat conduction problems. The temperature field at any time level is calculated in terms of the numerical Green’s function matrix of the model problem by considering an analytical time integral equation. After spatial discretization by the finite element method, the Green’s function matrix which transfers solution from t to t + Δ t is explicitly computed in nodal coordinates using efficient implicit and explicit Runge-Kutta methods. It is shown that the stability and the accuracy of the proposed method are highly improved when a sub-step procedure is used to calculate recursively the Green’s function matrix at the end of the first time step. As a result, with a suitable choice of the number of sub-steps, large time steps can be used without degenerating the numerical solution. Finally, the effectiveness of the present methodology is demonstrated by analyzing two numerical examples.

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

    Science.gov (United States)

    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.

  1. Comparing numerical methods for the solutions of the Chen system

    International Nuclear Information System (INIS)

    Noorani, M.S.M.; Hashim, I.; Ahmad, R.; Bakar, S.A.; Ismail, E.S.; Zakaria, A.M.

    2007-01-01

    In this paper, the Adomian decomposition method (ADM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the classical fourth-order Runge-Kutta (RK4) numerical solutions are made. In particular we look at the accuracy of the ADM as the Chen system changes from a non-chaotic system to a chaotic one. To highlight some computational difficulties due to a high Lyapunov exponent, a comparison with the Lorenz system is given

  2. THE DESIGN OF AXIAL PUMP ROTORS USING THE NUMERICAL METHODS

    Directory of Open Access Journals (Sweden)

    Ali BEAZIT

    2010-06-01

    Full Text Available The researches in rotor theory, the increasing use of computers and the connection between design and manufacturing of rotors, have determined the revaluation and completion of classical rotor geometry. This paper presents practical applications of mathematical description of rotor geometry. A program has been created to describe the rotor geometry for arbitrary shape of the blade. The results can be imported by GAMBIT - a processor for geometry with modeling and mesh generations, to create a mesh needed in hydrodynamics analysis of rotor CFD. The results obtained are applicable in numerical methods and are functionally convenient for CAD/CAM systems.

  3. Numerical integration for ab initio many-electron self energy calculations within the GW approximation

    International Nuclear Information System (INIS)

    Liu, Fang; Lin, Lin; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F.; Sharifzadeh, Sahar; Jornada, Felipe H. da; Deslippe, Jack; Yang, Chao

    2015-01-01

    We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies

  4. Numerical calculation of unsteady turbulent heat transfer in a circular tube considering for heat dissipation in a wale

    International Nuclear Information System (INIS)

    Groshev, A.I.; Slobodchuk, V.I.

    1986-01-01

    The results of numerical calculation of the conjugated problem of convective heat transfer under unsteady conditions are presented. The equations describing heat transfer take into account longitudinal heat diffusion in liquid and in a wall. The formulae for calculating local heat flows at the wall-liquid surface in the case of an arbitrary law of temperature variation at the outer wall surface along the channel length are proposed for steady-state heat transfer conditions

  5. Numerical Methods for Plate Forming by Line Heating

    DEFF Research Database (Denmark)

    Clausen, Henrik Bisgaard

    2000-01-01

    Line heating is the process of forming originally flat plates into a desired shape by means of heat treatment. Parameter studies are carried out on a finite element model to provide knowledge of how the process behaves with varying heating conditions. For verification purposes, experiments are ca...... are carried out; one set of experiments investigates the actual heat flux distribution from a gas torch and another verifies the validty of the FE calculations. Finally, a method to predict the heating pattern is described....

  6. Development and application of advanced methods for electronic structure calculations

    DEFF Research Database (Denmark)

    Schmidt, Per Simmendefeldt

    ground state energies, is used to calculate accurate adsorption energies for a wide range of reactions. The results are in good agreement with experimental values, where available. Additionally, a database consisting of 200 highly accurate adsorption energies is constructed to benchmark the accuracy......This thesis relates to improvements and applications of beyond-DFT methods for electronic structure calculations that are applied in computational material science. The improvements are of both technical and principal character. The well-known GW approximation is optimized for accurate calculations...... of electronic excitations in two-dimensional materials by exploiting exact limits of the screened Coulomb potential. This approach reduces the computational time by an order of magnitude, enabling large scale applications. The GW method is further improved by including so-called vertex corrections. This turns...

  7. Comparison of organ dosimetry methods and effective dose calculation methods for paediatric CT.

    Science.gov (United States)

    Brady, Z; Cain, T M; Johnston, P N

    2012-06-01

    Computed tomography (CT) is the single biggest ionising radiation risk from anthropogenic exposure. Reducing unnecessary carcinogenic risks from this source requires the determination of organ and tissue absorbed doses to estimate detrimental stochastic effects. In addition, effective dose can be used to assess comparative risk between exposure situations and facilitate dose reduction through optimisation. Children are at the highest risk from radiation induced carcinogenesis and therefore dosimetry for paediatric CT recipients is essential in addressing the ionising radiation health risks of CT scanning. However, there is no well-defined method in the clinical environment for routinely and reliably performing paediatric CT organ dosimetry and there are numerous methods utilised for estimating paediatric CT effective dose. Therefore, in this study, eleven computational methods for organ dosimetry and/or effective dose calculation were investigated and compared with absorbed doses measured using thermoluminescent dosemeters placed in a physical anthropomorphic phantom representing a 10 year old child. Three common clinical paediatric CT protocols including brain, chest and abdomen/pelvis examinations were evaluated. Overall, computed absorbed doses to organs and tissues fully and directly irradiated demonstrated better agreement (within approximately 50 %) with the measured absorbed doses than absorbed doses to distributed organs or to those located on the periphery of the scan volume, which showed up to a 15-fold dose variation. The disparities predominantly arose from differences in the phantoms used. While the ability to estimate CT dose is essential for risk assessment and radiation protection, identifying a simple, practical dosimetry method remains challenging.

