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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. Hybrid numerical calculation method for bend waveguides

    OpenAIRE

    Garnier , Lucas; Saavedra , C.; Castro-Beltran , Rigoberto; Lucio , José Luis; Bêche , Bruno

    2017-01-01

    National audience; The knowledge of how the light will behave in a waveguide with a radius of curvature becomes more and more important because of the development of integrated photonics, which include ring micro-resonators, phasars, and other devices with a radius of curvature. This work presents a numerical calculation method to determine the eigenvalues and eigenvectors of curved waveguides. This method is a hybrid method which uses at first conform transformation of the complex plane gene...

  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. 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); 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)

  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. 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

  8. Numerical method for two-phase flow discontinuity propagation calculation

    International Nuclear Information System (INIS)

    Toumi, I.; Raymond, P.

    1989-01-01

    In this paper, we present a class of numerical shock-capturing schemes for hyperbolic systems of conservation laws modelling two-phase flow. First, we solve the Riemann problem for a two-phase flow with unequal velocities. Then, we construct two approximate Riemann solvers: an one intermediate-state Riemann solver and a generalized Roe's approximate Riemann solver. We give some numerical results for one-dimensional shock-tube problems and for a standard two-phase flow heat addition problem involving two-phase flow instabilities

  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. 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

  11. 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.

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

    International Nuclear Information System (INIS)

    Toumi, I.; Caruge, D.

    1997-01-01

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

    International Nuclear Information System (INIS)

    Toumi, I.; Gallo, D.; Royer, E.

    1997-01-01

    This paper is devoted to new numerical methods developed for three dimensional two-phase flow calculations. These methods are finite volume numerical methods. They are based on an extension of Roe's approximate Riemann solver to define convective fluxes versus mean cell quantities. To go forward in time, a linearized conservative implicit integrating step is used, together with a Newton iterative method. We also present here some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. This kind of numerical method, which is widely used for fluid dynamic calculations, is proved to be very efficient for the numerical solution to two-phase flow problems. This numerical method has been implemented for the three dimensional thermal-hydraulic code FLICA-4 which is mainly dedicated to core thermal-hydraulic transient and steady-state analysis. Hereafter, we will also find some results obtained for the EPR reactor running in a steady-state at 60% of nominal power with 3 pumps out of 4, and a thermal-hydraulic core analysis for a 1300 MW PWR at low flow steam-line-break conditions. (author)

  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. Application of optimization numerical methods in calculation of the two-particle nuclear reactions

    International Nuclear Information System (INIS)

    Titarenko, N.N.

    1987-01-01

    An optimization packet of PEAK-OPT applied programs intended for solution of problems of absolute minimization of functions of many variables in calculations of cross sections of binary nuclear reactions is described. The main algorithms of computerized numerical solution of systems of nonlinear equations for the least square method are presented. Principles for plotting and functioning the optimization software as well as results of its practical application are given

  19. 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

    to this problem is to measure the velocity distribution of the membrane by means of a non-contact method, such as laser vibrometry. The measured velocity distribution can be used together with a numerical formulation such as the boundary element method for estimating the microphone response and other parameters......, e.g., the acoustic center. In this work, such a hybrid method is presented and examined. The velocity distributions of a number of condenser microphones have been determined using a laser vibrometer, and these measured velocity distributions have been used for estimating microphone responses......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...

  20. Calculation of infrared radiation in the atmosphere by a numerical method

    International Nuclear Information System (INIS)

    Nunes, G.S.S.; Viswanadham, Y.

    1981-01-01

    A numerical method is described for the calculations of the atmospheric infrared flux and radiative cooling rate in the atmosphere. It is suitable for use at all levels below lower stratosphere. The square root pressure correction factor is incorporated in the computation of the corrected optical depth. The water vapour flux emissivity data of Staley and Jurica are used in the model. The versatility of the computing scheme sugests that this method is adequate to evaluate infrared flux and flux divergence in the problems involving a large amount of atmospheric data. (Author) [pt

  1. Calculations of the electromechanical transfer processes using implicit methods of numerical integration

    Energy Technology Data Exchange (ETDEWEB)

    Pogosyan, T A

    1983-01-01

    The article is dedicated to the solution of systems of differential equations which describe the transfer processes in an electric power system (EES) by implicit methods of numerical integration. The distinguishing feature of the implicit methods (Euler's reverse method and the trapeze method) is their absolute stability and, consequently, the relatively small accumulation of errors in each step of integration. Therefore, they are found to be very convenient for solving problems of electric power engineering, when the transfer processes are described by a rigid system of differential equations. The rigidity is associated with the range of values of the time constants considered. The advantage of the implicit methods over explicit are shown in a specific example (calculation of the dynamic stability of the simplest electric power system), along with the field of use of the implicit methods and the expedience of their use in power engineering problems.

  2. 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.

  3. 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)

  4. Numerical calculations near spatial infinity

    International Nuclear Information System (INIS)

    Zenginoglu, Anil

    2007-01-01

    After describing in short some problems and methods regarding the smoothness of null infinity for isolated systems, I present numerical calculations in which both spatial and null infinity can be studied. The reduced conformal field equations based on the conformal Gauss gauge allow us in spherical symmetry to calculate numerically the entire Schwarzschild-Kruskal spacetime in a smooth way including spacelike, null and timelike infinity and the domain close to the singularity

  5. 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

  6. A numerical calculation method for flow discretisation in complex geometry with body-fitted grids

    International Nuclear Information System (INIS)

    Jin, X.

    2001-04-01

    A numerical calculation method basing on body fitted grids is developed in this work for computational fluid dynamics in complex geometry. The method solves the conservation equations in a general nonorthogonal coordinate system which matches the curvilinear boundary. The nonorthogonal, patched grid is generated by a grid generator which solves algebraic equations. By means of an interface its geometrical data can be used by this method. The conservation equations are transformed from the Cartesian system to a general curvilinear system keeping the physical Cartesian velocity components as dependent variables. Using a staggered arrangement of variables, the three Cartesian velocity components are defined on every cell surface. Thus the coupling between pressure and velocity is ensured, and numerical oscillations are avoided. The contravariant velocity for calculating mass flux on one cell surface is resulting from dependent Cartesian velocity components. After the discretisation and linear interpolation, a three dimensional 19-point pressure equation is found. Using the explicit treatment for cross-derivative terms, it reduces to the usual 7-point equation. Under the same data and process structure, this method is compatible with the code FLUTAN using Cartesian coordinates. In order to verify this method, several laminar flows are simulated in orthogonal grids at tilted space directions and in nonorthogonal grids with variations of cell angles. The simulated flow types are considered like various duct flows, transient heat conduction, natural convection in a chimney and natural convection in cavities. Their results achieve very good agreement with analytical solutions or empirical data. Convergence for highly nonorthogonal grids is obtained. After the successful validation of this method, it is applied for a reactor safety case. A transient natural convection flow for an optional sump cooling concept SUCO is simulated. The numerical result is comparable with the

  7. 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)

  8. 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

  9. Numerical method and calculation of two-phase swirling flows with rigid particles for technical applications

    Directory of Open Access Journals (Sweden)

    Akhmetov Vadim

    2017-01-01

    Full Text Available Swirling flow with particle deposition effects at the lateral surface is numerically investigated. The flow field calculation results have been obtained as the solutions of the Navier-Stokes equations. Various flow regimes with the formation of axial recirculation zones are presented. The convection-diffusion model is used for the determination of the flow particle concentration and the formation of typical sedimentation zones.

  10. Numerical calculation of acoustic radiation from band-vibrating structures via FEM/FAQP method

    Directory of Open Access Journals (Sweden)

    GAO Honglin

    2017-08-01

    Full Text Available The Finite Element Method (FEM combined with the Frequency Averaged Quadratic Pressure method (FAQP are used to calculate the acoustic radiation of structures excited in the frequency band. The surface particle velocity of stiffened cylindrical shells under frequency band excitation is calculated using finite element software, the normal vibration velocity is converted from the surface particle velocity to calculate the average energy source (frequency averaged across intensity, frequency averaged across pressure and frequency averaged across velocity, and the FAQP method is used to calculate the average sound pressure level within the bandwidth. The average sound pressure levels are then compared with the bandwidth using finite element and boundary element software, and the results show that FEM combined with FAQP is more suitable for high frequencies and can be used to calculate the average sound pressure level in the 1/3 octave band with good stability, presenting an alternative to applying frequency-by-frequency calculation and the average frequency process. The FEM/FAQP method can be used as a prediction method for calculating acoustic radiation while taking the randomness of vibration at medium and high frequencies into consideration.

  11. 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

  12. 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

  13. Numerical calculations in quantum field theories

    International Nuclear Information System (INIS)

    Rebbi, C.

    1984-01-01

    Four lecture notes are included: (1) motivation for numerical calculations in Quantum Field Theory; (2) numerical simulation methods; (3) Monte Carlo studies of Quantum Chromo Dynamics; and (4) systems with fermions. 23 references

  14. Expansion and compression shock wave calculation in pipes with the C.V.M. numerical method

    International Nuclear Information System (INIS)

    Raymond, P.; Caumette, P.; Le Coq, G.; Libmann, M.

    1983-03-01

    The Control Variables Method for fluid transients computations has been used to compute expansion and compression shock waves propagations. In this paper, first analytical solutions for shock wave and rarefaction wave propagation are detailed. Then after a rapid description of the C.V.M. technique and its stability and monotonicity properties, we will present some results about standard shock tube problem, reflection of shock wave, finally a comparison between experimental results obtained on the ELF facility and calculations is given

  15. Numerical weld modeling - a method for calculating weld-induced residual stresses

    International Nuclear Information System (INIS)

    Fricke, S.; Keim, E.; Schmidt, J.

    2001-01-01

    In the past, weld-induced residual stresses caused damage to numerous (power) plant parts, components and systems (Erve, M., Wesseling, U., Kilian, R., Hardt, R., Bruemmer, G., Maier, V., Ilg, U., 1994. Cracking in Stabilized Austenitic Stainless Steel Piping of German Boiling Water Reactors - Characteristic Features and Root Causes. 20. MPA-Seminar 1994, vol. 2, paper 29, pp.29.1-29.21). In the case of BWR nuclear power plants, this damage can be caused by the mechanism of intergranular stress corrosion cracking in austenitic piping or the core shroud in the reactor pressure vessel and is triggered chiefly by weld-induced residual stresses. One solution of this problem that has been used in the past involves experimental measurements of residual stresses in conjunction with weld optimization testing. However, the experimental analysis of all relevant parameters is an extremely tedious process. Numerical simulation using the finite element method (FEM) not only supplements this method but, in view of modern computer capacities, is also an equally valid alternative in its own right. This paper will demonstrate that the technique developed for numerical simulation of the welding process has not only been properly verified and validated on austenitic pipe welds, but that it also permits making selective statements on improvements to the welding process. For instance, numerical simulation can provide information on the starting point of welding for every weld bead, the effect of interpass cooling as far as a possible sensitization of the heat affected zone (HAZ) is concerned, the effect of gap width on the resultant weld residual stresses, or the effect of the 'last pass heat sink welding' (welding of the final passes while simultaneously cooling the inner surface with water) producing compressive stresses in the root area of a circumferential weld in an austenitic pipe. The computer program FERESA (finite element residual stress analysis) was based on a commercially

  16. 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.

  17. 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.

  18. 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)

    1998-12-31

    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.

  19. 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.

  20. A numerical method to calculate flow-induced vibrations in a turbulent flow

    International Nuclear Information System (INIS)

    Sadaoka, Noriyuki; Umegaki, Kikuo

    1993-01-01

    An unsteady fluid force on structures in a turbulent flow can cause their vibration. The phenomenon is the most important among various flow-induced vibrations and it is an important subject in design nuclear plant components such as heat exchangers. A new approach to simulate flow-induced vibrations is introduced. A fully coupled analysis of fluid-structure interaction has been realized in a turbulent flow field by integrating the following calculational steps: (a) solving turbulent flow by a direct simulation method where the ALE (arbitrary Lagrangian Eulerian) type approximation is adopted to take account of structure displacements; (b) estimating fluid force on structures by integrating fluid pressure and shear stress; (c) calculating dynamic response of structures and determining the amount of displacement; (d) regenerate curvilinear grids for new geometry using the boundary-fitted coordinate transformation method. Forced vibration of a circular cylinder in a cross flow were successfully simulated and the synchronization phenomena between Karman-vortices and cylinder vibrations were clearly seen

  1. Numerical Comparison of Various Methods of Transient Flow Calculation in Water Conveyance Systems with Pumping Station

    Directory of Open Access Journals (Sweden)

    Alireza Khoshfetrat

    2018-05-01

    Full Text Available Under transient flow condition, the behavior of water conveyance system varies according to their characteristics. In the present study, the pressure was measured using a fast and sensitive pressure gauge in Bukan and Piranshahr water conveyance system. The pressure simulation was conducted using Bentley Hammer software. The friction head loss was calculated by different methods. The results showed that Unsteady Vitkovsky method had minimum error comparing with other methods. Wave velocity increase had direct effect on maximum pressures while velocity decrease affected minimum pressures. In a shorter water conveyance system, the reduction of wave velocity had direct effect on maximum pressure. Destruction to the long conveyance system was more probable and maximum and minimum pressures occurred during the first period. Shorter conveyance system had more pressure fluctuations and the minimum pressure did not occur in the first period. Coincidence of periods happened at the beginning and continued untill the end of data recording in the longer conveyance system. However, as time passed by, such coincidence did not occure in shorter conveyance system.

  2. 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.

  3. 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.

  4. 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)

  5. Methods for the numerical calculation of the plasma potential from measured Langmuir probe characteristics

    International Nuclear Information System (INIS)

    Seifert, W.; Johanning, D.; Bankov, N.

    1986-01-01

    In a previous paper the results of the Langmuir probe experiment carried out on board of two INTERKOSMOS satellites have been described. The experiences have shown that the usage of high quality algorithms for analyzing the current-voltage-characteristics is necessary to yield real physical parameters. The key problem is the determination of the plasma potential. This paper reviews the different methods to determine the plasma potential especially under the circumstances of computer application. The test of the well developed methods shows, that for the evaluation of the applied methods a number of different factors, discussed in the following sections of this paper, has to be taken into account. The used test data are model values or real measurements obtained by the satellite missions IK-10, IK-18 and BULGARIA-1300. The computer procedures have been realized as FORTRAN-subroutines for the BESM 6 and ES 1040. (author)

  6. 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.)

  7. An approach to 3D magnetic field calculation using numerical and differential algebra methods

    International Nuclear Information System (INIS)

    Caspi, S.; Helm, M.; Laslett, L.J.; Brady, V.O.

    1992-01-01

    Motivated by the need for new means for specification and determination of 3D fields that are produced by electromagnetic lens elements in the region interior to coil windings and seeking to obtain techniques that will be convenient for accurate conductor placement and dynamical study of particle motion, we have conveniently gene the representation of a 2D magnetic field to 3D. We have shown that the 3 dimensioal magnetic field components of a multipole magnet in the curl-fire divergence-fire region near the axis r=0 can be derived from one dimensional functions A n (z) and their derivatives (part 1). In the region interior to coil windings of accelerator magnets the three spatial components of magnet fields can be expressed in terms of ''harmonic components'' proportional to functions sin (nθ) or cos (nθ) of the azimuthal angle. The r,z dependence of any such component can then be expressed in terms of powers of r times functions A n (z) and their derivatives. For twodimensional configurations B z of course is identically zero, the derivatives of A n (z) vanish, and the harmonic components of the transverse field then acquire a simple proportionality B r,n ∝ r n-1 sin (nθ),B θ,n ∝ r n-1 cos (nθ), whereas in a 3-D configuration the more complex nature of the field gives rise to additional so-called ''psuedomultipole'' components as judged by additional powers of r required in the development of the field. Computation of the 3-D magnetic field arising at a sequence of field points, as a direct result of a specified current configuration or coil geometry, can be calculated explicitly through use of the Biot-Savart law and from such data the coefficients can then be derived for a general development of the type indicated above. We indicate, discuss, and illustrate two means by which this development may be performed

  8. 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...... sets of interdiffusion coefficients. After that, the numerical inverse method was then adopted in a ternary Al-Cu-Ni finite diffusion couple. Based on the measured composition profiles, the ternary interdiffusion coefficients along the entire diffusion path of the target ternary diffusion couple were...... obtained by using the numerical inverse approach. The comprehensive comparisons between the computations and the experiments indicate that the numerical inverse method is also applicable to high-throughput determination of the composition-dependent interdiffusion coefficients in finite diffusion couples....

  9. Methods of numerical relativity

    International Nuclear Information System (INIS)

    Piran, T.

    1983-01-01

    Numerical Relativity is an alternative to analytical methods for obtaining solutions for Einstein equations. Numerical methods are particularly useful for studying generation of gravitational radiation by potential strong sources. The author reviews the analytical background, the numerical analysis aspects and techniques and some of the difficulties involved in numerical relativity. (Auth.)

  10. Numerical calculation of the tensor of diffusion in the nuclear reactor cells by Monte-Carlo method

    International Nuclear Information System (INIS)

    Gorodkov, S.S.; Kalugin, M.A.