  8. The method to calculate concentration of CO2 and H2S in the liquid phase.

    Directory of Open Access Journals (Sweden)

    YUDIN Pavel Evgenievich

    2017-08-01

    Full Text Available The article proposes the method to calculate the necessary concentration of dissolved gases in the liquid phase. It also deals with development of the computer program that could consider all the main parameters of the tests. The numerous mathematical calculations resulted in formulation of the method to calculate concentration of dissolved gases in the liquid phase. The implementation of the developed model in the form of the software product «Autoclave 2.1» is presented. The developed methodology for calculating the concentration of dissolved gases in the liquid phase is designed to perform accelerated tests that concern resistance of internal anticorrosive coatings of pipelines to aggressive media and explosive decompression, to intensify corrosion processes and to identify the main mechanisms and patterns of changes in the physical, mechanical and operational properties of coatings from hydrothermal influences of fishing environments.

  9. Comparative Study of the Volumetric Methods Calculation Using GNSS Measurements

    Science.gov (United States)

    Şmuleac, Adrian; Nemeş, Iacob; Alina Creţan, Ioana; Sorina Nemeş, Nicoleta; Şmuleac, Laura

    2017-10-01

    This paper aims to achieve volumetric calculations for different mineral aggregates using different methods of analysis and also comparison of results. To achieve these comparative studies and presentation were chosen two software licensed, namely TopoLT 11.2 and Surfer 13. TopoLT program is a program dedicated to the development of topographic and cadastral plans. 3D terrain model, level courves and calculation of cut and fill volumes, including georeferencing of images. The program Surfer 13 is produced by Golden Software, in 1983 and is active mainly used in various fields such as agriculture, construction, geophysical, geotechnical engineering, GIS, water resources and others. It is also able to achieve GRID terrain model, to achieve the density maps using the method of isolines, volumetric calculations, 3D maps. Also, it can read different file types, including SHP, DXF and XLSX. In these paper it is presented a comparison in terms of achieving volumetric calculations using TopoLT program by two methods: a method where we choose a 3D model both for surface as well as below the top surface and a 3D model in which we choose a 3D terrain model for the bottom surface and another 3D model for the top surface. The comparison of the two variants will be made with data obtained from the realization of volumetric calculations with the program Surfer 13 generating GRID terrain model. The topographical measurements were performed with equipment from Leica GPS 1200 Series. Measurements were made using Romanian position determination system - ROMPOS which ensures accurate positioning of reference and coordinates ETRS through the National Network of GNSS Permanent Stations. GPS data processing was performed with the program Leica Geo Combined Office. For the volumetric calculating the GPS used point are in 1970 stereographic projection system and for the altitude the reference is 1975 the Black Sea projection system.

  10. A New Method to Calculate Internal Rate of Return

    Directory of Open Access Journals (Sweden)

    azadeh zandi

    2015-09-01

    Full Text Available A number of methods have been developed to choose the best capital investment projects such as net present value, internal rate of return and etc. Internal rate of return method is probably the most popular method among managers and investors. But despite the popularity there are serious drawbacks and limitations in this method. After decades of efforts made by economists and experts to improve the method and its shortcomings, Magni in 2010 has revealed a new approach that can solves the most of internal rate of return method problems. This paper present a new method which is originated from Magni’s approach but has much more simple calculations and can resolve all the drawbacks of internal rate of return method.

  11. Perturbation method for calculating impurity binding energy in an ...

    Indian Academy of Sciences (India)

    Perturbation method is used to calculate the binding energy within the framework of effective mass approximation and taking into account the effect of dielectric mismatch between the dot and the barrier material. The ground-state binding energy of the donor is computed as a function of dot size for finite confinement.

  12. Visual Method for Spectral Energy Distribution Calculation of ...

    Indian Academy of Sciences (India)

    c Indian Academy of Sciences. Visual Method for Spectral Energy Distribution Calculation of Blazars. Y. Huang1,3 & J. H. Fan2,3,∗. 1School of Computer Science and Education Software, Guangzhou University,. Guangzhou 510006, China. 2Centre for Astrophysics, Guangzhou University, Guangzhou 510006, China.

  13. Simple Calculation Programs for Biology Methods in Molecular ...

    Indian Academy of Sciences (India)

    First page Back Continue Last page Overview Graphics. Simple Calculation Programs for Biology Methods in Molecular Biology. GMAP: A program for mapping potential restriction sites. RE sites in ambiguous and non-ambiguous DNA sequence; Minimum number of silent mutations required for introducing a RE sites; Set ...

  14. Perturbation method for calculating impurity binding energy in an ...

    Indian Academy of Sciences (India)

    Nilanjan Sil

    2017-12-18

    Dec 18, 2017 ... Abstract. In the present paper, we have studied the binding energy of the shallow donor hydrogenic impurity, which is confined in an inhomogeneous cylindrical quantum dot (CQD) of GaAs-AlxGa1−xAs. Perturbation method is used to calculate the binding energy within the framework of effective mass ...

  15. The algorithm of numerical calculation of constraints reactions in a dynamic system of transport machine

    Science.gov (United States)

    Akhtulov, A. L.

    2018-01-01

    The questions of construction and practical application of the automation system for the design of components and aggregates for the construction of transport vehicles are considered, taking into account their dynamic characteristics. Based on the results of the studies, a unified method for determining the reactions of bonds of a complex spatial structure is proposed. The technique, based on the method of substructures, allows us to determine the values of the transfer functions taking into account the reactions of the bonds. After the carried out researches it is necessary to note, that such approach gives the most satisfactory results and can be used for calculations of complex mechanical systems of machines and units of different purposes. The directions of increasing the degree of validity of technical decisions are shown, especially in the early stages of design, when the cost of errors is high, with careful thorough working out of all the elements of the design, which is really feasible only on the basis of automation of design and technological work.

  16. Efficient numerical technique for calculating the properties of interacting dimers in the Peierls-Hubbard model

    Science.gov (United States)

    Sous, John; Chakraborty, Monodeep; Krems, Roman; Berciu, Mona

    2017-04-01

    We develop a method to compute the Green's function for two particles in an infinite chain and coupled to phonons by interactions that modulate their hopping as described by the Peierls/Su-Schrieffer-Heeger (SSH) model. The method is based on a variational approximation to the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy and is shown to agree with exact digaonalization calculations. We show that the properties of bipolarons arising in such models is qualitatively different from those of the well-studied Holstein bipolarons. In particular, we show that depending on the particle statistics, strongly bound bipolarons may or may not form. In the case of hard-core bosons, we demonstrate novel effects for dimers such as sharp transitions and self-trapping. In the case of soft-core particles/ spinfull fermions, we show that the mediated interactions lead to overscreeing of the bare Hubbard U repulsion resulting in the formation of strongly bound bipolarons. This work was supported by NSERC of Canada and the Stewart Blusson Quantum Matter Institute.