    2009-01-01

    New algorithm based on the sequential application of the RMS path method has been proposed for the diffusion constants calculation. The offered algorithm conforms to the diffusion constants calculation in arbitrary segments of nuclear reactors without detail description of geometry, dependence of cross-sections from energy or neutron scattering anisotropy by kernel medium. The proposed algorithm is used for the diffusion constants calculation in uranium-graphite reactor sells

  11. 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

  12. Advances in Numerical Methods

    CERN Document Server

    Mastorakis, Nikos E

    2009-01-01

    Features contributions that are focused on significant aspects of current numerical methods and computational mathematics. This book carries chapters that advanced methods and various variations on known techniques that can solve difficult scientific problems efficiently.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. A Numerical Method for Calculating the Wave Drag of a Configuration from the Second Derivative of the Area Distribution of a Series of Equivalent Bodies of Revolution

    Science.gov (United States)

    Levy, Lionel L., Jr.; Yoshikawa, Kenneth K.

    1959-01-01

    A method based on linearized and slender-body theories, which is easily adapted to electronic-machine computing equipment, is developed for calculating the zero-lift wave drag of single- and multiple-component configurations from a knowledge of the second derivative of the area distribution of a series of equivalent bodies of revolution. The accuracy and computational time required of the method to calculate zero-lift wave drag is evaluated relative to another numerical method which employs the Tchebichef form of harmonic analysis of the area distribution of a series of equivalent bodies of revolution. The results of the evaluation indicate that the total zero-lift wave drag of a multiple-component configuration can generally be calculated most accurately as the sum of the zero-lift wave drag of each component alone plus the zero-lift interference wave drag between all pairs of components. The accuracy and computational time required of both methods to calculate total zero-lift wave drag at supersonic Mach numbers is comparable for airplane-type configurations. For systems of bodies of revolution both methods yield similar results with comparable accuracy; however, the present method only requires up to 60 percent of the computing time required of the harmonic-analysis method for two bodies of revolution and less time for a larger number of bodies.

  18. Numerical calculation of two-phase flows

    International Nuclear Information System (INIS)

    Travis, J.R.; Harlow, F.H.; Amsden, A.A.

    1975-06-01

    The theoretical study of time-varying two-phase flow problems in several space dimensions introduces such a complicated set of coupled nonlinear partial differential equations that numerical solution procedures for high-speed computers are required in almost all but the simplest examples. Efficient attainment of realistic solutions for practical problems requires a finite- difference formulation that is simultaneously implicit in the treatment of mass convection, equations of state, and the momentum coupling between phases. Such a method is described, the equations on which it is based are discussed, and its properties are illustrated by means of examples. In particular, the capability for calculating physical instabilities and other time-varying dynamics, at the same time avoiding numerical instability is emphasized. The computer code is applicable to problems in reactor safety analysis, the dynamics of fluidized dust beds, raindrops or aerosol transport, and a variety of similar circumstances, including the effects of phase transitions and the release of latent heat or chemical energy. (U.S.)

  19. Reactor Thermal Hydraulic Numerical Calculation And Modeling

    International Nuclear Information System (INIS)

    Duong Ngoc Hai; Dang The Ba

    2008-01-01

    In the paper the results of analysis of thermal hydraulic state models using the numerical codes such as COOLOD, EUREKA and RELAP5 for simulation of the reactor thermal hydraulic states are presented. The calculations, analyses of reactor thermal hydraulic state and safety were implemented using different codes. The received numerical results, which were compared each to other, to experiment measurement of Dalat (Vietnam) research reactor and published results, show their appropriateness and capacity for analyses of different appropriate cases. (author)

  20. 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.

  1. Numerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in single-cell traps.

    Science.gov (United States)

    Rosales, Carlos; Lim, Kian Meng

    2005-06-01

    This paper presents detailed numerical calculations of the dielectrophoretic force in traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that a small number of multipolar terms need to be considered in order to obtain accurate results for spheres, even in the proximity of the electrodes, and that the full MST calculation is only required in the study of non-spherical particles.

  2. Calculating qP-wave traveltimes in 2-D TTI media by high-order fast sweeping methods with a numerical quartic equation solver

    Science.gov (United States)

    Han, Song; Zhang, Wei; Zhang, Jie

    2017-09-01

    A fast sweeping method (FSM) determines the first arrival traveltimes of seismic waves by sweeping the velocity model in different directions meanwhile applying a local solver. It is an efficient way to numerically solve Hamilton-Jacobi equations for traveltime calculations. In this study, we develop an improved FSM to calculate the first arrival traveltimes of quasi-P (qP) waves in 2-D tilted transversely isotropic (TTI) media. A local solver utilizes the coupled slowness surface of qP and quasi-SV (qSV) waves to form a quartic equation, and solve it numerically to obtain possible traveltimes of qP-wave. The proposed quartic solver utilizes Fermat's principle to limit the range of the possible solution, then uses the bisection procedure to efficiently determine the real roots. With causality enforced during sweepings, our FSM converges fast in a few iterations, and the exact number depending on the complexity of the velocity model. To improve the accuracy, we employ high-order finite difference schemes and derive the second-order formulae. There is no weak anisotropy assumption, and no approximation is made to the complex slowness surface of qP-wave. In comparison to the traveltimes calculated by a horizontal slowness shooting method, the validity and accuracy of our FSM is demonstrated.

  3. Numerical calculations in elementary quantum mechanics using Feynman path integrals

    International Nuclear Information System (INIS)

    Scher, G.; Smith, M.; Baranger, M.

    1980-01-01

    We show that it is possible to do numerical calculations in elementary quantum mechanics using Feynman path integrals. Our method involves discretizing both time and space, and summing paths through matrix multiplication. We give numerical results for various one-dimensional potentials. The calculations of energy levels and wavefunctions take approximately 100 times longer than with standard methods, but there are other problems for which such an approach should be more efficient

  4. 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.

  5. 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)

  6. Essential numerical computer methods

    CERN Document Server

    Johnson, Michael L

    2010-01-01

    The use of computers and computational methods has become ubiquitous in biological and biomedical research. During the last 2 decades most basic algorithms have not changed, but what has is the huge increase in computer speed and ease of use, along with the corresponding orders of magnitude decrease in cost. A general perception exists that the only applications of computers and computer methods in biological and biomedical research are either basic statistical analysis or the searching of DNA sequence data bases. While these are important applications they only scratch the surface of the current and potential applications of computers and computer methods in biomedical research. The various chapters within this volume include a wide variety of applications that extend far beyond this limited perception. As part of the Reliable Lab Solutions series, Essential Numerical Computer Methods brings together chapters from volumes 210, 240, 321, 383, 384, 454, and 467 of Methods in Enzymology. These chapters provide ...

  7. 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

  8. Application of numerical methods to the determination of molecular wave functions; Application de methodes de calcul numerique a la determination de fonctions d'onde moleculaires

    Energy Technology Data Exchange (ETDEWEB)

    Douady, Jerome

    1969-10-01

    A simplified SCF Method is developed. The wave function of molecular systems and spin densities in the case of free radicals are computed from geometrical data. This method, including at the beginning a delocalization of electrons over all the molecular system, two methods which clear out bonding and anti-bonding interactions have been studied and programmed: a) overlap population analysis, b) localisation of molecular orbitals. These methods have been carried out in the case of organic compounds and free radicals. (author) [French] Mise en oeuvre d'une methode de champ self-consistant simplifie qui, a partir des donnees geometriques, permet de calculer la fonction d'onde des systemes moleculaires et les densites de spin dans le cas des radicaux libres. Cette methode introduisant au depart une delocalisation des electrons sur tout le systeme moleculaire, deux methodes permettant de rendre compte du caractere liant et antiliant de ces electrons ont ete etudiees et programmees: a) analyse des populations de recouvrement, b) localisation des orbitales moleculaires. Ces methodes ont ete appliquees a divers composes organiques radicalaires et non radicalaires. (auteur)

  9. A numerical calculation method for flow discretisation in complex geometry with body-fitted grids; Rechenverfahren zur Diskretisierung von Stroemungen in komplexer Geometrie mittels koerperangepasster Gitter

    Energy Technology Data Exchange (ETDEWEB)

    Jin, X.

    2001-04-01

    A numerical calculation method basing on body fitted grids is developed in this work for computational fluid dynamics in complex geometry. The method solves the conservation equations in a general nonorthogonal coordinate system which matches the curvilinear boundary. The nonorthogonal, patched grid is generated by a grid generator which solves algebraic equations. By means of an interface its geometrical data can be used by this method. The conservation equations are transformed from the Cartesian system to a general curvilinear system keeping the physical Cartesian velocity components as dependent variables. Using a staggered arrangement of variables, the three Cartesian velocity components are defined on every cell surface. Thus the coupling between pressure and velocity is ensured, and numerical oscillations are avoided. The contravariant velocity for calculating mass flux on one cell surface is resulting from dependent Cartesian velocity components. After the discretisation and linear interpolation, a three dimensional 19-point pressure equation is found. Using the explicit treatment for cross-derivative terms, it reduces to the usual 7-point equation. Under the same data and process structure, this method is compatible with the code FLUTAN using Cartesian coordinates. In order to verify this method, several laminar flows are simulated in orthogonal grids at tilted space directions and in nonorthogonal grids with variations of cell angles. The simulated flow types are considered like various duct flows, transient heat conduction, natural convection in a chimney and natural convection in cavities. Their results achieve very good agreement with analytical solutions or empirical data. Convergence for highly nonorthogonal grids is obtained. After the successful validation of this method, it is applied for a reactor safety case. A transient natural convection flow for an optional sump cooling concept SUCO is simulated. The numerical result is comparable with the

  10. Numerical calculations on heterogeneity of groundwater flow

    International Nuclear Information System (INIS)

    Follin, S.

    1992-01-01

    The upscaling of model parameters is a key issue in many research fields concerned with parameter heterogeneity. The upscaling process allows for fewer model blocks and relaxes the numerical problems caused by high contrasts in the hydraulic conductivity. The trade-offs are dependent on the object but the general drawback is an increasing uncertainty about the representativeness. The present study deals with numerical calculations of heterogeneity of groundwater flow and solute transport in hypothetical blocks of fractured hard rock in a '3m scale' and addresses both conceptual and practical problems in numerical simulation. Evidence that the hydraulic conductivity (K) of the rock mass between major fracture zones is highly heterogeneous in a 3m scale is provided by a large number of field investigations. The present uses the documented heterogeneity and investigates flow and transport in a two-dimensional stochastic continuum characterized by a variance in Y = In(K) of σ y 2 = 16, corresponding to about 12 log 10 cycles in K. The study considers anisotropy, channelling, non-Fickian and Fickian transport, and conditional simulation. The major conclusions are: * heterogeneity gives rise to anisotropy in the upscaling process, * the choice of support scale is crucial for the modelling of solute transport. As a consequence of the obtained results, a two-dimensional stochastic discontinuum model is presented, which provides a tool for linking stochastic continuum models to discrete fracture network models. (au) (14 figs., 136 refs.)

  11. 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.

  12. Introduction to precise numerical methods

    CERN Document Server

    Aberth, Oliver

    2007-01-01

    Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. All disc-based content for this title is now available on the Web. · Clearer, simpler descriptions and explanations ofthe various numerical methods· Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane.

  13. Uneconomical top calculation method

    International Nuclear Information System (INIS)

    De Noord, M.; Vanm Sambeek, E.J.W.

    2003-08-01

    The methodology used to calculate the financial gap of renewable electricity sources and technologies is described. This methodology is used for calculating the production subsidy levels (MEP subsidies) for new renewable electricity projects in 2004 and 2005 in the Netherlands [nl

  14. Numerical calculation of the Fresnel transform.

    Science.gov (United States)

    Kelly, Damien P

    2014-04-01

    In this paper, we address the problem of calculating Fresnel diffraction integrals using a finite number of uniformly spaced samples. General and simple sampling rules of thumb are derived that allow the user to calculate the distribution for any propagation distance. It is shown how these rules can be extended to fast-Fourier-transform-based algorithms to increase calculation efficiency. A comparison with other theoretical approaches is made.

  15. 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.

  16. 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.

  17. Numerical calculation of backfilling of scour holes

    DEFF Research Database (Denmark)

    Sumer, B. Mutlu; Baykal, Cüneyt; Fuhrman, David R.

    2014-01-01

    A fully-coupled hydrodynamic and morphologic CFD model is presented for simulating backfilling processes around structures. The hydrodynamic model is based on Reynolds-averaged Navier-Stokes equations, coupled with two-equation k-ω turbulence closure. The sediment transport model consists of sepa...... of structures: piles, and pipelines. Initial scour holes are generated by the same model. The numerical results appear to be in accord with the existing experimental information....

  18. 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.

  19. 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.

  20. Numerical calculation of hadron masses in lattice quantum chromodynamics

    International Nuclear Information System (INIS)

    Montvay, I.

    1985-07-01

    Recent numerical Monte Carlo simulations of the hadron spectrum are reviewed. After a general introduction, different ways of calculating the hadron masses in the ''quenched approximation'' (i.e. neglecting virtual quark loops) are described and the latest results are summarized. The pseudofermion method and the iterative hopping expansion method for the introduction of dynamical quarks is discussed, and the first results about the hadron spectrum including the effect of virtual quark loops are reviewed. A separate section is devoted to the discussion of the questions related to scaling with dynamical quarks. (orig./HSI)

  1. 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)

  2. 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

  3. Numerical shoves and countershoves in electron transport calculations

    International Nuclear Information System (INIS)

    Filippone, W.L.

    1986-01-01

    The justification for applying the relatively complex (compared to S/sub n/) streaming ray (SR) algorithm to electron transport problems is its potential for doing rapid and accurate calculations. Because of the Lagrangian treatment of the cell-uncollided electrons, the only significant sources of error are the numerical treatment of the scattering kernel and the spatial differencing scheme used for the cell-collided electrons. Considerable progress has been made in reducing the former source of error. If one is willing to pay the price, the latter source of error can be reduced to any desired level by refining the mesh size or by using high-order differencing schemes. Here the method of numerical shoves and countershoves is introduced, which reduces spatial differencing errors using relatively little additional computational effort

  4. 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

  5. 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...

  6. Recent status of numerical simulation studies for zeolites as highly-selective cesium adsorbents by first-principles calculation and Monte Carlo method

    International Nuclear Information System (INIS)

    Nakamura, Hiroki; Okumura, Masahiko; Machida, Masahiko

    2015-01-01

    The authors examined, based on first-principles calculation, the mechanism of mordenite as a species of zeolite to show high adsorption selectivity for Cs, with a focus on the pores as adsorption site. For increasing the adsorption selectivity for Cs, the following three conditions for mordenite were proposed: (1) to have many pores with a radius of about 3 Å, (2) relatively small ratio of Al and Si, and (3) uniform distribution of Al atoms around the pores to adsorb Cs. The superposition effect of the interaction obtained by embracing positive ions with all the pores was revealed to be important, which verified the importance of computational science. It was also successfully conducted to reproduce with Monte Carlo method the thermodynamic level data of ion exchange isotherms, which became engineering metrics after actual measurement. This method was able to reproduce the difference in properties shown by different zeolites, and also able to explain changes in the adsorption performance that depends on Al and Si ratio, which remained the findings from experience up to date, by utilizing the method to associate the result to microscopic factors. Based on these results, this paper discusses how far material development would be realized depending on the leadership of computational science, and what kinds of research and development would be required in the future. (A.O)

  7. Operator theory and numerical methods

    CERN Document Server

    Fujita, H; Suzuki, T

    2001-01-01

    In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method.

  8. Methods for magnetostatic field calculation

    International Nuclear Information System (INIS)

    Vorozhtsov, S.B.

    1984-01-01

    Two methods for magnetostatic field calculation: differential and integrat are considered. Both approaches are shown to have certain merits and drawbacks, choice of the method depend on the type of the solved problem. An opportunity of combination of these tWo methods in one algorithm (hybrid method) is considered

  9. 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...

  10. Numerical calculation of beam coupling impedances in synchrotron accelerators

    International Nuclear Information System (INIS)

    Haenichen, Lukas

    2016-01-01

    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

  11. 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

  12. 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

  13. Numerical methods in matrix computations

    CERN Document Server

    Björck, Åke

    2015-01-01

    Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work. Åke Björck is a professor emeritus at the Department of Mathematics, Linköping University. He is a Fellow of the Society of Industrial and Applied Mathematics.

  14. Calculation Methods for Wallenius’ Noncentral Hypergeometric Distribution

    DEFF Research Database (Denmark)

    Fog, Agner

    2008-01-01

    Two different probability distributions are both known in the literature as "the" noncentral hypergeometric distribution. Wallenius' noncentral hypergeometric distribution can be described by an urn model without replacement with bias. Fisher's noncentral hypergeometric distribution...... 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...... distribution are derived. Range of applicability, numerical problems, and efficiency are discussed for each method. Approximations to the mean and variance are also discussed. This distribution has important applications in models of biased sampling and in models of evolutionary systems....

  15. Numerical methods for image registration

    CERN Document Server

    Modersitzki, Jan

    2003-01-01

    Based on the author's lecture notes and research, this well-illustrated and comprehensive text is one of the first to provide an introduction to image registration with particular emphasis on numerical methods in medical imaging. Ideal for researchers in industry and academia, it is also a suitable study guide for graduate mathematicians, computer scientists, engineers, medical physicists, and radiologists.Image registration is utilised whenever information obtained from different viewpoints needs to be combined or compared and unwanted distortion needs to be eliminated. For example, CCTV imag

  16. Simple method for calculating island widths

    International Nuclear Information System (INIS)

    Cary, J.R.; Hanson, J.D.; Carreras, B.A.; Lynch, V.E.

    1989-01-01

    A simple method for calculating magnetic island widths has been developed. This method uses only information obtained from integrating along the closed field line at the island center. Thus, this method is computationally less intensive than the usual method of producing surfaces of section of sufficient detail to locate and resolve the island separatrix. This method has been implemented numerically and used to analyze the buss work islands of ATF. In this case the method proves to be accurate to at least within 30%. 7 refs

  17. Methods for Melting Temperature Calculation

    Science.gov (United States)

    Hong, Qi-Jun

    Melting temperature calculation has important applications in the theoretical study of phase diagrams and computational materials screenings. In this thesis, we present two new methods, i.e., the improved Widom's particle insertion method and the small-cell coexistence method, which we developed in order to capture melting temperatures both accurately and quickly. We propose a scheme that drastically improves the efficiency of Widom's particle insertion method by efficiently sampling cavities while calculating the integrals providing the chemical potentials of a physical system. This idea enables us to calculate chemical potentials of liquids directly from first-principles without the help of any reference system, which is necessary in the commonly used thermodynamic integration method. As an example, we apply our scheme, combined with the density functional formalism, to the calculation of the chemical potential of liquid copper. The calculated chemical potential is further used to locate the melting temperature. The calculated results closely agree with experiments. We propose the small-cell coexistence method based on the statistical analysis of small-size coexistence MD simulations. It eliminates the risk of a metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Using empirical potentials, we validate the method and systematically study the finite-size effect on the calculated melting points. The method converges to the exact result in the limit of a large system size. An accuracy within 100 K in melting temperature is usually achieved when the simulation contains more than 100 atoms. DFT examples of Tantalum, high-pressure Sodium, and ionic material NaCl are shown to demonstrate the accuracy and flexibility of the method in its practical applications. The method serves as a promising approach for large-scale automated material screening in which

  18. 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...

  19. Methods for enhancing numerical integration

    International Nuclear Information System (INIS)

    Doncker, Elise de

    2003-01-01

    We give a survey of common strategies for numerical integration (adaptive, Monte-Carlo, Quasi-Monte Carlo), and attempt to delineate their realm of applicability. The inherent accuracy and error bounds for basic integration methods are given via such measures as the degree of precision of cubature rules, the index of a family of lattice rules, and the discrepancy of uniformly distributed point sets. Strategies incorporating these basic methods often use paradigms to reduce the error by, e.g., increasing the number of points in the domain or decreasing the mesh size, locally or uniformly. For these processes the order of convergence of the strategy is determined by the asymptotic behavior of the error, and may be too slow in practice for the type of problem at hand. For certain problem classes we may be able to improve the effectiveness of the method or strategy by such techniques as transformations, absorbing a difficult part of the integrand into a weight function, suitable partitioning of the domain, transformations and extrapolation or convergence acceleration. Situations warranting the use of these techniques (possibly in an 'automated' way) are described and illustrated by sample applications

  20. Numerical calculation of two phase flow in a shock tube

    International Nuclear Information System (INIS)

    Rivard, W.C.; Travis, J.R.; Torrey, M.D.

    1976-01-01

    Numerical calculations of the dynamics of initially saturated water-steam mixtures in a shock tube demonstrate the accuracy and efficiency of a new solution technique for the transient, two-dimensional, two-fluid equations. The dependence of the calculated results on time step and cell size are investigated. The effects of boiling and condensation on the flow physics suggest the merits of basic fluid dynamic measurements for the determination and evaluation of mass exchange models

  1. On the theories, techniques, and computer codes used in numerical reactor criticality and burnup calculations

    International Nuclear Information System (INIS)

    El-Osery, I.A.

    1981-01-01

    The purpose of this paper is to discuss the theories, techniques and computer codes that are frequently used in numerical reactor criticality and burnup calculations. It is a part of an integrated nuclear reactor calculation scheme conducted by the Reactors Department, Inshas Nuclear Research Centre. The crude part in numerical reactor criticality and burnup calculations includes the determination of neutron flux distribution which can be obtained in principle as a solution of Boltzmann transport equation. Numerical methods used for solving transport equations are discussed. Emphasis are made on numerical techniques based on multigroup diffusion theory. These numerical techniques include nodal, modal, and finite difference ones. The most commonly known computer codes utilizing these techniques are reviewed. Some of the main computer codes that have been already developed at the Reactors Department and related to numerical reactor criticality and burnup calculations have been presented

  2. New nonlinear methods for linear transport calculations

    International Nuclear Information System (INIS)

    Adams, M.L.

    1993-01-01

    We present a new family of methods for the numerical solution of the linear transport equation. With these methods an iteration consists of an 'S N sweep' followed by an 'S 2 -like' calculation. We show, by analysis as well as numerical results, that iterative convergence is always rapid. We show that this rapid convergence does not depend on a consistent discretization of the S 2 -like equations - they can be discretized independently from the S N equations. We show further that independent discretizations can offer significant advantages over consistent ones. In particular, we find that in a wide range of problems, an accurate discretization of the S 2 -like equation can be combined with a crude discretization of the S N equations to produce an accurate S N answer. We demonstrate this by analysis as well as numerical results. (orig.)

  3. 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.

  4. Numerical methods: Analytical benchmarking in transport theory

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    1988-01-01

    Numerical methods applied to reactor technology have reached a high degree of maturity. Certainly one- and two-dimensional neutron transport calculations have become routine, with several programs available on personal computer and the most widely used programs adapted to workstation and minicomputer computational environments. With the introduction of massive parallelism and as experience with multitasking increases, even more improvement in the development of transport algorithms can be expected. Benchmarking an algorithm is usually not a very pleasant experience for the code developer. Proper algorithmic verification by benchmarking involves the following considerations: (1) conservation of particles, (2) confirmation of intuitive physical behavior, and (3) reproduction of analytical benchmark results. By using today's computational advantages, new basic numerical methods have been developed that allow a wider class of benchmark problems to be considered

  5. 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

  6. 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)

  7. 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...... World Academic Press, UK. All rights reserved....

  8. Numerical Calculation of the Output Power of a MHD Generator

    Directory of Open Access Journals (Sweden)

    Adrian CARABINEANU

    2014-12-01

    Full Text Available Using Lazăr Dragoş’s analytic solution for the electric potential we perform some numerical calculations in order to find the characteristics of a Faraday magnetohydrodymamics (MHD power generator (total power, useful power and Joule dissipation power.

  9. 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

  10. 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.

  11. Numerical method for partial equilibrium flow

    International Nuclear Information System (INIS)

    Ramshaw, J.D.; Cloutman, L.D.; Los Alamos, New Mexico 87545)

    1981-01-01

    A numerical method is presented for chemically reactive fluid flow in which equilibrium and nonequilibrium reactions occur simultaneously. The equilibrium constraints on the species concentrations are established by a quadratic iterative procedure. If the equilibrium reactions are uncoupled and of second or lower order, the procedure converges in a single step. In general, convergence is most rapid when the reactions are weakly coupled. This can frequently be achieved by a judicious choice of the independent reactions. In typical transient calculations, satisfactory accuracy has been achieved with about five iterations per time step

  12. Elements of calculation of reactivity by numerical processing

    International Nuclear Information System (INIS)

    Hedde, J.

    1968-01-01

    In order to explore the new opportunities provided by numerical techniques, the author describes the theoretical optimal conditions of a calculation in real time of reactivity from counting samples produced by a nuclear reactor. These optimal conditions can be the better approached if a more complex processing is adopted. A compromise is to be searched between the desired precision and simplicity of the numerical processing hardware. An example is reported to assess result accuracy on a wide power evolution range with a structure of reduced complexity [fr

  13. 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.

  14. 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.

  15. Current system of the solar wind: results of numerical calculation

    International Nuclear Information System (INIS)

    Pisanko, Yu.V.

    1985-01-01

    Results of numerical calculations of surface current in the interplanetary current layer and steady volume current in the solar wind for heliocentric distances (1-10)Rsub(s) (Rsub(s) is the Sun radius) are given. The strength of current dependence on spatial coordinates is considered. Stationary nondissipative magnetohydrodynamic corona expansion (SNMCE) in the reference system rotating with the Sun is studied. Calculations show that three-dimensional current system of nonaxial-symmetric and nonsymmetric relatively to helioequator plane of SNMCE is more complicated than the zonal ring current around the Sun, which is the only component of the current system in spatial symmetric case

  16. Advanced Dynamics Analytical and Numerical Calculations with MATLAB

    CERN Document Server

    Marghitu, Dan B

    2012-01-01

    Advanced Dynamics: Analytical and Numerical Calculations with MATLAB provides a thorough, rigorous presentation of kinematics and dynamics while using MATLAB as an integrated tool to solve problems. Topics presented are explained thoroughly and directly, allowing fundamental principles to emerge through applications from areas such as multibody systems, robotics, spacecraft and design of complex mechanical devices. This book differs from others in that it uses symbolic MATLAB for both theory and applications. Special attention is given to solutions that are solved analytically and numerically using MATLAB. The illustrations and figures generated with MATLAB reinforce visual learning while an abundance of examples offer additional support. This book also: Provides solutions analytically and numerically using MATLAB Illustrations and graphs generated with MATLAB reinforce visual learning for students as they study Covers modern technical advancements in areas like multibody systems, robotics, spacecraft and des...

  17. 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

  18. Calculational methods for lattice cells

    International Nuclear Information System (INIS)

    Askew, J.R.

    1980-01-01

    At the current stage of development, direct simulation of all the processes involved in the reactor to the degree of accuracy required is not an economic proposition, and this is achieved by progressive synthesis of models for parts of the full space/angle/energy neutron behaviour. The split between reactor and lattice calculations is one such simplification. Most reactors are constructed of repetitions of similar geometric units, the fuel elements, having broadly similar properties. Thus the provision of detailed predictions of their behaviour is an important step towards overall modelling. We shall be dealing with these lattice methods in this series of lectures, but will refer back from time to time to their relationship with overall reactor calculation The lattice cell is itself composed of somewhat similar sub-units, the fuel pins, and will itself often rely upon a further break down of modelling. Construction of a good model depends upon the identification, on physical and mathematical grounds, of the most helpful division of the calculation at this level

  19. Radiation transport calculation methods in BNCT

    International Nuclear Information System (INIS)

    Koivunoro, H.; Seppaelae, T.; Savolainen, S.

    2000-01-01

    Boron neutron capture therapy (BNCT) is used as a radiotherapy for malignant brain tumours. Radiation dose distribution is necessary to determine individually for each patient. Radiation transport and dose distribution calculations in BNCT are more complicated than in conventional radiotherapy. Total dose in BNCT consists of several different dose components. The most important dose component for tumour control is therapeutic boron dose D B . The other dose components are gamma dose D g , incident fast neutron dose D f ast n and nitrogen dose D N . Total dose is a weighted sum of the dose components. Calculation of neutron and photon flux is a complex problem and requires numerical methods, i.e. deterministic or stochastic simulation methods. Deterministic methods are based on the numerical solution of Boltzmann transport equation. Such are discrete ordinates (SN) and spherical harmonics (PN) methods. The stochastic simulation method for calculation of radiation transport is known as Monte Carlo method. In the deterministic methods the spatial geometry is partitioned into mesh elements. In SN method angular integrals of the transport equation are replaced with weighted sums over a set of discrete angular directions. Flux is calculated iteratively for all these mesh elements and for each discrete direction. Discrete ordinates transport codes used in the dosimetric calculations are ANISN, DORT and TORT. In PN method a Legendre expansion for angular flux is used instead of discrete direction fluxes, land the angular dependency comes a property of vector function space itself. Thus, only spatial iterations are required for resulting equations. A novel radiation transport code based on PN method and tree-multigrid technique (TMG) has been developed at VTT (Technical Research Centre of Finland). Monte Carlo method solves the radiation transport by randomly selecting neutrons and photons from a prespecified boundary source and following the histories of selected particles

  20. NUMERICAL AND ANALYTIC METHODS OF ESTIMATION BRIDGES’ CONSTRUCTIONS

    Directory of Open Access Journals (Sweden)

    Y. Y. Luchko

    2010-03-01

    Full Text Available In this article the numerical and analytical methods of calculation of the stressed-and-strained state of bridge constructions are considered. The task on increasing of reliability and accuracy of the numerical method and its solution by means of calculations in two bases are formulated. The analytical solution of the differential equation of deformation of a ferro-concrete plate under the action of local loads is also obtained.

  1. An outline review of numerical transport methods

    International Nuclear Information System (INIS)

    Budd, C.

    1981-01-01

    A brief review is presented of numerical methods for solving the neutron transport equation in the context of reactor physics. First the various forms of transport equation are given. Second, the various ways of classifying numerical transport methods are discussed. Finally each method (or class of methods) is outlined in turn. (U.K.)

  2. Numerical methods for hydrodynamic stability problems

    International Nuclear Information System (INIS)

    Fujimura, Kaoru

    1985-11-01

    Numerical methods for solving the Orr-Sommerfeld equation, which is the fundamental equation of the hydrodynamic stability theory for various shear flows, are reviewed and typical numerical results are presented. The methods of asymptotic solution, finite difference methods, initial value methods and expansions in orthogonal functions are compared. (author)

  3. Numerical methods used in simulation

    International Nuclear Information System (INIS)

    Caseau, Paul; Perrin, Michel; Planchard, Jacques

    1978-01-01

    The fundamental numerical problem posed by simulation problems is the stability of the resolution diagram. The system of the most used equations is defined, since there is a family of models of increasing complexity with 3, 4 or 5 equations although only models with 3 and 4 equations have been used extensively. After defining what is meant by explicit or implicit, the best established stability results is given for one-dimension problems and then for two-dimension problems. It is shown that two types of discretisation may be defined: four and eight point diagrams (in one or two dimensions) and six and ten point diagrams (in one or two dimensions). To end, some results are given on problems that are not usually treated very much, i.e. non-asymptotic stability and the stability of diagrams based on finite elements [fr

  4. Numerical Calculation of the Flow in a Centrifugal Compressor Volute

    International Nuclear Information System (INIS)

    Seong, Seon Mo; Kang, Shin Hyoung; Cho, Kyung Seok; Kim, Woo June

    2007-01-01

    Flows in the centrifugal compressor volute with circular cross section are numerically investigated. The computational domain contained inlet passage, impeller, radial and axial diffuser, and volute. The volute grid for the calculation utilized a multi-block arrangement to form a butterfly grid and flow calculations are performed using commercial CFD software, CFX-TASCflow. The centrifugal compressor of this study has the inlet passage like steps and axial diffuser after radial diffuser because of the shape of the motor cooling fins and installation constraints. Due to this feature the swirling flow pattern is different from the other investigations. The loss in through the inlet passage was considerable and the flow inside volute is very complex and three dimensional with strong vortex and recirculation through volute tongue

  5. 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.

  6. 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.

  7. Experimental verification of numerical calculations of railway passenger seats

    Science.gov (United States)

    Ligaj, B.; Wirwicki, M.; Karolewska, K.; Jasińska, A.

    2018-04-01

    The construction of railway seats is based on industry regulations and the requirements of end users, i.e. passengers. The two main documents in this context are the UIC 566 (3rd Edition, dated 7 January 1994) and the EN 12663-1: 2010+A1:2014. The study was to carry out static load tests of passenger seat frames. The paper presents the construction of the test bench and the results of experimental and numerical studies of passenger seat rail frames. The test bench consists of a frame, a transverse beam, two electric cylinders with a force value of 6 kN, and a strain gauge amplifier. It has a modular structure that allows for its expansion depending on the structure of the seats. Comparing experimental results with numerical results for points A and B allowed to determine the existing differences. It follows from it that higher stress values are obtained by numerical calculations in the range of 0.2 MPa to 35.9 MPa.

  8. Numerical computer methods part D

    CERN Document Server

    Johnson, Michael L

    2004-01-01

    The aim of this volume is to brief researchers of the importance of data analysis in enzymology, and of the modern methods that have developed concomitantly with computer hardware. It is also to validate researchers' computer programs with real and synthetic data to ascertain that the results produced are what they expected. Selected Contents: Prediction of protein structure; modeling and studying proteins with molecular dynamics; statistical error in isothermal titration calorimetry; analysis of circular dichroism data; model comparison methods.

  9. 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

  10. 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

  11. 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.

  12. Numerical computer methods part E

    CERN Document Server

    Johnson, Michael L

    2004-01-01

    The contributions in this volume emphasize analysis of experimental data and analytical biochemistry, with examples taken from biochemistry. They serve to inform biomedical researchers of the modern data analysis methods that have developed concomitantly with computer hardware. Selected Contents: A practical approach to interpretation of SVD results; modeling of oscillations in endocrine networks with feedback; quantifying asynchronous breathing; sample entropy; wavelet modeling and processing of nasal airflow traces.