  17. Thick-Restart Lanczos Method for Electronic Structure Calculations

    International Nuclear Information System (INIS)

    Simon, Horst D.; Wang, L.-W.; Wu, Kesheng

    1999-01-01

    This paper describes two recent innovations related to the classic Lanczos method for eigenvalue problems, namely the thick-restart technique and dynamic restarting schemes. Combining these two new techniques we are able to implement an efficient eigenvalue problem solver. This paper will demonstrate its effectiveness on one particular class of problems for which this method is well suited: linear eigenvalue problems generated from non-self-consistent electronic structure calculations

  18. Experimental validation of numerical simulations: a comparison of computational fluid dynamics and the oil film method.

    Science.gov (United States)

    Stoiber, M; Grasl, C; Pirker, S; Huber, L; Gittler, P; Schima, H

    2007-04-01

    Today Computational Fluid Dynamics (CFD) is used for simulating flow in many applications. The quality of the results, however, depends on various factors, like grid quality, boundary conditions and the computational model of the fluid. For this reason, it is important to validate the performed computation with experimental results. In this work, a comparison of numerical simulation with the oil film method was performed for two cardiovascular applications. The investigations were conducted at various geometries, such as a bended cannula tubing, an impeller of a magnetically levitated rotary blood pump and tips of inflow cannulas. The oil film for the experimental validation was composed of black oil color and varnish. In the numerical simulation, color abrasion was displayed with a special post-processing tool by means of wall-attached pathlines. With the proper choice of numerical parameters, the computer simulations and the oil film method demonstrated good correlation. Improper generation of the simulation grid did lead to divergent results between the numerical simulation and the experiment. For the pump impeller as well as for the inflow cannulas, the calculation and the experiment showed similar flow patterns with backflow and stall zones. The oil film method represents a fast and simple approach to help validate numerical simulations of fluid flow. The experimentally generated near wall flow patterns can be easily compared with the solution of the CFD analysis.

  19. Mixed dual finite element methods for the numerical treatment of the diffusion equation in hexagonal geometry

    International Nuclear Information System (INIS)

    Schneider, D.

    2001-01-01

    The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P N approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)

  20. Numerical Calculation of the Peaking Factor of a Water-Cooled W/Cu Monoblock for a Divertor

    Science.gov (United States)

    Han, Le; Chang, Haiping; Zhang, Jingyang; Xu, Tiejun

    2015-09-01

    In order to accurately predict the incident critical heat flux (ICHF, the heat flux at the heated surface when CHF occurs) of a water-cooled W/Cu monoblock for a divertor, the exact knowledge of its peaking factors (fp) under one-sided heating conditions with different design parameters is a key issue. In this paper, the heat conduction in the solid domain of a water-cooled W/Cu monoblock is calculated numerically by assuming the local heat transfer coefficients (HTC) of the cooling wall to be functions of the local wall temperature, so as to obtain fp. The reliability of the calculation method is validated by an experimental example result, with the maximum error of 2.1% only. The effects of geometric and flow parameters on the fp of a water-cooled W/Cu monoblock are investigated. Within the scope of this study, it is shown that the fp increases with increasing dimensionless W/Cu monoblock width and armour thickness (the shortest distance between the heated surface and Cu layer), and the maximum increases are 43.8% and 22.4% respectively. The dimensionless W/Cu monoblock height and Cu thickness have little effect on fp. The increase of Reynolds number and Jakob number causes the increase of fp, and the maximum increases are 6.8% and 9.6% respectively. Based on the calculated results, an empirical correlation on peaking factor is obtained via regression. These results provide a valuable reference for the thermal-hydraulic design of water-cooled divertors. supported by National Magnetic Confinement Fusion Science Program of China (No. 2010GB104005) and Funding of Jiangsu Innovation Program for Graduate Education, China (CXLX12_0170), the Fundamental Research Funds for the Central Universities of China

  1. Numerical Calculation of the Peaking Factor of a Water-Cooled W/Cu Monoblock for a Divertor

    International Nuclear Information System (INIS)

    Han Le; Chang Haiping; Zhang Jingyang; Xu Tiejun

    2015-01-01

    In order to accurately predict the incident critical heat flux (ICHF, the heat flux at the heated surface when CHF occurs) of a water-cooled W/Cu monoblock for a divertor, the exact knowledge of its peaking factors (f p ) under one-sided heating conditions with different design parameters is a key issue. In this paper, the heat conduction in the solid domain of a water-cooled W/Cu monoblock is calculated numerically by assuming the local heat transfer coefficients (HTC) of the cooling wall to be functions of the local wall temperature, so as to obtain f p . The reliability of the calculation method is validated by an experimental example result, with the maximum error of 2.1% only. The effects of geometric and flow parameters on the f p of a water-cooled W/Cu monoblock are investigated. Within the scope of this study, it is shown that the f p increases with increasing dimensionless W/Cu monoblock width and armour thickness (the shortest distance between the heated surface and Cu layer), and the maximum increases are 43.8% and 22.4% respectively. The dimensionless W/Cu monoblock height and Cu thickness have little effect on f p . The increase of Reynolds number and Jakob number causes the increase of f p , and the maximum increases are 6.8% and 9.6% respectively. Based on the calculated results, an empirical correlation on peaking factor is obtained via regression. These results provide a valuable reference for the thermal-hydraulic design of water-cooled divertors. (paper)

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

    Energy Technology Data Exchange (ETDEWEB)

    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.

  3. Numerical evaluation of methods for computing tomographic projections

    International Nuclear Information System (INIS)

    Zhuang, W.; Gopal, S.S.; Hebert, T.J.