  13. 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)

  14. 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)

  15. Numerical fluid flow and heat transfer calculations on multiprocessor systems

    Energy Technology Data Exchange (ETDEWEB)

    Oehman, G.A.; Malen, T.E.; Kuusela, P.

    1989-01-01

    The first part of the report presents the basic principles of parallel processing, and factors influencing tbe efficiency of practical applications are discussed. In a multiprocessor computer, different parts of the program code are executed in parallel, i.e. simultaneous with respect to time, on different processors, and thus it becomes possible to decrease the overall computation time by a factor, which in the ideal case is equal to the number of processors. The application study starts from the numerical solution of the twodimesional Laplace equation, which describes the steady heat conduction in a solid plate and advances through the solution of the three dimensional Laplace equation to the case of study laminar fluid flow in a twodimensional box at Reynolds numbers up to 20. Hereby the stream function-vorticity method is first applied and the SIMPLER method. The conventional (sequential) numerical algoritms for these fluid flow and heat transfer problems are found not to be ideally suited for conversion to parallel computation, but sped-up ratios considerably above 50 % of the theoretical maximum are regularly achieved in the runs. The numerical procedures we coded in the OCCAM-2 language and the test runs were performed at who Akademi on the imperimental HATHI-computers containing 16 T4l4 and 100 INMOS T800 transputers respectively.

  16. Numerical fluid flow and heat transfer calculations on multiprocessor systems

    Energy Technology Data Exchange (ETDEWEB)

    Oehman, G.A.; Malen, T.E.; Kuusela, P.

    1989-12-31

    The first part of the report presents the basic principles of parallel processing, and factors influencing tbe efficiency of practical applications are discussed. In a multiprocessor computer, different parts of the program code are executed in parallel, i.e. simultaneous with respect to time, on different processors, and thus it becomes possible to decrease the overall computation time by a factor, which in the ideal case is equal to the number of processors. The application study starts from the numerical solution of the twodimesional Laplace equation, which describes the steady heat conduction in a solid plate and advances through the solution of the three dimensional Laplace equation to the case of study laminar fluid flow in a twodimensional box at Reynolds numbers up to 20. Hereby the stream function-vorticity method is first applied and the SIMPLER method. The conventional (sequential) numerical algoritms for these fluid flow and heat transfer problems are found not to be ideally suited for conversion to parallel computation, but sped-up ratios considerably above 50 % of the theoretical maximum are regularly achieved in the runs. The numerical procedures we coded in the OCCAM-2 language and the test runs were performed at who Akademi on the imperimental HATHI-computers containing 16 T4l4 and 100 INMOS T800 transputers respectively.

  17. Monte Carlo methods to calculate impact probabilities

    Science.gov (United States)

    Rickman, H.; Wiśniowski, T.; Wajer, P.; Gabryszewski, R.; Valsecchi, G. B.

    2014-09-01

    Context. Unraveling the events that took place in the solar system during the period known as the late heavy bombardment requires the interpretation of the cratered surfaces of the Moon and terrestrial planets. This, in turn, requires good estimates of the statistical impact probabilities for different source populations of projectiles, a subject that has received relatively little attention, since the works of Öpik (1951, Proc. R. Irish Acad. Sect. A, 54, 165) and Wetherill (1967, J. Geophys. Res., 72, 2429). Aims: We aim to work around the limitations of the Öpik and Wetherill formulae, which are caused by singularities due to zero denominators under special circumstances. Using modern computers, it is possible to make good estimates of impact probabilities by means of Monte Carlo simulations, and in this work, we explore the available options. Methods: We describe three basic methods to derive the average impact probability for a projectile with a given semi-major axis, eccentricity, and inclination with respect to a target planet on an elliptic orbit. One is a numerical averaging of the Wetherill formula; the next is a Monte Carlo super-sizing method using the target's Hill sphere. The third uses extensive minimum orbit intersection distance (MOID) calculations for a Monte Carlo sampling of potentially impacting orbits, along with calculations of the relevant interval for the timing of the encounter allowing collision. Numerical experiments are carried out for an intercomparison of the methods and to scrutinize their behavior near the singularities (zero relative inclination and equal perihelion distances). Results: We find an excellent agreement between all methods in the general case, while there appear large differences in the immediate vicinity of the singularities. With respect to the MOID method, which is the only one that does not involve simplifying assumptions and approximations, the Wetherill averaging impact probability departs by diverging toward

  18. Calculation methods in program CCRMN

    Energy Technology Data Exchange (ETDEWEB)

    Chonghai, Cai [Nankai Univ., Tianjin (China). Dept. of Physics; Qingbiao, Shen [Chinese Nuclear Data Center, Beijing, BJ (China)

    1996-06-01

    CCRMN is a program for calculating complex reactions of a medium-heavy nucleus with six light particles. In CCRMN, the incoming particles can be neutrons, protons, {sup 4}He, deuterons, tritons and {sup 3}He. the CCRMN code is constructed within the framework of the optical model, pre-equilibrium statistical theory based on the exciton model and the evaporation model. CCRMN is valid in 1{approx} MeV energy region, it can give correct results for optical model quantities and all kinds of reaction cross sections. This program has been applied in practical calculations and got reasonable results.

  19. Accuracy requirements for the calculation of gravitational waveforms from coalescing compact binaries in numerical relativity

    International Nuclear Information System (INIS)

    Miller, Mark

    2005-01-01

    I discuss the accuracy requirements on numerical relativity calculations of inspiraling compact object binaries whose extracted gravitational waveforms are to be used as templates for matched filtering signal extraction and physical parameter estimation in modern interferometric gravitational wave detectors. Using a post-Newtonian point particle model for the premerger phase of the binary inspiral, I calculate the maximum allowable errors for the mass and relative velocity and positions of the binary during numerical simulations of the binary inspiral. These maximum allowable errors are compared to the errors of state-of-the-art numerical simulations of multiple-orbit binary neutron star calculations in full general relativity, and are found to be smaller by several orders of magnitude. A post-Newtonian model for the error of these numerical simulations suggests that adaptive mesh refinement coupled with second-order accurate finite difference codes will not be able to robustly obtain the accuracy required for reliable gravitational wave extraction on Terabyte-scale computers. I conclude that higher-order methods (higher-order finite difference methods and/or spectral methods) combined with adaptive mesh refinement and/or multipatch technology will be needed for robustly accurate gravitational wave extraction from numerical relativity calculations of binary coalescence scenarios

  20. Numerical method of singular problems on singular integrals

    International Nuclear Information System (INIS)

    Zhao Huaiguo; Mou Zongze

    1992-02-01

    As first part on the numerical research of singular problems, a numerical method is proposed for singular integrals. It is shown that the procedure is quite powerful for solving physics calculation with singularity such as the plasma dispersion function. Useful quadrature formulas for some class of the singular integrals are derived. In general, integrals with more complex singularities can be dealt by this method easily

  1. 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.

  2. Numerical calculation of velocity distribution near a vertical flat plate immersed in bubble flow

    International Nuclear Information System (INIS)

    Matsuura, Akihiro; Nakamura, Hajime; Horihata, Hideyuki; Hiraoka, Setsuro; Aragaki, Tsutomu; Yamada, Ikuho; Isoda, Shinji.

    1992-01-01

    Liquid and gas velocity distributions for bubble flow near a vertical flat plate were calculated numerically by using the SIMPLER method, where the flow was assumed to be laminar, two-dimensional, and at steady state. The two-fluid flow model was used in the numerical analysis. To calculate the drag force on a small bubble, Stokes' law for a rigid sphere is applicable. The dimensionless velocity distributions which were arranged with characteristic boundary layer thickness and maximum liquid velocity were adjusted with a single line and their forms were similar to that for single-phase wall-jet flow. The average wall shear stress derived from the velocity gradient at the plate wall was strongly affected by bubble diameter but not by inlet liquid velocity. The present dimensionless velocity distributions obtained numerically agreed well with previous experimental results, and the proposed numerical algorithm was validated. (author)

  3. Numerically induced pressure excursions in two-phase-flow calculations. Final report

    International Nuclear Information System (INIS)

    Mahaffy, J.H.; Liles, D.R.

    1983-01-01

    Pressure spikes that cannot be traced to any physical origin sometimes are observed when standard Eulerian finite-difference methods are used to calculate two-phase-flow transients. This problem occurs with varying frequency in nuclear reactor safety codes such as RELAP, RETRAN, COBRA, and TRAC. These spikes usually result from numerical water packing or from interactions between spatial discretization and heat transfer

  4. T.I.G. Welding of stainless steel. Numerical modelling for temperatures calculation in the Haz

    International Nuclear Information System (INIS)

    Martinez-Conesa, E. J.; Estrems-Amestoy, M.; Miguel-Eguia, V.; Garrido-Hernandez, A.; Guillen-Martinez, J. A.

    2010-01-01

    In this work, a numerical method for calculating the temperature field into the heat affected zone for butt welded joints is presented. The method has been developed for sheet welding and takes into account a bidimensional heat flow. It has built a computer program by MS-Excel books and Visual Basic for Applications (VBA). The model has been applied to the TIG process of AISI 304 stainless steel 2mm thickness sheet. The welding process has been considered without input materials. The numerical method may be used to help the designers to predict the temperature distribution in welded joints. (Author) 12 refs.

  5. Calculating the albedo characteristics by the method of transmission probabilities

    International Nuclear Information System (INIS)

    Lukhvich, A.A.; Rakhno, I.L.; Rubin, I.E.

    1983-01-01

    The possibility to use the method of transmission probabilities for calculating the albedo characteristics of homogeneous and heterogeneous zones is studied. The transmission probabilities method is a numerical method for solving the transport equation in the integrated form. All calculations have been conducted as a one-group approximation for the planes and rods with different optical thicknesses and capture-to-scattering ratios. Above calculations for plane and cylindrical geometries have shown the possibility to use the numerical method of transmission probabilities for calculating the albedo characteristics of homogeneous and heterogeneous zones with high accuracy. In this case the computer time consumptions are minimum even with the cylindrical geometry, if the interpolation calculation of characteristics is used for the neutrons of the first path

  6. 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

  7. 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

  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. 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

  10. 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.

  11. 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...

  12. Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

    International Nuclear Information System (INIS)

    Klein, R I; Stone, J M

    2007-01-01

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

  13. A numerical method for a transient two-fluid model

    International Nuclear Information System (INIS)

    Le Coq, G.; Libmann, M.

    1978-01-01

    The transient boiling two-phase flow is studied. In nuclear reactors, the driving conditions for the transient boiling are a pump power decay or/and an increase in heating power. The physical model adopted for the two-phase flow is the two fluid model with the assumption that the vapor remains at saturation. The numerical method for solving the thermohydraulics problems is a shooting method, this method is highly implicit. A particular problem exists at the boiling and condensation front. A computer code using this numerical method allow the calculation of a transient boiling initiated by a steady state for a PWR or for a LMFBR

  14. Hybrid methods for airframe noise numerical prediction

    Energy Technology Data Exchange (ETDEWEB)

    Terracol, M.; Manoha, E.; Herrero, C.; Labourasse, E.; Redonnet, S. [ONERA, Department of CFD and Aeroacoustics, BP 72, Chatillon (France); Sagaut, P. [Laboratoire de Modelisation en Mecanique - UPMC/CNRS, Paris (France)

    2005-07-01

    This paper describes some significant steps made towards the numerical simulation of the noise radiated by the high-lift devices of a plane. Since the full numerical simulation of such configuration is still out of reach for present supercomputers, some hybrid strategies have been developed to reduce the overall cost of such simulations. The proposed strategy relies on the coupling of an unsteady nearfield CFD with an acoustic propagation solver based on the resolution of the Euler equations for midfield propagation in an inhomogeneous field, and the use of an integral solver for farfield acoustic predictions. In the first part of this paper, this CFD/CAA coupling strategy is presented. In particular, the numerical method used in the propagation solver is detailed, and two applications of this coupling method to the numerical prediction of the aerodynamic noise of an airfoil are presented. Then, a hybrid RANS/LES method is proposed in order to perform some unsteady simulations of complex noise sources. This method allows for significant reduction of the cost of such a simulation by considerably reducing the extent of the LES zone. This method is described and some results of the numerical simulation of the three-dimensional unsteady flow in the slat cove of a high-lift profile are presented. While these results remain very difficult to validate with experiments on similar configurations, they represent up to now the first 3D computations of this kind of flow. (orig.)

  15. Spectral Methods in Numerical Plasma Simulation

    DEFF Research Database (Denmark)

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

    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...

  16. 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.

  17. Methods for calculating radiation attenuation in shields

    Energy Technology Data Exchange (ETDEWEB)

    Butler, J; Bueneman, D; Etemad, A; Lafore, P; Moncassoli, A M; Penkuhn, H; Shindo, M; Stoces, B

    1964-10-01

    In recent years the development of high-speed digital computers of large capacity has revolutionized the field of reactor shield design. For compact special-purpose reactor shields, Monte-Carlo codes in two- and three dimensional geometries are now available for the proper treatment of both the neutron and gamma- ray problems. Furthermore, techniques are being developed for the theoretical optimization of minimum-weight shield configurations for this type of reactor system. In the design of land-based power reactors, on the other hand, there is a strong incentive to reduce the capital cost of the plant, and economic considerations are also relevant to reactors designed for merchant ship propulsion. In this context simple methods are needed which are economic in their data input and computing time requirements and which, at the same time, are sufficiently accurate for design work. In general the computing time required for Monte-Carlo calculations in complex geometry is excessive for routine design calculations and the capacity of the present codes is inadequate for the proper treatment of large reactor shield systems in three dimensions. In these circumstances a wide range of simpler techniques are currently being employed for design calculations. The methods of calculation for neutrons in reactor shields fall naturally into four categories: Multigroup diffusion theory; Multigroup diffusion with removal sources; Transport codes; and Monte Carlo methods. In spite of the numerous Monte- Carlo techniques which are available for penetration and back scattering, serious problems are still encountered in practice with the scattering of gamma rays from walls of buildings which contain critical facilities and also concrete-lined discharge shafts containing irradiated fuel elements. The considerable volume of data in the unclassified literature on the solution of problems of this type in civil defence work appears not to have been evaluated for reactor shield design. In

  18. 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)

  19. A strong shock tube problem calculated by different numerical schemes

    Science.gov (United States)

    Lee, Wen Ho; Clancy, Sean P.

    1996-05-01

    Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 109 and density ratio of 103 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the Lagrangian methods.

  20. A strong shock tube problem calculated by different numerical schemes

    International Nuclear Information System (INIS)

    Lee, W.H.; Clancy, S.P.

    1996-01-01

    Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 10 9 and density ratio of 10 3 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the Lagrangian methods. copyright 1996 American Institute of Physics

  1. Development of numerical methods for thermohydraulic problems in reactor safety

    International Nuclear Information System (INIS)

    Chabrillac, M.; Kavenoky, A.; Le Coq, G.; L'Heriteau, J.P.; Stewart, B.; Rousseau, J.C.

    1976-01-01

    Numerical methods are being developed for the LOCA calculation; the first part is devoted to the BERTHA model and the associated characteristic treatment for the first seconds of the blowdown, the second part presents the problems encountered for accounting for velocity difference between phases. The FLIRA treatment of the reflooding is presented in the last part: this treatment allows the calculation of the quenching front velocity

  2. 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...

  3. 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

  4. 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...

  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. Overview of multifluid-flow-calculation methods

    International Nuclear Information System (INIS)

    Stewart, H.B.

    1981-01-01

    Two categories of numerical methods which may be useful in multiphase flow research are discussed. The first category includes methods which are specifically intended for accurate computation of discontinuities, such as the method of characteristics, particle-in-cell method, flux-corrected transport, and random choice methods. Methods in this category could be applied to research on rocket exhaust plumes and interior ballistics. The second category includes methods for smooth, subsonic flows, such as fractional step methods, semi-implicit method, and methods which treat convection implicitly. The subsonic flow methods could be of interest for ice flows

  7. 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.

  8. 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.

  9. 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

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

    Indian Academy of Sciences (India)

    Theoretical and numerical research has been previously done on ESPs to predict the efficiency ... Lagrangian simulations of particle transport in wire–plate ESP were .... The collection efficiency can be defined as the ratio of the number of ...

  11. 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

  12. 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.

  13. 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

  14. 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.

  15. Direct numerical methods of mathematical modeling in mechanical structural design

    International Nuclear Information System (INIS)

    Sahili, Jihad; Verchery, Georges; Ghaddar, Ahmad; Zoaeter, Mohamed

    2002-01-01

    Full text.Structural design and numerical methods are generally interactive; requiring optimization procedures as the structure is analyzed. This analysis leads to define some mathematical terms, as the stiffness matrix, which are resulting from the modeling and then used in numerical techniques during the dimensioning procedure. These techniques and many others involve the calculation of the generalized inverse of the stiffness matrix, called also the 'compliance matrix'. The aim of this paper is to introduce first, some different existing mathematical procedures, used to calculate the compliance matrix from the stiffness matrix, then apply direct numerical methods to solve the obtained system with the lowest computational time, and to compare the obtained results. The results show a big difference of the computational time between the different procedures

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

    International Nuclear Information System (INIS)

    Schwerg, Juljan Nikolai

    2010-01-01

    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 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

  17. 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

  18. 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

  19. A hybrid numerical method for orbit correction

    International Nuclear Information System (INIS)

    White, G.; Himel, T.; Shoaee, H.

    1997-09-01

    The authors describe a simple hybrid numerical method for beam orbit correction in particle accelerators. The method overcomes both degeneracy in the linear system being solved and respects boundaries on the solution. It uses the Singular Value Decomposition (SVD) to find and remove the null-space in the system, followed by a bounded Linear Least Squares analysis of the remaining recast problem. It was developed for correcting orbit and dispersion in the B-factory rings

  20. Conservative numerical methods for solitary wave interactions

    Energy Technology Data Exchange (ETDEWEB)

    Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)

    2003-07-18

    The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.

  1. Fast numerical calculations of ion-atom collisions

    International Nuclear Information System (INIS)

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

    1979-01-01

    When an ion impinges on an atom, the cross sections for electronic transitions can be described in the independent electron model by functions of single electron amplitudes. A single centered expansion of the time-dependent wave function of an electron about the heavier nucleus, with charge Z/sub N/, is shown to be moderately successful in explaining the dependence of K-shell hole production on the charge, Z/sub p/, of the projectile. However, capture of electrons by the projectile is important for a complete understanding and can be incorporated, in principle, in the single-center approach by evaluation of a transition matrix element involving a final state on the projectile. This is not an easy theoretical problem even in an asymmetric (Z/sub p/ much less than Z/sub N/) collision, because long times are involved which aggravate the inadequacies of a coupled-state calculation where the continuum is replaced by a discrete set of pseudostates. Nevertheless a method was devised which allows convergence in the truncated expansion of Hilbert states. Comparisons are made to experiment. Future developments are discussed

  2. Theoretical and numerical method in aeroacoustics

    Directory of Open Access Journals (Sweden)

    Nicuşor ALEXANDRESCU

    2010-06-01

    Full Text Available The paper deals with the mathematical and numerical modeling of the aerodynamic noisegenerated by the fluid flow interaction with the solid structure of a rotor blade.Our analysis use Lighthill’s acoustic analogy. Lighthill idea was to express the fundamental equationsof motion into a wave equation for acoustic fluctuation with a source term on the right-hand side. Theobtained wave equation is solved numerically by the spatial discretization. The method is applied inthe case of monopole source placed in different points of blade surfaces to find this effect of noisepropagation.

  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 methods for differential equations and applications

    International Nuclear Information System (INIS)

    Ixaru, L.G.

    1984-01-01

    This book is addressed to persons who, without being professionals in applied mathematics, are often faced with the problem of numerically solving differential equations. In each of the first three chapters a definite class of methods is discussed for the solution of the initial value problem for ordinary differential equations: multistep methods; one-step methods; and piecewise perturbation methods. The fourth chapter is mainly focussed on the boundary value problems for linear second-order equations, with a section devoted to the Schroedinger equation. In the fifth chapter the eigenvalue problem for the radial Schroedinger equation is solved in several ways, with computer programs included. (Auth.)

  5. 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)

  6. New numerical methods for quantum field theories on the continuum

    Energy Technology Data Exchange (ETDEWEB)

    Emirdag, P.; Easter, R.; Guralnik, G.S.; Hahn, S.C

    2000-03-01

    The Source Galerkin Method is a new numerical technique that is being developed to solve Quantum Field Theories on the continuum. It is not based on Monte Carlo techniques and has a measure to evaluate relative errors. It promises to increase the accuracy and speed of calculations, and takes full advantage of symmetries of the theory. The application of this method to the non-linear {sigma} model is outlined.

  7. 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...

  8. 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

  9. Methods for calculating anisotropic transfer cross sections

    International Nuclear Information System (INIS)

    Cai, Shaohui; Zhang, Yixin.

    1985-01-01

    The Legendre moments of the group transfer cross section, which are widely used in the numerical solution of the transport calculation can be efficiently and accurately constructed from low-order (K = 1--2) successive partial range moments. This is convenient for the generation of group constants. In addition, a technique to obtain group-angle correlation transfer cross section without Legendre expansion is presented. (author)

  10. Advances in computational methods for Quantum Field Theory calculations

    NARCIS (Netherlands)

    Ruijl, B.J.G.

    2017-01-01

    In this work we describe three methods to improve the performance of Quantum Field Theory calculations. First, we simplify large expressions to speed up numerical integrations. Second, we design Forcer, a program for the reduction of four-loop massless propagator integrals. Third, we extend the R*

  11. 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…

  12. 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

  13. 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.

  14. 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.

  15. 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...

  16. 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

  17. 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.

  18. 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

  19. Simplified dose calculation method for mantle technique

    International Nuclear Information System (INIS)

    Scaff, L.A.M.

    1984-01-01

    A simplified dose calculation method for mantle technique is described. In the routine treatment of lymphom as using this technique, the daily doses at the midpoints at five anatomical regions are different because the thicknesses are not equal. (Author) [pt

  20. 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 ...

  1. Range calculations using multigroup transport methods

    International Nuclear Information System (INIS)

    Hoffman, T.J.; Robinson, M.T.; Dodds, H.L. Jr.

    1979-01-01

    Several aspects of radiation damage effects in fusion reactor neutron and ion irradiation environments are amenable to treatment by transport theory methods. In this paper, multigroup transport techniques are developed for the calculation of particle range distributions. These techniques are illustrated by analysis of Au-196 atoms recoiling from (n,2n) reactions with gold. The results of these calculations agree very well with range calculations performed with the atomistic code MARLOWE. Although some detail of the atomistic model is lost in the multigroup transport calculations, the improved computational speed should prove useful in the solution of fusion material design problems

  2. 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.)

  3. Eigenvalue translation method for mode calculations

    International Nuclear Information System (INIS)

    Gerck, E.; Cruz, C.H.B.

    1978-11-01

    A new method is described for the first few modes calculations in a interferometer that has several advantages over the ALLMAT subroutine, the Prony Method and the Fox and Li Method. In the illustrative results shown for the same cases it can be seen that the eigenvalue translation method is typically 100 fold times faster than the usual Fox and Li Method and 10 times faster than ALLMAT [pt

  4. Calculation methods for determining dose equivalent

    International Nuclear Information System (INIS)

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

    1987-11-01

    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 [1] 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. The effective dose equivalent determined using ICRP-26 methods is significantly smaller than the dose equivalent determined by traditional methods. No existing personnel dosimeter or health physics instrument can determine effective dose equivalent. At the present time, the conversion of dosimeter response to dose equivalent is based on calculations for maximal or ''cap'' values using homogeneous spherical or cylindrical phantoms. The evaluated dose equivalent is, therefore, a poor approximation of the effective dose equivalent as defined by ICRP Publication 26. 3 refs., 2 figs., 1 tab

  5. Some applications of perturbation theory to numerical integration methods for the Schroedinger equation

    International Nuclear Information System (INIS)

    Killingbeck, J.

    1979-01-01

    By using the methods of perturbation theory it is possible to construct simple formulae for the numerical integration of the Schroedinger equation, and also to calculate expectation values solely by means of simple eigenvalue calculations. (Auth.)

  6. 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.

  7. Velocity field calculation for non-orthogonal numerical grids

    Energy Technology Data Exchange (ETDEWEB)

    Flach, G. P. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)

    2015-03-01

    Computational grids containing cell faces that do not align with an orthogonal (e.g. Cartesian, cylindrical) coordinate system are routinely encountered in porous-medium numerical simulations. Such grids are referred to in this study as non-orthogonal grids because some cell faces are not orthogonal to a coordinate system plane (e.g. xy, yz or xz plane in Cartesian coordinates). Non-orthogonal grids are routinely encountered at the Savannah River Site in porous-medium flow simulations for Performance Assessments and groundwater flow modeling. Examples include grid lines that conform to the sloping roof of a waste tank or disposal unit in a 2D Performance Assessment simulation, and grid surfaces that conform to undulating stratigraphic surfaces in a 3D groundwater flow model. Particle tracking is routinely performed after a porous-medium numerical flow simulation to better understand the dynamics of the flow field and/or as an approximate indication of the trajectory and timing of advective solute transport. Particle tracks are computed by integrating the velocity field from cell to cell starting from designated seed (starting) positions. An accurate velocity field is required to attain accurate particle tracks. However, many numerical simulation codes report only the volumetric flowrate (e.g. PORFLOW) and/or flux (flowrate divided by area) crossing cell faces. For an orthogonal grid, the normal flux at a cell face is a component of the Darcy velocity vector in the coordinate system, and the pore velocity for particle tracking is attained by dividing by water content. For a non-orthogonal grid, the flux normal to a cell face that lies outside a coordinate plane is not a true component of velocity with respect to the coordinate system. Nonetheless, normal fluxes are often taken as Darcy velocity components, either naively or with accepted approximation. To enable accurate particle tracking or otherwise present an accurate depiction of the velocity field for a non

  8. Improvement of patient return electrodes in electrosurgery by experimental investigations and numerical field calculations.

    Science.gov (United States)

    Golombeck, M A; Dössel, O; Raiser, J

    2003-09-01

    Numerical field calculations and experimental investigations were performed to examine the heating of the surface of human skin during the application of a new electrode design for the patient return electrode. The new electrode is characterised by an equipotential ring around the central electrode pads. A multi-layer thigh model was used, to which the patient return electrode and the active electrode were connected. The simulation geometry and the dielectric tissue parameters were set according to the frequency of the current. The temperature rise at the skin surface due to the flow of current was evaluated using a two-step numerical solving procedure. The results were compared with experimental thermographical measurements that yielded a mean value of maximum temperature increase of 3.4 degrees C and a maximum of 4.5 degrees C in one test case. The calculated heating patterns agreed closely with the experimental results. However, the calculated mean value in ten different numerical models of the maximum temperature increase of 12.5 K (using a thermodynamic solver) exceeded the experimental value owing to neglect of heat transport by blood flow and also because of the injection of a higher test current, as in the clinical tests. The implementation of a simple worst-case formula that could significantly simplify the numerical process led to a substantial overestimation of the mean value of the maximum skin temperature of 22.4 K and showed only restricted applicability. The application of numerical methods confirmed the experimental assertions and led to a general understanding of the observed heating effects and hotspots. Furthermore, it was possible to demonstrate the beneficial effects of the new electrode design with an equipotential ring. These include a balanced heating pattern and the absence of hotspots.

  9. 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...

  10. convergent methods for calculating thermodynamic Green functions

    OpenAIRE

    Bowen, S. P.; Williams, C. D.; Mancini, J. D.

    1984-01-01

    A convergent method of approximating thermodynamic Green functions is outlined briefly. The method constructs a sequence of approximants which converges independently of the strength of the Hamiltonian's coupling constants. Two new concepts associated with the approximants are introduced: the resolving power of the approximation, and conditional creation (annihilation) operators. These ideas are illustrated on an exactly soluble model and a numerical example. A convergent expression for the s...

  11. 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)

  12. Improvement of numerical analysis method for FBR core characteristics. 3

    International Nuclear Information System (INIS)

    Takeda, Toshikazu; Yamamoto, Toshihisa; Kitada, Takanori; Katagi, Yousuke

    1998-03-01

    As the improvement of numerical analysis method for FBR core characteristics, studies on several topics have been conducted; multiband method, Monte Carlo perturbation and nodal transport method. This report is composed of the following three parts. Part 1: Improvement of Reaction Rate Calculation Method in the Blanket Region Based on the Multiband Method; A method was developed for precise evaluation of the reaction rate distribution in the blanket region using the multiband method. With the 3-band parameters obtained from the ordinary fitting method, major reaction rates such as U-238 capture, U-235 fission, Pu-239 fission and U-238 fission rate distributions were analyzed. Part 2: Improvement of Estimation Method for Reactivity Based on Monte-Carlo Perturbation Theory; Perturbation theory based on Monte-Carlo perturbation theory have been investigated and introduced into the calculational code. The Monte-Carlo perturbation code was applied to MONJU core and the calculational results were compared to the reference. Part 3: Improvement of Nodal Transport Calculation for Hexagonal Geometry; A method to evaluate the intra-subassembly power distribution from the nodal averaged neutron flux and surface fluxes at the node boundaries, was developed based on the transport theory. (J.P.N.)

  13. Reactor perturbation calculations by Monte Carlo methods

    International Nuclear Information System (INIS)

    Gubbins, M.E.

    1965-09-01

    Whilst Monte Carlo methods are useful for reactor calculations involving complicated geometry, it is difficult to apply them to the calculation of perturbation worths because of the large amount of computing time needed to obtain good accuracy. Various ways of overcoming these difficulties are investigated in this report, with the problem of estimating absorbing control rod worths particularly in mind. As a basis for discussion a method of carrying out multigroup reactor calculations by Monte Carlo methods is described. Two methods of estimating a perturbation worth directly, without differencing two quantities of like magnitude, are examined closely but are passed over in favour of a third method based on a correlation technique. This correlation method is described, and demonstrated by a limited range of calculations for absorbing control rods in a fast reactor. In these calculations control rod worths of between 1% and 7% in reactivity are estimated to an accuracy better than 10% (3 standard errors) in about one hour's computing time on the English Electric KDF.9 digital computer. (author)

  14. 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.

  15. 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)

  16. Numerical calculation of ion polarization in the NICA collider

    Science.gov (United States)

    Kovalenko, A. D.; Butenko, A. V.; Kekelidze, V. D.; Mikhaylov, V. A.; Kondratenko, M. A.; Kondratenko, A. M.; Filatov, Yu N.

    2016-02-01

    The NICA Collider with two solenoid Siberian snakes is “transparent” to the spin. The collider transparent to the spin provides a unique capability to control any polarization direction of protons and deuterons using additional weak solenoids without affecting orbital parameters of the beam. The spin tune induced by the control solenoids must significantly exceed the strength of the zero-integer spin resonance, which contains a coherent part associated with errors in the collider's magnetic structure and an incoherent part associated with the beam emittances. We present calculations of the coherent part of the resonance strength in the NICA collider for proton and deuteron beams.

  17. Numerical calculation of ion polarization in the NICA collider

    International Nuclear Information System (INIS)

    Kovalenko, A D; Butenko, A V; Kekelidze, V D; Mikhaylov, V A; Filatov, Yu N; Kondratenko, M A; Kondratenko, A M

    2016-01-01

    The NICA Collider with two solenoid Siberian snakes is “transparent” to the spin. The collider transparent to the spin provides a unique capability to control any polarization direction of protons and deuterons using additional weak solenoids without affecting orbital parameters of the beam. The spin tune induced by the control solenoids must significantly exceed the strength of the zero-integer spin resonance, which contains a coherent part associated with errors in the collider's magnetic structure and an incoherent part associated with the beam emittances. We present calculations of the coherent part of the resonance strength in the NICA collider for proton and deuteron beams. (paper)

  18. 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 ...

  19. Numerical methods for engine-airframe integration

    International Nuclear Information System (INIS)

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

    1986-01-01

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

  20. fp shell spectroscopy: numerical calculations and theoretical aspects

    International Nuclear Information System (INIS)

    Pasquini, E.A.

    1976-01-01

    The fp shell spectroscopy is reviewed and the fsup(n) model is introduced. It is shown that the two-body Hamiltonian monopolar terms play a very important part in the behavior of these spectra, and that realistic interactions do not reproduce them. The detailed study of the following nuclei was undertaken: 47 Ca, 48 Ca, 49 Ca, 56 Ni, 48 Sc, 50 Sc, 50 Ti, 46 Ti, 50 Cr, 47 V and 49 Cr. It is shown that very precise values of the few parameters defining the monopolar contributions could be extracted from the comparison between calculations and experimental data. The study of the binding energies of all the nuclei from 40 Ca to 56 Ni shows that it is necessary to introduce three-body forces. The results also reveal the effect of nondiagonal multipoles which are well reproduced by realistic interactions. A better understanding of the electromagnetic behavior of the fsup(n) nuclei of their conjugaison properties and of the relation between 42 Sc and 48 Sc was obtained. Several calculations of two-body transfer amplitudes were proposed [fr

  1. 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....

  2. Numerical calculation of two-phase turbulent jets

    Energy Technology Data Exchange (ETDEWEB)

    Saif, A.A.

    1995-05-01

    Two-phase turbulent round jets were numerically simulated using a multidimensional two-phase CFD code based on the two-fluid model. The turbulence phenomena were treated with the standard k-{epsilon} model. It was modified to take into account the additional dissipation of turbulent kinetic energy by the dispersed phase. Within the context of the two-fluid model it is more appropriate and physically justified to treat the diffusion by an interfacial force in the momentum equation. In this work, the diffusion force and the additional dissipation effect by the dispersed phase were modeled starting from the classical turbulent energy spectrum analysis. A cut-off frequency was proposed to decrease the dissipation effect by the dispersed phase when large size particles are introduced in the flow. The cut-off frequency combined with the bubble-induced turbulence effect allows for an increase in turbulence for large particles. Additional care was taken in choosing the right kind of experimental data from the literature so that a good separate effect test was possible for their models. The models predicted the experimental data very closely and they were general enough to predict extreme limit cases: water-bubble and air-droplet jets.