    1994-01-01

    Methods for computing forward/back projections of 2-D images can be viewed as numerical integration techniques. The accuracy of any ray-driven projection method can be improved by increasing the number of ray-paths that are traced per projection bin. The accuracy of pixel-driven projection methods can be increased by dividing each pixel into a number of smaller sub-pixels and projecting each sub-pixel. The authors compared four competing methods of computing forward/back projections: bilinear interpolation, ray-tracing, pixel-driven projection based upon sub-pixels, and pixel-driven projection based upon circular, rather than square, pixels. This latter method is equivalent to a fast, bi-nonlinear interpolation. These methods and the choice of the number of ray-paths per projection bin or the number of sub-pixels per pixel present a trade-off between computational speed and accuracy. To solve the problem of assessing backprojection accuracy, the analytical inverse Fourier transform of the ramp filtered forward projection of the Shepp and Logan head phantom is derived

  4. Transport survey calculations using the spectral collocation method

    International Nuclear Information System (INIS)

    Painter, S.L.; Lyon, J.F.

    1989-01-01

    A novel transport survey code has been developed and is being used to study the sensitivity of stellarator reactor performance to various transport assumptions. Instead of following one of the usual approaches, the steady-state transport equation are solved in integral form using the spectral collocation method. This approach effectively combine the computational efficiency of global models with the general nature of 1-D solutions. A compact torsatron reactor test case was used to study the convergence properties and flexibility of the new method. The heat transport model combined Shaing's model for ripple-induced neoclassical transport, the Chang-Hinton model for axisymmetric neoclassical transport, and neoalcator scaling for anomalous electron heat flux. Alpha particle heating, radiation losses, classical electron-ion heat flow, and external heating were included. For the test problem, the method exhibited some remarkable convergence properties. As the number of basis functions was increased, the maximum, pointwise error in the integrated power balance decayed exponentially until the numerical noise level as reached. Better than 10% accuracy in the globally-averaged quantities was achieved with only 5 basis functions; better than 1% accuracy was achieved with 10 basis functions. The numerical method was also found to be very general. Extreme temperature gradients at the plasma edge which sometimes arise from the neoclassical models and are difficult to resolve with finite-difference methods were easily resolved. 8 refs., 6 figs

  5. Depth compensating calculation method of computer-generated holograms using symmetry and similarity of zone plates

    Science.gov (United States)

    Wei, Hui; Gong, Guanghong; Li, Ni

    2017-10-01

    Computer-generated hologram (CGH) is a promising 3D display technology while it is challenged by heavy computation load and vast memory requirement. To solve these problems, a depth compensating CGH calculation method based on symmetry and similarity of zone plates is proposed and implemented on graphics processing unit (GPU). An improved LUT method is put forward to compute the distances between object points and hologram pixels in the XY direction. The concept of depth compensating factor is defined and used for calculating the holograms of points with different depth positions instead of layer-based methods. The proposed method is suitable for arbitrary sampling objects with lower memory usage and higher computational efficiency compared to other CGH methods. The effectiveness of the proposed method is validated by numerical and optical experiments.

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

    Science.gov (United States)

    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.

  7. Numerical calculation of the geometric efficiency of circular detector and surface source arrangements

    International Nuclear Information System (INIS)

    Wilson, O.J.

    1980-05-01

    This report describes a numerical technique of determining the geometric efficiency of circular detector and various surface source arrangements. Circular sources are primarily discussed, but most other surface shapes can be accommodated by the technique

  8. On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

    Science.gov (United States)

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

    2011-11-01

    Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

  9. Resampling Approach for Determination of the Method for Reference Interval Calculation in Clinical Laboratory Practice▿

    Science.gov (United States)

    Pavlov, Igor Y.; Wilson, Andrew R.; Delgado, Julio C.

    2010-01-01

    Reference intervals (RI) play a key role in clinical interpretation of laboratory test results. Numerous articles are devoted to analyzing and discussing various methods of RI determination. The two most widely used approaches are the parametric method, which assumes data normality, and a nonparametric, rank-based procedure. The decision about which method to use is usually made arbitrarily. The goal of this study was to demonstrate that using a resampling approach for the comparison of RI determination techniques could help researchers select the right procedure. Three methods of RI calculation—parametric, transformed parametric, and quantile-based bootstrapping—were applied to multiple random samples drawn from 81 values of complement factor B observations and from a computer-simulated normally distributed population. It was shown that differences in RI between legitimate methods could be up to 20% and even more. The transformed parametric method was found to be the best method for the calculation of RI of non-normally distributed factor B estimations, producing an unbiased RI and the lowest confidence limits and interquartile ranges. For a simulated Gaussian population, parametric calculations, as expected, were the best; quantile-based bootstrapping produced biased results at low sample sizes, and the transformed parametric method generated heavily biased RI. The resampling approach could help compare different RI calculation methods. An algorithm showing a resampling procedure for choosing the appropriate method for RI calculations is included. PMID:20554803

  10. Comparison of analytical methods for calculation of wind loads

    Science.gov (United States)

    Minderman, Donald J.; Schultz, Larry L.

    1989-01-01

    The following analysis is a comparison of analytical methods for calculation of wind load pressures. The analytical methods specified in ASCE Paper No. 3269, ANSI A58.1-1982, the Standard Building Code, and the Uniform Building Code were analyzed using various hurricane speeds to determine the differences in the calculated results. The winds used for the analysis ranged from 100 mph to 125 mph and applied inland from the shoreline of a large open body of water (i.e., an enormous lake or the ocean) a distance of 1500 feet or ten times the height of the building or structure considered. For a building or structure less than or equal to 250 feet in height acted upon by a wind greater than or equal to 115 mph, it was determined that the method specified in ANSI A58.1-1982 calculates a larger wind load pressure than the other methods. For a building or structure between 250 feet and 500 feet tall acted upon by a wind rangind from 100 mph to 110 mph, there is no clear choice of which method to use; for these cases, factors that must be considered are the steady-state or peak wind velocity, the geographic location, the distance from a large open body of water, and the expected design life and its risk factor.