  3. Numerical calculation of air velocity and temperature in ice rinks

    Energy Technology Data Exchange (ETDEWEB)

    Bellache, O.; Galanis, N. [Sherbrooke Univ., PQ (Canada); Ouzzane, M.; Sunye, R. [Natural Resources Canada, Varennes, PQ (Canada). CANMET Energy Diversification Laboratory

    2002-07-01

    A computational fluid dynamic (CFD) model was developed to predict the energy consumption at an ice rink. Ice rinks in Canada consume approximately 3500 GWh of electricity annually and generate about 300,000 tons of gases contributing to the greenhouse effect. This newly developed model also considers ice quality and comfort conditions in the arena. The typical 2D configuration includes refrigeration loads as well as heat transfer coefficients between the air and the ice. The effects of heat losses through the ice rink envelope are also determined. A comparison of prediction results from 4 different formulations confirms that there are important differences in air velocities near the walls and in the temperature gradient near the ice. The turbulent mixed convection model gives the best estimate of the refrigeration load. It was determined that a good ventilation should circulate air throughout the building to avoid stagnant areas. Air velocities must be low near the stands where the temperature should be around 20 degrees C. Air temperature near the ice should be low to preserve ice quality and to reduce the refrigeration load. The complexity of this geometry has been taken into account in a numerical simulation of the hydrodynamic and thermal fields in the ice rink. 9 refs., 2 tabs., 5 figs.

  4. 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...

  5. 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...

  6. 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

  7. 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.)

  8. Numerical investigations of instationary heating processes at motor bearings by means of differently coupled methods of calculation; Numerische Untersuchungen instationaerer Aufheizvorgaenge an einem Motorlager unter Verwendung verschiedener gekoppelter Berechnungsmethoden

    Energy Technology Data Exchange (ETDEWEB)

    Disch, Mario; Wittmeier, Felix; Widdecke, Nils; Wiedemann, Jochen [Forschungsinstitut fuer Fahrzeugmotoren und Kraftfahrwesen (FKFS), Stuttgart (Germany); Reister, Heinrich; Weidmann, Ernst-Peter [Daimler AG, Sindelfingen (Germany)

    2012-11-01

    In the vehicle development process at Daimler, thermal protection is an important task that has to be fulfilled. In the early stages of car development numerical analysis techniques are used to ensure that all critical components stay well below given temperature limits. Especially engine mounts are in the focus of investigation due to the geometrical design and the arrangement next to hot exhaust components. For a better understanding of the complex heat transfer mechanisms taking place in this part and as a first step into transient full Vehicle Thermal Management (VTM) computation, two different transient computational analyses are performed and described in this paper. The first one is the Conjugate Heat Transfer method (CHT) in which convection, conduction and radiation phenomena are solved simultaneously. The second one is a COSIM-method in which fluid and solid structures are splitted into two different simulations and brought to interaction by exchanging data at predetermined points. The major problem in transient computation is that thermal time scales on solid and fluid structures vary over a wide range. Using CHT a fine temporal discretization is needed for fluid and solid computation causing an enormous computational effort. In the COSIM-method solid structures are computed unsteady while the corresponding fluid is treated as steady and recalculated after each exchange. Corresponding measurements at an engine mount test rig show that both transient coupling schemes fit well to unsteady experimental results. In conclusion it can be said that the COSIM-method is an effective alternative to CHT computations for transient thermal applications. Computational and modeling effort can be reduced considerably especially for larger time scales which are relevant for full VTM computations. (orig.)

  9. Criticality calculation by the LTSN method

    International Nuclear Information System (INIS)

    Batistela, Claudia H.F.; Vilhena, Marco T. de; Borges, Volnei

    1997-01-01

    This work evaluates criticality parameters (multiplication factor and critical thickness) by the LTS N method in unidimensional slabs homogeneous and heterogeneous considering one-group model and isotropic scattering. The idea of the LTS N method encompasses the following steps: application of the Laplace transform into a set of discrete ordinates equations, analytical solution of the algebraic linear system for the transformed angular fluxes and their reconstruction by the Heaviside expansion technique. The novel feature of the proposed method is based upon the criticality parameters determination by solving a transcendental equation. Numerical results are reported. 12 refs., 2 tabs

  10. Numerical methods in dynamic fracture mechanics

    International Nuclear Information System (INIS)

    Beskos, D.E.

    1987-01-01

    A review of numerical methods for the solution of dynamic problems of fracture mechanics is presented. Finite difference, finite element and boundary element methods as applied to linear elastic or viscoelastic and non-linear elastoplastic or elastoviscoplastic dynamic fracture mechanics problems are described and critically evaluated. Both cases of stationary cracks and rapidly propagating cracks of simple I, II, III or mixed modes are considered. Harmonically varying with time or general transient dynamic disturbances in the form of external loading or incident waves are taken into account. Determination of the dynamic stress intensity factor for stationary cracks or moving cracks with known velocity history as well as determination of the crack-tip propagation history for given dynamic fracture toughness versus crack velocity relation are described and illustrated by means of certain representative examples. Finally, a brief assessment of the present state of knowledge is made and research needs are identified

  11. 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

  12. 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

  13. 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...

  14. 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

  15. Learning from numerical calculations of ion-atom collisions

    International Nuclear Information System (INIS)

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

    1982-01-01

    Violent collisions of two independent many-particle systems, victims, are discussed in the atomic sphere. The asymmetric region where the charge of the projectile Zsub(p) is less than the target nuclear charge Zsub(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 (Zsub(p) approx. equal to Zsub(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. (orig.)

  16. Comparative Study of Daylighting Calculation Methods

    Directory of Open Access Journals (Sweden)

    Mandala Ariani

    2018-01-01

    Full Text Available The aim of this study is to assess five daylighting calculation method commonly used in architectural study. The methods used include hand calculation methods (SNI/DPMB method and BRE Daylighting Protractors, scale models studied in an artificial sky simulator and computer programs using Dialux and Velux lighting software. The test room is conditioned by the uniform sky conditions, simple room geometry with variations of the room reflectance (black, grey, and white color. The analyses compared the result (including daylight factor, illumination, and coefficient of uniformity value and examines the similarity and contrast the result different. The color variations trial is used to analyses the internally reflection factor contribution to the result.

  17. 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

  18. 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

  19. Monte Carlo method for array criticality calculations

    International Nuclear Information System (INIS)

    Dickinson, D.; Whitesides, G.E.

    1976-01-01

    The Monte Carlo method for solving neutron transport problems consists of mathematically tracing paths of individual neutrons collision by collision until they are lost by absorption or leakage. The fate of the neutron after each collision is determined by the probability distribution functions that are formed from the neutron cross-section data. These distributions are sampled statistically to establish the successive steps in the neutron's path. The resulting data, accumulated from following a large number of batches, are analyzed to give estimates of k/sub eff/ and other collision-related quantities. The use of electronic computers to produce the simulated neutron histories, initiated at Los Alamos Scientific Laboratory, made the use of the Monte Carlo method practical for many applications. In analog Monte Carlo simulation, the calculation follows the physical events of neutron scattering, absorption, and leakage. To increase calculational efficiency, modifications such as the use of statistical weights are introduced. The Monte Carlo method permits the use of a three-dimensional geometry description and a detailed cross-section representation. Some of the problems in using the method are the selection of the spatial distribution for the initial batch, the preparation of the geometry description for complex units, and the calculation of error estimates for region-dependent quantities such as fluxes. The Monte Carlo method is especially appropriate for criticality safety calculations since it permits an accurate representation of interacting units of fissile material. Dissimilar units, units of complex shape, moderators between units, and reflected arrays may be calculated. Monte Carlo results must be correlated with relevant experimental data, and caution must be used to ensure that a representative set of neutron histories is produced

  20. Comparison of methods for calculating decay lifetimes

    International Nuclear Information System (INIS)

    Tobocman, W.

    1978-01-01

    A simple scattering model is used to test alternative methods for calculating decay lifetimes, or equivalently, resonance widths. We consider the scattering of s-wave particles by a square well with a square barrier. Exact values for resonance energies and resonance widths are compared with values calculated from Wigner-Weisskopf perturbation theory and from the Garside-MacDonald projection operator formalism. The Garside-MacDonald formalism gives essentially exact results while the predictions of the Wigner-Weisskopf formalism are fairly poor

  1. An analytical method for neutron thermalization calculations in heterogenous reactors

    Energy Technology Data Exchange (ETDEWEB)

    Pop-Jordanov, J [Boris Kidric Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

    1965-07-01

    It is well known that the use of the diffusion approximation for stunumerical methods are rather laborious and require the use of large digital computers. In this paper, the use of the diffusion approximation in absorbing media has been avoided, but the treatment remained analytical, thus simplifying practical calculations.

  2. An analytical method for neutron thermalization calculations in heterogenous reactors

    International Nuclear Information System (INIS)

    Pop-Jordanov, J.

    1965-01-01

    It is well known that the use of the diffusion approximation for studying neutron thermalization in heterogeneous reactors may result in considerable errors. On the other hand, more exact numerical methods are rather laborious and require the use of large digital computers. In this paper, the use of the diffusion approximation in absorbing media has been avoided, but the treatment remained analytical, thus simplifying practical calculations

  3. 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

  4. 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

  5. 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.

  6. Sputtering calculations with the discrete ordinated method

    International Nuclear Information System (INIS)

    Hoffman, T.J.; Dodds, H.L. Jr.; Robinson, M.T.; Holmes, D.K.

    1977-01-01

    The purpose of this work is to investigate the applicability of the discrete ordinates (S/sub N/) method to light ion sputtering problems. In particular, the neutral particle discrete ordinates computer code, ANISN, was used to calculate sputtering yields. No modifications to this code were necessary to treat charged particle transport. However, a cross section processing code was written for the generation of multigroup cross sections; these cross sections include a modification to the total macroscopic cross section to account for electronic interactions and small-scattering-angle elastic interactions. The discrete ordinates approach enables calculation of the sputtering yield as functions of incident energy and angle and of many related quantities such as ion reflection coefficients, angular and energy distributions of sputtering particles, the behavior of beams penetrating thin foils, etc. The results of several sputtering problems as calculated with ANISN are presented

  7. 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...

  8. 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

  9. 7 CFR 51.308 - Methods of sampling and calculation of percentages.

    Science.gov (United States)

    2010-01-01

    ..., CERTIFICATION, AND STANDARDS) United States Standards for Grades of Apples Methods of Sampling and Calculation of Percentages § 51.308 Methods of sampling and calculation of percentages. (a) When the numerical... 7 Agriculture 2 2010-01-01 2010-01-01 false Methods of sampling and calculation of percentages. 51...

  10. 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

  11. Numerical method improvement for a subchannel code

    Energy Technology Data Exchange (ETDEWEB)

    Ding, W.J.; Gou, J.L.; Shan, J.Q. [Xi' an Jiaotong Univ., Shaanxi (China). School of Nuclear Science and Technology

    2016-07-15

    Previous studies showed that the subchannel codes need most CPU time to solve the matrix formed by the conservation equations. Traditional matrix solving method such as Gaussian elimination method and Gaussian-Seidel iteration method cannot meet the requirement of the computational efficiency. Therefore, a new algorithm for solving the block penta-diagonal matrix is designed based on Stone's incomplete LU (ILU) decomposition method. In the new algorithm, the original block penta-diagonal matrix will be decomposed into a block upper triangular matrix and a lower block triangular matrix as well as a nonzero small matrix. After that, the LU algorithm is applied to solve the matrix until the convergence. In order to compare the computational efficiency, the new designed algorithm is applied to the ATHAS code in this paper. The calculation results show that more than 80 % of the total CPU time can be saved with the new designed ILU algorithm for a 324-channel PWR assembly problem, compared with the original ATHAS code.

  12. Direct Discrete Method for Neutronic Calculations

    International Nuclear Information System (INIS)

    Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid

    2002-01-01

    The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for a cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)

  13. 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.

  14. Patient safety: numerical skills and drug calculation abilities of nursing students and registered nurses.

    Science.gov (United States)

    McMullan, Miriam; Jones, Ray; Lea, Susan

    2010-04-01

    This paper is a report of a correlational study of the relations of age, status, experience and drug calculation ability to numerical ability of nursing students and Registered Nurses. Competent numerical and drug calculation skills are essential for nurses as mistakes can put patients' lives at risk. A cross-sectional study was carried out in 2006 in one United Kingdom university. Validated numerical and drug calculation tests were given to 229 second year nursing students and 44 Registered Nurses attending a non-medical prescribing programme. The numeracy test was failed by 55% of students and 45% of Registered Nurses, while 92% of students and 89% of nurses failed the drug calculation test. Independent of status or experience, older participants (> or = 35 years) were statistically significantly more able to perform numerical calculations. There was no statistically significant difference between nursing students and Registered Nurses in their overall drug calculation ability, but nurses were statistically significantly more able than students to perform basic numerical calculations and calculations for solids, oral liquids and injections. Both nursing students and Registered Nurses were statistically significantly more able to perform calculations for solids, liquid oral and injections than calculations for drug percentages, drip and infusion rates. To prevent deskilling, Registered Nurses should continue to practise and refresh all the different types of drug calculations as often as possible with regular (self)-testing of their ability. Time should be set aside in curricula for nursing students to learn how to perform basic numerical and drug calculations. This learning should be reinforced through regular practice and assessment.

  15. 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)

  16. Development and Application of a Numerical Framework for Improving Building Foundation Heat Transfer Calculations

    Science.gov (United States)

    Kruis, Nathanael J. F.

    Heat transfer from building foundations varies significantly in all three spatial dimensions and has important dynamic effects at all timescales, from one hour to several years. With the additional consideration of moisture transport, ground freezing, evapotranspiration, and other physical phenomena, the estimation of foundation heat transfer becomes increasingly sophisticated and computationally intensive to the point where accuracy must be compromised for reasonable computation time. The tools currently available to calculate foundation heat transfer are often either too limited in their capabilities to draw meaningful conclusions or too sophisticated to use in common practices. This work presents Kiva, a new foundation heat transfer computational framework. Kiva provides a flexible environment for testing different numerical schemes, initialization methods, spatial and temporal discretizations, and geometric approximations. Comparisons within this framework provide insight into the balance of computation speed and accuracy relative to highly detailed reference solutions. The accuracy and computational performance of six finite difference numerical schemes are verified against established IEA BESTEST test cases for slab-on-grade heat conduction. Of the schemes tested, the Alternating Direction Implicit (ADI) scheme demonstrates the best balance between accuracy, performance, and numerical stability. Kiva features four approaches of initializing soil temperatures for an annual simulation. A new accelerated initialization approach is shown to significantly reduce the required years of presimulation. Methods of approximating three-dimensional heat transfer within a representative two-dimensional context further improve computational performance. A new approximation called the boundary layer adjustment method is shown to improve accuracy over other established methods with a negligible increase in computation time. This method accounts for the reduced heat transfer

  17. Homotopy analysis method for neutron diffusion calculations

    International Nuclear Information System (INIS)

    Cavdar, S.

    2009-01-01

    The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on a fundamental concept in differential geometry and topology, the homotopy. It has proved useful for problems involving algebraic, linear/non-linear, ordinary/partial differential and differential-integral equations being an analytic, recursive method that provides a series sum solution. It has the advantage of offering a certain freedom for the choice of its arguments such as the initial guess, the auxiliary linear operator and the convergence control parameter, and it allows us to effectively control the rate and region of convergence of the series solution. HAM is applied for the fixed source neutron diffusion equation in this work, which is a part of our research motivated by the question of whether methods for solving the neutron diffusion equation that yield straightforward expressions but able to provide a solution of reasonable accuracy exist such that we could avoid analytic methods that are widely used but either fail to solve the problem or provide solutions through many intricate expressions that are likely to contain mistakes or numerical methods that require powerful computational resources and advanced programming skills due to their very nature or intricate mathematical fundamentals. Fourier basis are employed for expressing the initial guess due to the structure of the problem and its boundary conditions. We present the results in comparison with other widely used methods of Adomian Decomposition and Variable Separation.

  18. Comparison of results of experimental research with numerical calculations of a model one-sided seal

    Directory of Open Access Journals (Sweden)

    Joachimiak Damian

    2015-06-01

    Full Text Available Paper presents the results of experimental and numerical research of a model segment of a labyrinth seal for a different wear level. The analysis covers the extent of leakage and distribution of static pressure in the seal chambers and the planes upstream and downstream of the segment. The measurement data have been compared with the results of numerical calculations obtained using commercial software. Based on the flow conditions occurring in the area subjected to calculations, the size of the mesh defined by parameter y+ has been analyzed and the selection of the turbulence model has been described. The numerical calculations were based on the measurable thermodynamic parameters in the seal segments of steam turbines. The work contains a comparison of the mass flow and distribution of static pressure in the seal chambers obtained during the measurement and calculated numerically in a model segment of the seal of different level of wear.

  19. Burnup calculations using Monte Carlo method

    International Nuclear Information System (INIS)

    Ghosh, Biplab; Degweker, S.B.