  11. Comparison between calculation methods of dose rates in gynecologic brachytherapy

    International Nuclear Information System (INIS)

    Vianello, E.A.; Biaggio, M.F.; D R, M.F.; Almeida, C.E. de

    1998-01-01

    In treatments with radiations for gynecologic tumors is necessary to evaluate the quality of the results obtained by different calculation methods for the dose rates on the points of clinical interest (A, rectal, vesicle). The present work compares the results obtained by two methods. The Manual Calibration Method (MCM) tri dimensional (Vianello E., et.al. 1998), using orthogonal radiographs for each patient in treatment, and the Theraplan/T P-11 planning system (Thratonics International Limited 1990) this last one verified experimentally (Vianello et.al. 1996). The results show that MCM can be used in the physical-clinical practice with a percentile difference comparable at the computerized programs. (Author)

  12. Numerical Calculation of Effect of Elastic Deformation on Aerodynamic Characteristics of a Rocket

    Directory of Open Access Journals (Sweden)

    Laith K. Abbas

    2014-01-01

    Full Text Available The application and workflow of Computational Fluid Dynamics (CFD/Computational Structure Dynamics (CSD on solving the static aeroelastic problem of a slender rocket are introduced. To predict static aeroelastic behavior accurately, two-way coupling and inertia relief methods are used to calculate the static deformations and aerodynamic characteristics of the deformed rocket. The aerodynamic coefficients of rigid rocket are computed firstly and compared with the experimental data, which verified the accuracy of CFD output. The results of the analysis for elastic rocket in the nonspinning and spinning states are compared with the rigid ones. The results highlight that the rocket deformation aspects are decided by the normal force distribution along the rocket length. Rocket deformation becomes larger with increasing the flight angle of attack. Drag and lift force coefficients decrease and pitching moment coefficients increase due to rocket deformations, center of pressure location forwards, and stability of the rockets decreases. Accordingly, the flight trajectory may be affected by the change of these aerodynamic coefficients and stability.

  13. Mathematical model of complex technical asymmetric system based on numerical-analytical boundary elements method

    Directory of Open Access Journals (Sweden)

    Dina V. Lazareva

    2015-06-01

    Full Text Available A new mathematical model of asymmetric support structure frame type is built on the basis of numerical-analytical boundary elements method (BEM. To describe the design scheme used is the graph theory. Building the model taken into account is the effect of frame members restrained torsion, which presence is due to the fact that these elements are thin-walled. The built model represents a real object as a two-axle semi-trailer platform. To implement the BEM algorithm obtained are analytical expressions of the fundamental functions and vector load components. The effected calculations are based on the semi-trailer two different models, using finite elements and boundary elements methods. The analysis showed that the error between the results obtained on the basis of two numerical methods and experimental data is about 4%, that indicates the adequacy of the proposed mathematical model.

  14. Numerical methods and applications in many fermion systems

    Energy Technology Data Exchange (ETDEWEB)

    Luitz, David J.

    2013-02-07

    This thesis presents results covering several topics in correlated many fermion systems. A Monte Carlo technique (CT-INT) that has been implemented, used and extended by the author is discussed in great detail in chapter 3. The following chapter discusses how CT-INT can be used to calculate the two particle Green's function and explains how exact frequency summations can be obtained. A benchmark against exact diagonalization is presented. The link to the dynamical cluster approximation is made in the end of chapter 4, where these techniques are of immense importance. In chapter 5 an extensive CT-INT study of a strongly correlated Josephson junction is shown. In particular, the signature of the first order quantum phase transition between a Kondo and a local moment regime in the Josephson current is discussed. The connection to an experimental system is made with great care by developing a parameter extraction strategy. As a final result, we show that it is possible to reproduce experimental data from a numerically exact CT-INT model-calculation. The last topic is a study of graphene edge magnetism. We introduce a general effective model for the edge states, incorporating a complicated interaction Hamiltonian and perform an exact diagonalization study for different parameter regimes. This yields a strong argument for the importance of forbidden umklapp processes and of the strongly momentum dependent interaction vertex for the formation of edge magnetism. Additional fragments concerning the use of a Legendre polynomial basis for the representation of the two particle Green's function, the analytic continuation of the self energy for the Anderson Kane Mele Model as well as the generation of test data with a given covariance matrix are documented in the appendix. A final appendix provides some very important matrix identities that are used for the discussion of technical details of CT-INT.

  15. Numerical Calculation of Secondary Flow in Pump Volute and Circular Casings using 3D Viscous Flow Techniques

    Directory of Open Access Journals (Sweden)

    K. Majidi

    2000-01-01

    Full Text Available The flow field in volute and circular casings interacting with a centrifugal impeller is obtained by numerical analysis. In the present study, effects of the volute and circular casings on the flow pattern have been investigated by successively combining a volute casing and a circular casing with a single centrifugal impeller. The numerical calculations are carried out with a multiple frame of reference to predict the flow field inside the entire impeller and casings. The impeller flow field is solved in a rotating frame and the flow field in the casings in a stationary frame. The static pressure and velocity in the casing and impeller, and the static pressures and secondary velocity vectors at several cross-sectional planes of the casings are calculated. The calculations show that the curvature of the casings creates pressure gradients that cause vortices at cross-sectional planes of the casings.

  16. An observational study of agreement between percentage pain reduction calculated from visual analog or numerical rating scales versus that reported by parturients during labor epidural analgesia.

    Science.gov (United States)

    Pratici, E; Nebout, S; Merbai, N; Filippova, J; Hajage, D; Keita, H

    2017-05-01

    This study aimed to determine the level of agreement between calculated percentage pain reduction, derived from visual analog or numerical rating scales, and patient-reported percentage pain reduction in patients having labor epidural analgesia. In a prospective observational study, parturients were asked to rate their pain intensity on a visual analog scale and numerical rating scale, before and 30min after initiation of epidural analgesia. The percentage pain reduction 30min after epidural analgesia was calculated by the formula: 100×(score before epidural analgesia-score 30min after epidural analgesia)/score before epidural analgesia. To evaluate agreement between calculated percentage pain reduction and patient-reported percentage pain reduction, we computed the concordance correlation coefficient and performed Bland-Altman analysis. Ninety-seven women in labor were enrolled in the study, most of whom were nulliparous, with a singleton fetus and in spontaneous labor. The concordance correlation coefficient with patient-reported percentage pain reduction was 0.76 (95% CI 0.6 to 0.8) and 0.77 (95% CI 0.6 to 0.8) for the visual analog and numerical rating scale, respectively. The Bland-Altman mean difference between calculated percentage pain reduction and patient-reported percentage pain reduction for the visual analog and numerical rating scales was -2.0% (limits of agreement at 29.8%) and 0 (limits of agreement at 28.2%), respectively. The agreement between calculated percentage pain reduction from a visual analog or numerical rating scale and patient-reported percentage pain reduction in the context of labor epidural analgesia was moderate. The difference could range up to 30%. Patient-reported percentage pain reduction has advantages as a measurement tool for assessing pain management for childbirth but differences compared with other assessment methods should be taken into account. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

    Science.gov (United States)

    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.