    2009-01-01

    In the recent years, interest in burnup calculations using Monte Carlo methods has gained momentum. Previous burn up codes have used multigroup transport theory based calculations followed by diffusion theory based core calculations for the neutronic portion of codes. The transport theory methods invariably make approximations with regard to treatment of the energy and angle variables involved in scattering, besides approximations related to geometry simplification. Cell homogenisation to produce diffusion, theory parameters adds to these approximations. Moreover, while diffusion theory works for most reactors, it does not produce accurate results in systems that have strong gradients, strong absorbers or large voids. Also, diffusion theory codes are geometry limited (rectangular, hexagonal, cylindrical, and spherical coordinates). Monte Carlo methods are ideal to solve very heterogeneous reactors and/or lattices/assemblies in which considerable burnable poisons are used. The key feature of this approach is that Monte Carlo methods permit essentially 'exact' modeling of all geometrical detail, without resort to ene and spatial homogenization of neutron cross sections. Monte Carlo method would also be better for in Accelerator Driven Systems (ADS) which could have strong gradients due to the external source and a sub-critical assembly. To meet the demand for an accurate burnup code, we have developed a Monte Carlo burnup calculation code system in which Monte Carlo neutron transport code is coupled with a versatile code (McBurn) for calculating the buildup and decay of nuclides in nuclear materials. McBurn is developed from scratch by the authors. In this article we will discuss our effort in developing the continuous energy Monte Carlo burn-up code, McBurn. McBurn is intended for entire reactor core as well as for unit cells and assemblies. Generally, McBurn can do burnup of any geometrical system which can be handled by the underlying Monte Carlo transport code

  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. A numerical method to compute interior transmission eigenvalues

    International Nuclear Information System (INIS)

    Kleefeld, Andreas

    2013-01-01

    In this paper the numerical calculation of eigenvalues of the interior transmission problem arising in acoustic scattering for constant contrast in three dimensions is considered. From the computational point of view existing methods are very expensive, and are only able to show the existence of such transmission eigenvalues. Furthermore, they have trouble finding them if two or more eigenvalues are situated closely together. We present a new method based on complex-valued contour integrals and the boundary integral equation method which is able to calculate highly accurate transmission eigenvalues. So far, this is the first paper providing such accurate values for various surfaces different from a sphere in three dimensions. Additionally, the computational cost is even lower than those of existing methods. Furthermore, the algorithm is capable of finding complex-valued eigenvalues for which no numerical results have been reported yet. Until now, the proof of existence of such eigenvalues is still open. Finally, highly accurate eigenvalues of the interior Dirichlet problem are provided and might serve as test cases to check newly derived Faber–Krahn type inequalities for larger transmission eigenvalues that are not yet available. (paper)

  2. 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)

  3. Nested element method in multidimensional neutron diffusion calculations

    International Nuclear Information System (INIS)

    Altiparmakov, D.V.

    1983-01-01

    A new numerical method is developed that is particularly efficient in solving the multidimensional neutron diffusion equation in geometrically complex systems. The needs for a generally applicable and fast running computer code have stimulated the inroad of a nonclassical (R-function) numerical method into the nuclear field. By using the R-functions, the geometrical components of the diffusion problem are a priori analytically implemented into the approximate solution. The class of functions, to which the approximate solution belongs, is chosen as close to the exact solution class as practically acceptable from the time consumption point of view. That implies a drastic reduction of the number of degrees of freedom, compared to the other methods. Furthermore, the reduced number of degrees of freedom enables calculation of large multidimensional problems on small computers

  4. 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.

  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 Calculation and Measurement of Nonlinear Acoustic Fields in Ultrasound Diagnosis

    Science.gov (United States)

    Kawagishi, Tetsuya; Saito, Shigemi; Mine, Yoshitaka

    2002-05-01

    In order to develop a tool for designing on the ultrasonic probe and its peripheral devices for tissue-harmonic-imaging systems, a study is carried out to compare the calculation and observation results of nonlinear acoustic fields for a diagnostic ultrasound system. The pulsed ultrasound with a center frequency of 2.5 MHz is emanated from a weakly focusing sector probe with a 6.5 mm aperture radius and a 50 mm focal length into an agar phantom with an attenuation coefficient of about 0.6 dB/cm/MHz or 1.2 dB/cm/MHz. The nonlinear acoustic field is measured using a needle-type hydrophone. The calculation is based on the Khokhlov-Zabolotskaya-Kuznetsov(KZK) equation which is modified so that the frequency dependence of the attenuation coefficient is the same as that in biological tissue. This equation is numerically solved with the implicit backward method employing the iterative method. The measured and calculated amplitude spectra show good agreement with each other.

  7. 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...... thecontact area and the distribution of contact pressure. The numerical simulation of resistancewelding is illustrated by a spot welding example that includes subsequent tensile shear testing...

  8. Method for consequence calculations for severe accidents

    International Nuclear Information System (INIS)

    Nielsen, F.; Thykier-Nielsen, S.; Walmod-Larsen, O.

    1986-08-01

    This report was commissioned by the Swedish State Power Board, who wanted a method for calculation of radiation doses in the surroundings of nuclear power plants caused by severe accidents. The PLUCON4 code were used for the calculations. A TC-SV-accident at Ringhals 1 wer chosen as example. A transient without shutdown leads to core meltdown through the reactor vessel. The pressure peak at the moment of vessel failure opens a safety valve in the dry well. Meteorolgical data for two years from the Ringhals meteorological tower were analysed to find representative weather situations. As typical weather were chosen Pasquill D with wind speed 8 m/s, and as extreme weather were chosen Pasquill F with wind speed 4.8 m/s. (author)

  9. 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.

  10. 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

  11. 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.

  12. 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)

  13. 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

  14. Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

    Science.gov (United States)

    Merker, L.; Costi, T. A.

    2012-08-01

    We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat Cimp to be calculated accurately from local static correlation functions; specifically via Cimp=(∂Eionic)/(∂T)+(1)/(2)(∂Ehyb)/(∂T), where Eionic and Ehyb are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to Cimp. For the nondegenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high-temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two-state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The approach could also be of interest within other impurity solvers, for example, within quantum Monte Carlo techniques.

  15. 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

  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. Efficient O(N) integration for all-electron electronic structure calculation using numeric basis functions

    International Nuclear Information System (INIS)

    Havu, V.; Blum, V.; Havu, P.; Scheffler, M.

    2009-01-01

    We consider the problem of developing O(N) scaling grid-based operations needed in many central operations when performing electronic structure calculations with numeric atom-centered orbitals as basis functions. We outline the overall formulation of localized algorithms, and specifically the creation of localized grid batches. The choice of the grid partitioning scheme plays an important role in the performance and memory consumption of the grid-based operations. Three different top-down partitioning methods are investigated, and compared with formally more rigorous yet much more expensive bottom-up algorithms. We show that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as the more rigorous bottom-up approaches.

  18. Dissipative exciton transfer in donor-bridge-acceptor systems: numerical renormalization group calculation of equilibrium properties

    Energy Technology Data Exchange (ETDEWEB)

    Tornow, Sabine [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg, 86135 Augsburg (Germany); Tong, Ning-Hua [Institut fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, 76128 Karlsruhe (Germany); Bulla, Ralf [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg, 86135 Augsburg (Germany)

    2006-07-05

    We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.

  19. Dissipative exciton transfer in donor-bridge-acceptor systems: numerical renormalization group calculation of equilibrium properties.

    Science.gov (United States)

    Tornow, Sabine; Tong, Ning-Hua; Bulla, Ralf

    2006-07-05

    We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.

  20. On nitrogen condensation in hypersonic nozzle flows: Numerical method and parametric study

    KAUST Repository

    Lin, Longyuan; Cheng, Wan; Luo, Xisheng; Qin, Fenghua

    2013-01-01

    A numerical method for calculating two-dimensional planar and axisymmetric hypersonic nozzle flows with nitrogen condensation is developed. The classical nucleation theory with an empirical correction function and the modified Gyarmathy model

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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

  6. 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

  7. 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.

  8. 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.

  9. Numerical Simulation of Partially-Coherent Broadband Optical Imaging Using the FDTD Method

    Science.gov (United States)

    Çapoğlu, İlker R.; White, Craig A.; Rogers, Jeremy D.; Subramanian, Hariharan; Taflove, Allen; Backman, Vadim

    2012-01-01

    Rigorous numerical modeling of optical systems has attracted interest in diverse research areas ranging from biophotonics to photolithography. We report the full-vector electromagnetic numerical simulation of a broadband optical imaging system with partially-coherent and unpolarized illumination. The scattering of light from the sample is calculated using the finite-difference time-domain (FDTD) numerical method. Geometrical optics principles are applied to the scattered light to obtain the intensity distribution at the image plane. Multilayered object spaces are also supported by our algorithm. For the first time, numerical FDTD calculations are directly compared to and shown to agree well with broadband experimental microscopy results. PMID:21540939

  10. 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.

  11. 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

  12. OEDIPE: a new graphical user interface for fast construction of numerical phantoms and MCNP calculations.

    Science.gov (United States)

    Franck, D; de Carlan, L; Pierrat, N; Broggio, D; Lamart, S

    2007-01-01

    Although great efforts have been made to improve the physical phantoms used to calibrate in vivo measurement systems, these phantoms represent a single average counting geometry and usually contain a uniform distribution of the radionuclide over the tissue substitute. As a matter of fact, significant corrections must be made to phantom-based calibration factors in order to obtain absolute calibration efficiencies applicable to a given individual. The importance of these corrections is particularly crucial when considering in vivo measurements of low energy photons emitted by radionuclides deposited in the lung such as actinides. Thus, it was desirable to develop a method for calibrating in vivo measurement systems that is more sensitive to these types of variability. Previous works have demonstrated the possibility of such a calibration using the Monte Carlo technique. Our research programme extended such investigations to the reconstruction of numerical anthropomorphic phantoms based on personal physiological data obtained by computed tomography. New procedures based on a new graphical user interface (GUI) for development of computational phantoms for Monte Carlo calculations and data analysis are being developed to take advantage of recent progress in image-processing codes. This paper presents the principal features of this new GUI. Results of calculations and comparison with experimental data are also presented and discussed in this work.

  13. 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.

  14. Numerical methods in physical and economic sciences

    International Nuclear Information System (INIS)

    Lions, J.L.; Marchouk, G.I.

    1974-01-01

    This book is the first of a series to be published simultaneously in French and Russian. Some results obtained in the framework of an agreement of French-Soviet scientific collaboration in the field of the information processing are exposed. In the first part, the iterative methods for solving linear systems are studied with new methods which are compared to already known methods. Iterative methods of minimization of quadratic functionals are then studied. In the second part, the optimization problems with one or many criteria, issued from Physics and Economics problems are considered and splitting and decentralizing methods systematically studied [fr

  15. A density gradient theory based method for surface tension calculations

    DEFF Research Database (Denmark)

    Liang, Xiaodong; Michelsen, Michael Locht; Kontogeorgis, Georgios

    2016-01-01

    The density gradient theory has been becoming a widely used framework for calculating surface tension, within which the same equation of state is used for the interface and bulk phases, because it is a theoretically sound, consistent and computationally affordable approach. Based on the observation...... that the optimal density path from the geometric mean density gradient theory passes the saddle point of the tangent plane distance to the bulk phases, we propose to estimate surface tension with an approximate density path profile that goes through this saddle point. The linear density gradient theory, which...... assumes linearly distributed densities between the two bulk phases, has also been investigated. Numerical problems do not occur with these density path profiles. These two approximation methods together with the full density gradient theory have been used to calculate the surface tension of various...

  16. 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...

  17. Numerical methods on flow instabilities in steam generator

    International Nuclear Information System (INIS)

    Yoshikawa, Ryuji; Hamada, Hirotsugu; Ohshima, Hiroyuki; Yanagisawa, Hideki

    2008-06-01

    The phenomenon of two-phase flow instability is important for the design and operation of many industrial systems and equipment, such as steam generators. The designer's job is to predict the threshold of flow instability in order to design around it or compensate for it. So it is essential to understand the physical phenomena governing such instability and to develop computational tools to model the dynamics of boiling systems. In Japan Atomic Energy Agency, investigations on heat transfer characteristics of steam generator are being performed for the development of Sodium-cooled Fast Breeder Reactor. As one part of the research work, the evaluations of two-phase flow instability in the steam generator are being carried out experimentally and numerically. In this report, the numerical methods were studied for two-phase flow instability analysis in steam generator. For numerical simulation purpose, the special algorithm to calculate inlet flow rate iteratively with inlet pressure and outlet pressure as boundary conditions for the density-wave instability analysis was established. There was no need to solve property derivatives and large matrices, so the spurious numerical instabilities caused by discontinuous property derivatives at boiling boundaries were avoided. Large time-step was possible. The flow instability in single heat transfer tube was successfully simulated with homogeneous equilibrium model by using the present algorithm. Then the drift-flux model including the effects of subcooled boiling and two phase slip was adopted to improve the accuracy. The computer code was developed after selecting the correlations of drift velocity and distribution parameter. The capability of drift flux model together with the present algorithm for simulating density-wave instability in single tube was confirmed. (author)

  18. A sub-structure method for multidimensional integral transport calculations

    International Nuclear Information System (INIS)

    Kavenoky, A.; Stankovski, Z.

    1983-03-01

    A new method has been developed for fine structure burn-up calculations of very heterogeneous large size media. It is a generalization of the well-known surface-source method, allowing coupling actual two-dimensional heterogeneous assemblies, called sub-structures. The method has been applied to a rectangular medium, divided into sub-structures, containing rectangular and/or cylindrical fuel, moderator and structure elements. The sub-structures are divided into homogeneous zones. A zone-wise flux expansion is used to formulate a direct collision probability problem within it (linear or flat flux expansion in the rectangular zones, flat flux in the others). The coupling of the sub-structures is performed by making extra assumptions on the currents entering and leaving the interfaces. The accuracies and computing times achieved are illustrated by numerical results on two benchmark problems

  19. 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.

  20. 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.

  1. Numerical calculation of electromagnetic properties including chirality parameters for uniaxial bianisotropic media

    International Nuclear Information System (INIS)

    Amirkhizi, Alireza V; Nemat-Nasser, Sia

    2008-01-01

    Through the use of conductive straight wires or coils the electromagnetic properties of a composite material can be modified. The asymmetric geometry of the coils creates an overall chiral response. The polarization vectors rotate as an electromagnetic wave travels through such a medium. To calculate the chirality of a medium prior to its manufacturing, we developed a method to extract all four electromagnetic material parameter tensors for a general uniaxial bianisotropic composite based on the numerical simulation of the electromagnetic fields. Our method uses appropriate line and surface field averages in a single unit cell of the periodic structure of the composite material. These overall field quantities have physical meaning only when the microscopic variation of the electromagnetic fields in the scale of the unit cell is not important, that is when the wavelength of interest is significantly larger than the maximum linear dimension of the unit cell. The overall constitutive relations of the periodic structure can then be obtained from the relations among the average quantities

  2. Time-dependent magnetization of a type-II superconductor numerically calculated by using the flux-creep equation

    International Nuclear Information System (INIS)

    Lee, J. H.; Park, I. S.; Ahmad, D.; Kim, D.; Kim, Y. C.; Ko, R. K.; Jeong, D. Y.

    2012-01-01

    The macroscopic magnetic behaviors of a type-II superconductor, such as the field- or the temperature-dependent magnetization, have been described by using critical state models. However, because the models are time-independent, the magnetic relaxation in a type-II superconductor cannot be described by them, and the time dependence of the magnetization can affect the field or the temperature-dependent magnetization curve described by the models. In order to avoid the time independence of critical state models, we try the numerical calculation used by Qin et al., who mainly calculated the temperature dependence of the ac susceptibility χ(T). Their calculation showed that the frequency-dependent χ(T) could be obtained by using the flux-creep equation. We calculated the field-dependent magnetization and magnetic relaxation by using a numerical method. The calculated field-dependent magnetization M(H) curves shows the shapes of a typical type-II superconductor. The calculated magnetic relaxation do not show a logarithmic decay of the magnetization, but the addition of a surface barrier to the relaxation calculation caused a clear logarithmic decay of the magnetization, producing a crossover at a mid-time. This means that the logarithmic magnetic relaxation is caused by not only flux creep but also a combination of flux creep and a surface barrier.

  3. Computing and physical methods to calculate Pu

    International Nuclear Information System (INIS)

    Mohamed, Ashraf Elsayed Mohamed

    2013-01-01

    Main limitations due to the enhancement of the plutonium content are related to the coolant void effect as the spectrum becomes faster, the neutron flux in the thermal region tends towards zero and is concentrated in the region from 10 Ke to 1 MeV. Thus, all captures by 240 Pu and 242 Pu in the thermal and epithermal resonance disappear and the 240 Pu and 242 Pu contributions to the void effect became positive. The higher the Pu content and the poorer the Pu quality, the larger the void effect. The core control in nominal or transient conditions Pu enrichment leads to a decrease in (B eff.), the efficiency of soluble boron and control rods. Also, the Doppler effect tends to decrease when Pu replaces U, so, that in case of transients the core could diverge again if the control is not effective enough. As for the voiding effect, the plutonium degradation and the 240 Pu and 242 Pu accumulation after multiple recycling lead to spectrum hardening and to a decrease in control. One solution would be to use enriched boron in soluble boron and shutdown rods. In this paper, I discuss and show the advanced computing and physical methods to calculate Pu inside the nuclear reactors and glovebox and the different solutions to be used to overcome the difficulties that effect, on safety parameters and on reactor performance, and analysis the consequences of plutonium management on the whole fuel cycle like Raw materials savings, fraction of nuclear electric power involved in the Pu management. All through two types of scenario, one involving a low fraction of the nuclear park dedicated to plutonium management, the other involving a dilution of the plutonium in all the nuclear park. (author)

  4. Perturbation method for calculation of narrow-band impedance and trapped modes

    International Nuclear Information System (INIS)

    Heifets, S.A.