  18. Numerical modeling of isothermal compositional grading by convex splitting methods

    KAUST Repository

    Li, Yiteng

    2017-04-09

    In this paper, an isothermal compositional grading process is simulated based on convex splitting methods with the Peng-Robinson equation of state. We first present a new form of gravity/chemical equilibrium condition by minimizing the total energy which consists of Helmholtz free energy and gravitational potential energy, and incorporating Lagrange multipliers for mass conservation. The time-independent equilibrium equations are transformed into a system of transient equations as our solution strategy. It is proved our time-marching scheme is unconditionally energy stable by the semi-implicit convex splitting method in which the convex part of Helmholtz free energy and its derivative are treated implicitly and the concave parts are treated explicitly. With relaxation factor controlling Newton iteration, our method is able to converge to a solution with satisfactory accuracy if a good initial estimate of mole compositions is provided. More importantly, it helps us automatically split the unstable single phase into two phases, determine the existence of gas-oil contact (GOC) and locate its position if GOC does exist. A number of numerical examples are presented to show the performance of our method.

  19. Thermal disadvantage factor calculation by the multiregion collision probability method

    International Nuclear Information System (INIS)

    Ozgener, B.; Ozgener, H.A.

    2004-01-01

    A multi-region collision probability formulation that is capable of applying white boundary condition directly is presented and applied to thermal neutron transport problems. The disadvantage factors computed are compared with their counterparts calculated by S N methods with both direct and indirect application of white boundary condition. The results of the ABH and collision probability method with indirect application of white boundary condition are also considered and comparisons with benchmark Monte Carlo results are carried out. The studies show that the proposed formulation is capable of calculating thermal disadvantage factor with sufficient accuracy without resorting to the fictitious scattering outer shell approximation associated with the indirect application of the white boundary condition in collision probability solutions

  20. The application of advanced rotor (performance) methods for design calculations

    Energy Technology Data Exchange (ETDEWEB)

    Bussel, G.J.W. van [Delft Univ. of Technology, Inst. for Wind Energy, Delft (Netherlands)

    1997-08-01

    The calculation of loads and performance of wind turbine rotors has been a topic for research over the last century. The principles for the calculation of loads on rotor blades with a given specific geometry, as well as the development of optimal shaped rotor blades have been published in the decades that significant aircraft development took place. Nowadays advanced computer codes are used for specific problems regarding modern aircraft, and application to wind turbine rotors has also been performed occasionally. The engineers designing rotor blades for wind turbines still use methods based upon global principles developed in the beginning of the century. The question what to expect in terms of the type of methods to be applied in a design environment for the near future is addressed here. (EG) 14 refs.

  1. Process control and optimization with simple interval calculation method

    DEFF Research Database (Denmark)

    Pomerantsev, A.; Rodionova, O.; Høskuldsson, Agnar

    2006-01-01

    for the quality improvement in the course of production. The latter is an active quality optimization, which takes into account the actual history of the process. The advocate approach is allied to the conventional method of multivariate statistical process control (MSPC) as it also employs the historical process......Methods of process control and optimization are presented and illustrated with a real world example. The optimization methods are based on the PLS block modeling as well as on the simple interval calculation methods of interval prediction and object status classification. It is proposed to employ...... the series of expanding PLS/SIC models in order to support the on-line process improvements. This method helps to predict the effect of planned actions on the product quality and thus enables passive quality control. We have also considered an optimization approach that proposes the correcting actions...

  2. Process control and optimization with simple interval calculation method

    DEFF Research Database (Denmark)

    Pomerantsev, A.; Rodionova, O.; Høskuldsson, Agnar

    2006-01-01

    Methods of process control and optimization are presented and illustrated with a real world example. The optimization methods are based on the PLS block modeling as well as on the simple interval calculation methods of interval prediction and object status classification. It is proposed to employ...... the series of expanding PLS/SIC models in order to support the on-line process improvements. This method helps to predict the effect of planned actions on the product quality and thus enables passive quality control. We have also considered an optimization approach that proposes the correcting actions...... for the quality improvement in the course of production. The latter is an active quality optimization, which takes into account the actual history of the process. The advocate approach is allied to the conventional method of multivariate statistical process control (MSPC) as it also employs the historical process...

  3. Mathematical analysis and numerical methods for science and technology

    CERN Document Server

    Dautray, Robert

    These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which ...

  4. Numerical simulation of explosive welding using Smoothed Particle Hydrodynamics method

    Directory of Open Access Journals (Sweden)

    J Feng

    2017-09-01

    Full Text Available In order to investigate the mechanism of explosive welding and the influences of explosive welding parameters on the welding quality, this paper presents numerical simulation of the explosive welding of Al-Mg plates using Smoothed Particle Hydrodynamics method. The multi-physical phenomena of explosive welding, including acceleration of the flyer plate driven by explosive detonation, oblique collision of the flyer and base plates, jetting phenomenon and the formation of wavy interface can be reproduced in the simulation. The characteristics of explosive welding are analyzed based on the simulation results. The mechanism of wavy interface formation is mainly due to oscillation of the collision point on the bonding surfaces. In addition, the impact velocity and collision angle increase with the increase of the welding parameters, such as explosive thickness and standoff distance, resulting in enlargement of the interfacial waves.

  5. Numerical methods for Eulerian and Lagrangian conservation laws

    CERN Document Server

    Després, Bruno

    2017-01-01

    This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.

  6. Performance of Several High Order Numerical Methods for Supersonic Combustion

    Science.gov (United States)

    Sjoegreen, Bjoern; Yee, H. C.; Don, Wai Sun; Mansour, Nagi N. (Technical Monitor)

    2001-01-01

    The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.

  7. A mathematical model and numerical method for thermoelectric DNA sequencing

    Science.gov (United States)

    Shi, Liwei; Guilbeau, Eric J.; Nestorova, Gergana; Dai, Weizhong

    2014-05-01

    Single nucleotide polymorphisms (SNPs) are single base pair variations within the genome that are important indicators of genetic predisposition towards specific diseases. This study explores the feasibility of SNP detection using a thermoelectric sequencing method that measures the heat released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a DNA strand. We propose a three-dimensional mathematical model that governs the DNA sequencing device with a reaction zone that contains DNA template/primer complex immobilized to the surface of the lower channel wall. The model is then solved numerically. Concentrations of reactants and the temperature distribution are obtained. Results indicate that when the nucleoside is complementary to the next base in the DNA template, polymerization occurs lengthening the complementary polymer and releasing thermal energy with a measurable temperature change, implying that the thermoelectric conceptual device for sequencing DNA may be feasible for identifying specific genes in individuals.

  8. Numerical methods for two-phase flow with contact lines

    Energy Technology Data Exchange (ETDEWEB)

    Walker, Clauido

    2012-07-01

    This thesis focuses on numerical methods for two-phase flows, and especially flows with a moving contact line. Moving contact lines occur where the interface between two fluids is in contact with a solid wall. At the location where both fluids and the wall meet, the common continuum descriptions for fluids are not longer valid, since the dynamics around such a contact line are governed by interactions at the molecular level. Therefore the standard numerical continuum models have to be adjusted to handle moving contact lines. In the main part of the thesis a method to manipulate the position and the velocity of a contact line in a two-phase solver, is described. The Navier-Stokes equations are discretized using an explicit finite difference method on a staggered grid. The position of the interface is tracked with the level set method and the discontinuities at the interface are treated in a sharp manner with the ghost fluid method. The contact line is tracked explicitly and its dynamics can be described by an arbitrary function. The key part of the procedure is to enforce a coupling between the contact line and the Navier-Stokes equations as well as the level set method. Results for different contact line models are presented and it is demonstrated that they are in agreement with analytical solutions or results reported in the literature.The presented Navier-Stokes solver is applied as a part in a multiscale method to simulate capillary driven flows. A relation between the contact angle and the contact line velocity is computed by a phase field model resolving the micro scale dynamics in the region around the contact line. The relation of the microscale model is then used to prescribe the dynamics of the contact line in the macro scale solver. This approach allows to exploit the scale separation between the contact line dynamics and the bulk flow. Therefore coarser meshes can be applied for the macro scale flow solver compared to global phase field simulations

  9. Testing the QA Method for Calculating Jet v_{2}

    CERN Document Server

    Mueller, Jason

    2014-01-01

    For the summer, I was assigned to work on the ALICE experiment with Alice Ohlson. I wrote several programs throughout the summer that were used to calculate jet v 2 using a non-standard method described by my supervisor in her Ph.D. thesis. Though the project is not yet complete, significant progress has been made, and the results so far seem promising.

  10. A method of calculating the Jost function for analytic potentials

    International Nuclear Information System (INIS)

    Rakityansky, S.A.; Amos, K.

    1995-01-01

    A combination of the variable-constant and complex coordinate rotation methods is used to solve the two-body Schroedinger equation. The equation is replaced by a system of linear first-order differential equations, which enables one to perform direct calculation of the Jost function for all complex momenta of physical interest including the spectral points corresponding to bound and resonance states. 16 refs., 2 tabs., 2 figs

  11. Applying probabilistic methods for assessments and calculations for accident prevention

    International Nuclear Information System (INIS)

    Anon.

    1984-01-01

    The guidelines for the prevention of accidents require plant design-specific and radioecological calculations to be made in order to show that maximum acceptable expsoure values will not be exceeded in case of an accident. For this purpose, main parameters affecting the accident scenario have to be determined by probabilistic methods. This offers the advantage that parameters can be quantified on the basis of unambigious and realistic criteria, and final results can be defined in terms of conservativity. (DG) [de

  12. Benchmark calculations for evaluation methods of gas volumetric leakage rate

    International Nuclear Information System (INIS)

    Asano, R.; Aritomi, M.; Matsuzaki, M.

    1998-01-01

    A containment function of radioactive materials transport casks is essential for safe transportation to prevent the radioactive materials from being released into environment. Regulations such as IAEA standard determined the limit of radioactivity to be released. Since is not practical for the leakage tests to measure directly the radioactivity release from a package, as gas volumetric leakages rates are proposed in ANSI N14.5 and ISO standards. In our previous works, gas volumetric leakage rates for several kinds of gas from various leaks were measured and two evaluation methods, 'a simple evaluation method' and 'a strict evaluation method', were proposed based on the results. The simple evaluation method considers the friction loss of laminar flow with expansion effect. The strict evaluating method considers an exit loss in addition to the friction loss. In this study, four worked examples were completed for on assumed large spent fuel transport cask (Type B Package) with wet or dry capacity and at three transport conditions; normal transport with intact fuels or failed fuels, and an accident in transport. The standard leakage rates and criteria for two kinds of leak test were calculated for each example by each evaluation method. The following observations are made based upon the calculations and evaluations: the choked flow model of ANSI method greatly overestimates the criteria for tests ; the laminar flow models of both ANSI and ISO methods slightly overestimate the criteria for tests; the above two results are within the design margin for ordinary transport condition and all methods are useful for the evaluation; for severe condition such as failed fuel transportation, it should pay attention to apply a choked flow model of ANSI method. (authors)

  13. A numerical method for determining the radial wave motion correction in plane wave couplers

    DEFF Research Database (Denmark)

    Cutanda Henriquez, Vicente; Barrera Figueroa, Salvador; Torras Rosell, Antoni

    2016-01-01

    Microphones are used for realising the unit of sound pressure level, the pascal (Pa). Electro-acoustic reciprocity is the preferred method for the absolute determination of the sensitivity. This method can be applied in different sound fields: uniform pressure, free field or diffuse field. Pressure...... solution is an analytical expression that estimates the difference between the ideal plane wave sound field and a more complex lossless sound field created by a non-planar movement of the microphone’s membranes. Alternatively, a correction may be calculated numerically by introducing a full model...

  14. A Numerical Method for Obtaining Monoenergetic Neutron Flux Distributions and Transmissions in Multiple-Region Slabs

    Science.gov (United States)

    Schneider, Harold

    1959-01-01

    This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.

  15. Monitoring the convection coefficient in fermentative processes using numerical methods.

    Science.gov (United States)

    da Paz, Priscila Marques; de Oliveira, Juliana

    2018-02-13

    This work is based on the importance of monitoring the thermodynamic variables of sugarcane juice fermentation by Saccharomyces cerevisiae, using a numerical technique, and providing artifices that lead to the best performance of this bioprocess. Different combinations of yeast quantity were added to diverse dilutions of cane juice, allowing the evaluation of the fermentation performance. This was conducted by observing the temperature signal obtained from thermal probes inserted in the experimental set up. The best performances are utilized in the mathematical model evaluation. Thus, the signal reconstructed by the appropriate inverse problem and subsequently, regularized by the simplified method of least squares (the method used for adjusting the defined parameters) allows a common method to process the convection coefficient that can be monitored and controlled within an actuation range. This leads to an increased level of refinement in the technique. Results show that it is possible to determine the best parameters for this technique and observe the occurrence of fermentation by monitoring the temperature signal, thereby ensuring the realization of a high-quality and high-performance bioprocess.

  16. Numerical calculation of the conductivity of percolation clusters and the use of special purpose computers

    International Nuclear Information System (INIS)

    Herrmann, H.J.

    1989-01-01

    Electrical conductivity diffusion or phonons, have an anomalous behaviour on percolation clusters at the percolation threshold due to the fractality of these clusters. The results that have been found numerically for this anomalous behaviour are reviewed. A special purpose computer built for this purpose is described and the evaluation of the data from this machine is discussed

  17. Analytical and numerical calculation of magnetic field distribution in the slotted air-gap of tangential surface permanent-magnet motors

    Directory of Open Access Journals (Sweden)

    Boughrara Kamel

    2009-01-01

    Full Text Available This paper deals with the analytical and numerical analysis of the flux density distribution in the slotted air gap of permanent magnet motors with surface mounted tangentially magnetized permanent magnets. Two methods for magnetostatic field calculations are developed. The first one is an analytical method in which the effect of stator slots is taken into account by modulating the magnetic field distribution by the complex relative air gap permeance. The second one is a numerical method using 2-D finite element analysis with consideration of Dirichlet and anti-periodicity (periodicity boundary conditions and Lagrange Multipliers for simulation of movement. The results obtained by the analytical method are compared to the results of finite-element analysis.

  18. Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method

    International Nuclear Information System (INIS)

    Onishi, Yuki; Takiyasu, Jumpei; Amaya, Kenji; Yakuwa, Hiroshi; Hayabusa, Keisuke

    2012-01-01

    Highlights: ► A novel numerical method to analyze time dependent localized corrosion is developed. ► It takes electromigration, mass diffusion, chemical reactions, and moving boundaries. ► Our method perfectly satisfies the conservation of mass and electroneutrality. ► The behavior of typical crevice corrosion is successfully simulated. ► Both verification and validation of our method are carried out. - Abstract: A novel numerical method for time-dependent localized corrosion analysis is presented. Electromigration, mass diffusion, chemical reactions, and moving boundaries are considered in the numerical simulation of localized corrosion of engineering alloys in an underwater environment. Our method combines the finite volume method (FVM) and the voxel method. The FVM is adopted in the corrosion rate calculation so that the conservation of mass is satisfied. A newly developed decoupled algorithm with a projection method is introduced in the FVM to decouple the multiphysics problem into the electrostatic, mass transport, and chemical reaction analyses with electroneutrality maintained. The polarization curves for the corroding metal are used as boundary conditions for the metal surfaces to calculate the corrosion rates. The voxel method is adopted in updating the moving boundaries of cavities without remeshing and mesh-to-mesh solution mapping. Some modifications of the standard voxel method, which represents the boundaries as zigzag-shaped surfaces, are introduced to generate smooth surfaces. Our method successfully reproduces the numerical and experimental results of a capillary electrophoresis problem. Furthermore, the numerical results are qualitatively consistent with the experimental results for several examples of crevice corrosion.

  19. Calculation and Comparison of Turbulence Attenuation by Different Methods

    Directory of Open Access Journals (Sweden)

    L. Dordova

    2010-04-01

    Full Text Available This paper is focused on the effect of turbulence in atmospheric transmission media. A short introduction of the origin of turbulent atmosphere is given. Two classical methods for the calculation of turbulence attenuation are mentioned and briefly described in the paper – the Rytov approximation and Andrews’s method, and a new technique designed by the authors of this paper – the method of available power – is presented in short as well. We have run simulations in Matlab to compare the results of turbulence attenuation given by the classical methods and by the new technique - the method of available power. These calculations were performed for communication wavelengths of 850 nm and 1550 nm. The distance between the optical transmitter and receiver of horizontal links was set to values ranging from 0 m to 2500 m. We have taken into account the homogenous turbulence with low (10^-16 m^-2/3, medium (10^-15 m^-2/3 and high (10^-14 m^-2/3 structure parameter of refractive index Cn2.

  20. Unfolding method for first-principles LCAO electronic structure calculations

    Science.gov (United States)

    Lee, Chi-Cheng; Yamada-Takamura, Yukiko; Ozaki, Taisuke

    2013-08-01

    Unfolding the band structure of a supercell to a normal cell enables us to investigate how symmetry breakers such as surfaces and impurities perturb the band structure of the normal cell. We generalize the unfolding method, originally developed based on Wannier functions, to the linear combination of atomic orbitals (LCAO) method, and present a general formula to calculate the unfolded spectral weight. The LCAO basis set is ideal for the unfolding method because the basis functions allocated to each atomic species are invariant regardless of the existence of surface and impurity. The unfolded spectral weight is well defined by the property of the LCAO basis functions. In exchange for the property, the non-orthogonality of the LCAO basis functions has to be taken into account. We show how the non-orthogonality can be properly incorporated in the general formula. As an illustration of the method, we calculate the dispersive quantized spectral weight of a ZrB2 slab and show strong spectral broadening in the out-of-plane direction, demonstrating the usefulness of the unfolding method.