    1987-01-01

    An iterative method for calculation of the narrow-band impedance is described for a system with a small variation in boundary conditions, so that the variation can be considered as a perturbation. The results are compared with numeric calculations. The method is used to relate the origin of the trapped modes with the degeneracy of the spectrum of an unperturbed system. The method also can be applied to transverse impedance calculations. 6 refs., 6 figs., 1 tab

  5. 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...

  6. Numerical Methods for Partial Differential Equations.

    Science.gov (United States)

    1984-01-09

    iteration or the conjugate gradient method. The smoothing sweeps are used to annihilate the highly oscillatory (compared to the grid spacing) components of...53 52 "-󈧯 33 41 *32 * . 31 * 21 - 11 O- carrius plane rotacions o I ~~arr: ’.trix vrS2-0 Cf A Figure 4. QM fiitorization of a BLTE (1,2) mnitrix

  7. 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...

  8. 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.

  9. 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.

  10. 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

  11. 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

  12. Method for consequence calculations for severe accidents

    International Nuclear Information System (INIS)

    Nielsen, F.; Thykier-Nielsn, S.

    1987-03-01

    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 Forsmark reactor No 3. The assumption used for the calculations were a 0.06% release of iodine and cesium corresponding to a 0.1% release through the FILTRA plant at Barsebaeck. The calculations were made by means of the PLUCON4 code. Meteorological data for two years from the Forsmark meteorological tower were analysed to find representative weather situations. As typical weather pasquill D was chosen with wind speed 5 m/s, and as extreme weather, Pasquill F with wind speed 2 m/s. 23 tabs., 36 ills., 21 refs. (author)

  13. Method for consequence calculations for servere accidents

    International Nuclear Information System (INIS)

    Nielsen, F.

    1987-01-01

    With the exception of the part about collective doses, this report was commissioned by the Swedish State Power Board. The part about collective doses was commissioned by the Swedish National Institute of Radiation Protection. The report contains a calculation of radiation doses in the sursurroundings caused by a theoretical core meltdown accident at one of the Barsebaeck reactors with filtered venting through the FILTRA plant. The calculations were made by means of the PLUCON4 code. The assumption used for the calculations were givon by the Swedish National Institute of Radiation Protection as follows: Pasquill D with wind speed 3 m/s and a mixing layer at 300 m height. Elevation of the release: 100 m with no energy release. The release starts 12 hours after shut-down and its duration is one hour. The release contains 100% of the noble gasses and 0,1% of all other isotopes in a 1800 MW t -reactor. (author)

  14. Method for consequence calculations for severe accidents

    International Nuclear Information System (INIS)

    Nielsen, F.

    1988-07-01

    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 Forsmark reactor No 3. The accident sequence chosen for the calculating was a release caused by total power failure. The calculations were made by means of the PLUCON4 code. Meteorological data for two years from the Forsmark meteorological tower were analysed to find representative weather situations. As typical weather, Pasquill D was chosen with a wind speed of 5 m/s, and as extreme weather, Pasquill F with a wind speed of 2 m/s. 23 tabs., 37 ills., 20 refs. (author)

  15. Methods for thermal reactor lattice calculations

    International Nuclear Information System (INIS)

    Schneider, A.

    1976-12-01

    The American code HAMMER and the British code WIMS, for the analysis of thermal reactor lattices, have been investigated. The primary objective of this investigation was to identify the causes for the discrepancies that exist between the calculated and the experimentally determined reactivity of clean critical experiments. Three phases have been undertaken in the research: (a) Detailed comparison between the group cross-sections used by the codes; (b) Definition of the various approximations incorporated into the codes; (c) Comparison between the values of a variety of reaction rates calculated by the two codes. It was concluded that the main cause of discrepancy between calculations and experiments is due to data inaccuracies, while approximations introduced in solving the transport equation are of smaller importance

  16. Evaluation bases for calculation methods in radioecology

    International Nuclear Information System (INIS)

    Bleck-Neuhaus, J.; Boikat, U.; Franke, B.; Hinrichsen, K.; Hoepfner, U.; Ratka, R.; Steinhilber-Schwab, B.; Teufel, D.; Urbach, M.

    1982-03-01

    The seven contributions in this book deal with the state and problems of radioecology. In particular it analyses: The propagation of radioactive materials in the atmosphere, the transfer of radioactive substances from the soil into plants, respectively from animal feed into meat, the exposure pathways for, and high-risk groups of the population, the uncertainties and the band width of the ingestion factor, as well as the treatment of questions of radioecology in practice. The calculation model is assessed and the difficulty evaluated of laying down data in the general calculation basis. (DG) [de

  17. 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.

  18. Numerical Methods for Bayesian Inverse Problems

    KAUST Repository

    Ernst, Oliver; Sprungk, Bjorn; Cliffe, K. Andrew; Starkloff, Hans-Jorg

    2014-01-01

    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.

  19. Tensor viscosity method for convection in numerical fluid dynamics

    International Nuclear Information System (INIS)

    Dukowicz, J.K.; Ramshaw, J.D.

    1979-01-01

    A new method, called the tensor viscosity method, is described for differencing the convective terms in multidimensional numerical fluid dynamics. The method is the proper generalization to two or three dimensions of interpolated donor cell differencing in one dimension, and is designed to achieve numerical stability with minimal numerical damping. It is a single-step method that is distinguished by simplicity and case of implementation, even in the case of an arbitrary non-rectangular mesh. It should therefore be useful in finite-element as well as finite-difference formulations

  20. Numerical Methods for a Class of Differential Algebraic Equations

    Directory of Open Access Journals (Sweden)

    Lei Ren

    2017-01-01

    Full Text Available This paper is devoted to the study of some efficient numerical methods for the differential algebraic equations (DAEs. At first, we propose a finite algorithm to compute the Drazin inverse of the time varying DAEs. Numerical experiments are presented by Drazin inverse and Radau IIA method, which illustrate that the precision of the Drazin inverse method is higher than the Radau IIA method. Then, Drazin inverse, Radau IIA, and Padé approximation are applied to the constant coefficient DAEs, respectively. Numerical results demonstrate that the Padé approximation is powerful for solving constant coefficient DAEs.

  1. 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.

  2. Advanced Numerical and Theoretical Methods for Photonic Crystals and Metamaterials

    Science.gov (United States)

    Felbacq, Didier

    2016-11-01

    This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB® is presented. The codes are limited to 2D problems and can be easily translated in Python or Scilab, and used directly with Octave as well.

  3. Introduction to numerical methods for time dependent differential equations

    CERN Document Server

    Kreiss, Heinz-Otto

    2014-01-01

    Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the t

  4. Numerical calculation of the entanglement entropy for scalar field in dilaton spacetimes

    Science.gov (United States)

    Huang, Shifeng; Fang, Xiongjun; Jing, Jiliang

    2018-06-01

    Using coupled harmonic oscillators model, we numerical analyze the entanglement entropy of massless scalar field in Gafinkle-Horowitz-Strominger (GHS) dilaton spacetime and Gibbons-Maeda (GM) dilaton spacetime. By numerical fitting, we find that the entanglement entropy of the dilaton black holes receive contribution from dilaton charge and is proportional to the area of the event horizon. It is interesting to note that the results of numerical fitting are coincide with ones obtained by using brick wall method and Euclidean path integral approach.

  5. Numerical Calculation of the Swirling Flow in a Centrifugal Compressor Volute

    International Nuclear Information System (INIS)

    Seong, Seon Mo; Kang, Shin Hyoung; Cho, Kyung Seok; Kim, Woo June

    2007-01-01

    Flows in the centrifugal compressor volute with circular cross section are numerically investigated. The computational grid for the calculation utilized a multi-block arrangement to form a butterfly grid and flow calculations are performed using commercial CFD software, CFX-TASCflow. The centrifugal compressor of this study has axial diffuser after radial diffuser because of the shape of inlet duct and installation constraints. Due to this feature the swirling flow pattern is different from the other investigations. The flow inside volute is very complex and three dimensional with strong vortex and recirculation through volute tongue. The calculation results show circumferential variations of the swirl and through flow velocity and pressure distribution. The mechanism deciding flow structure is explained by considering the force balance in volute cross section. And static pressure recovery and total pressure loss are estimated from the calculated results and compared with Japikse model

  6. 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)

  7. Stabilizing canonical-ensemble calculations in the auxiliary-field Monte Carlo method

    Science.gov (United States)

    Gilbreth, C. N.; Alhassid, Y.

    2015-03-01

    Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.

  8. 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

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

    International Nuclear Information System (INIS)

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

    1975-11-01

    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

  10. Planning design of Ukrainian mines by the means of numerical calculations

    Energy Technology Data Exchange (ETDEWEB)

    Ruppel, Ulrich; Scior, Carsten [DMT GmbH und Co. KG (DMT), Essen (Germany). Rock Mechanic Dept.

    2008-08-21

    Using a mine in the Ukraine as an example it is shown how the DMT performs rock mechanical and support planning or roadways in hard coal mines worldwide. Therefore it is necessary to analyse existing measurements and operating experience within a few days as well as organising further surveys on site on short notice. Based on these results the numerical models are calibrated. Using the numerical simulation technology it is possible for DMT to quantify and analyse the rock mechanical impact of different support systems within a short time. Finally the results of the numerical calculations are set in comparison in a rating matrix. Besides making a decision on implementing new roadway and support systems with the objective to use the roadways up to the second longwall panel, the rating matrix is also used for analysing the optimization potentials of existing support systems. This allows the recommendations to immediate improvement of the strata control in the miner's roadways. (orig.)

  11. 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.)

  12. Efficient parallel implicit methods for rotary-wing aerodynamics calculations

    Science.gov (United States)

    Wissink, Andrew M.

    Euler/Navier-Stokes Computational Fluid Dynamics (CFD) methods are commonly used for prediction of the aerodynamics and aeroacoustics of modern rotary-wing aircraft. However, their widespread application to large complex problems is limited lack of adequate computing power. Parallel processing offers the potential for dramatic increases in computing power, but most conventional implicit solution methods are inefficient in parallel and new techniques must be adopted to realize its potential. This work proposes alternative implicit schemes for Euler/Navier-Stokes rotary-wing calculations which are robust and efficient in parallel. The first part of this work proposes an efficient parallelizable modification of the Lower Upper-Symmetric Gauss Seidel (LU-SGS) implicit operator used in the well-known Transonic Unsteady Rotor Navier Stokes (TURNS) code. The new hybrid LU-SGS scheme couples a point-relaxation approach of the Data Parallel-Lower Upper Relaxation (DP-LUR) algorithm for inter-processor communication with the Symmetric Gauss Seidel algorithm of LU-SGS for on-processor computations. With the modified operator, TURNS is implemented in parallel using Message Passing Interface (MPI) for communication. Numerical performance and parallel efficiency are evaluated on the IBM SP2 and Thinking Machines CM-5 multi-processors for a variety of steady-state and unsteady test cases. The hybrid LU-SGS scheme maintains the numerical performance of the original LU-SGS algorithm in all cases and shows a good degree of parallel efficiency. It experiences a higher degree of robustness than DP-LUR for third-order upwind solutions. The second part of this work examines use of Krylov subspace iterative solvers for the nonlinear CFD solutions. The hybrid LU-SGS scheme is used as a parallelizable preconditioner. Two iterative methods are tested, Generalized Minimum Residual (GMRES) and Orthogonal s-Step Generalized Conjugate Residual (OSGCR). The Newton method demonstrates good

  13. Numerical simulation methods for phase-transitional flow

    NARCIS (Netherlands)

    Pecenko, A.

    2010-01-01

    The object of the present dissertation is a numerical study of multiphase flow of one fluid component. In particular, the research described in this thesis focuses on the development of numerical methods that are based on a diffuse-interface model (DIM). With this approach, the modeling problem

  14. Assessing numerical methods used in nuclear aerosol transport models

    International Nuclear Information System (INIS)

    McDonald, B.H.

    1987-01-01

    Several computer codes are in use for predicting the behaviour of nuclear aerosols released into containment during postulated accidents in water-cooled reactors. Each of these codes uses numerical methods to discretize and integrate the equations that govern the aerosol transport process. Computers perform only algebraic operations and generate only numbers. It is in the numerical methods that sense can be made of these numbers and where they can be related to the actual solution of the equations. In this report, the numerical methods most commonly used in the aerosol transport codes are examined as special cases of a general solution procedure, the Method of Weighted Residuals. It would appear that the numerical methods used in the codes are all capable of producing reasonable answers to the mathematical problem when used with skill and care. 27 refs

  15. Basic numerical processing, calculation, and working memory in children with dyscalculia and/or ADHD symptoms.

    Science.gov (United States)

    Kuhn, Jörg-Tobias; Ise, Elena; Raddatz, Julia; Schwenk, Christin; Dobel, Christian

    2016-09-01

    Deficits in basic numerical skills, calculation, and working memory have been found in children with developmental dyscalculia (DD) as well as children with attention-deficit/hyperactivity disorder (ADHD). This paper investigates cognitive profiles of children with DD and/or ADHD symptoms (AS) in a double dissociation design to obtain a better understanding of the comorbidity of DD and ADHD. Children with DD-only (N = 33), AS-only (N = 16), comorbid DD+AS (N = 20), and typically developing controls (TD, N = 40) were assessed on measures of basic numerical processing, calculation, working memory, processing speed, and neurocognitive measures of attention. Children with DD (DD, DD+AS) showed deficits in all basic numerical skills, calculation, working memory, and sustained attention. Children with AS (AS, DD+AS) displayed more selective difficulties in dot enumeration, subtraction, verbal working memory, and processing speed. Also, they generally performed more poorly in neurocognitive measures of attention, especially alertness. Children with DD+AS mostly showed an additive combination of the deficits associated with DD-only and A_Sonly, except for subtraction tasks, in which they were less impaired than expected. DD and AS appear to be related to largely distinct patterns of cognitive deficits, which are present in combination in children with DD+AS.

  16. 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

  17. Soil structure interaction calculations: a comparison of methods

    Energy Technology Data Exchange (ETDEWEB)

    Wight, L.; Zaslawsky, M.

    1976-07-22

    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.

  18. The multigrid method for reactor calculations

    International Nuclear Information System (INIS)

    Douglas, S.R.

    1991-07-01

    Iterative solutions to linear systems of equations are discussed. The emphasis is on the concepts that affect convergence rates of these solution methods. The multigrid method is described, including the smoothing property, restriction, and prolongation. A simple example is used to illustrate the ideas

  19. 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.

  20. 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

  1. 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

  2. Failure Probability Calculation Method Using Kriging Metamodel-based Importance Sampling Method

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Seunggyu [Korea Aerospace Research Institue, Daejeon (Korea, Republic of); Kim, Jae Hoon [Chungnam Nat’l Univ., Daejeon (Korea, Republic of)

    2017-05-15

    The kernel density was determined based on sampling points obtained in a Markov chain simulation and was assumed to be an important sampling function. A Kriging metamodel was constructed in more detail in the vicinity of a limit state. The failure probability was calculated based on importance sampling, which was performed for the Kriging metamodel. A pre-existing method was modified to obtain more sampling points for a kernel density in the vicinity of a limit state. A stable numerical method was proposed to find a parameter of the kernel density. To assess the completeness of the Kriging metamodel, the possibility of changes in the calculated failure probability due to the uncertainty of the Kriging metamodel was calculated.

  3. Numerical Calculation of Distribution of Induced Carge Density on Planar Confined Surfaces

    International Nuclear Information System (INIS)

    Bolotov, V.; Druzhchenko, R.; Karazin, V.; Lominadze, J.; Kharadze, F.

    2007-01-01

    The calculation method of distribution of induced charge density on planar surfaces, including fractal structures of Sierpinski carpet type, is propesed. The calculation scheme is based on the fact that simply connected conducting surface of arbitrary geometry is an equipotential surface. (author)

  4. 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.

  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. Calculation of radon concentration in water by toluene extraction method

    Energy Technology Data Exchange (ETDEWEB)

    Saito, Masaaki [Tokyo Metropolitan Isotope Research Center (Japan)

    1997-02-01

    Noguchi method and Horiuchi method have been used as the calculation method of radon concentration in water. Both methods have two problems in the original, that is, the concentration calculated is changed by the extraction temperature depend on the incorrect solubility data and the concentration calculated are smaller than the correct values, because the radon calculation equation does not true to the gas-liquid equilibrium theory. However, the two problems are solved by improving the radon equation. I presented the Noguchi-Saito equation and the constant B of Horiuchi-Saito equation. The calculating results by the improved method showed about 10% of error. (S.Y.)

  7. Study on application of green's function method in thermal stress rapid calculation

    International Nuclear Information System (INIS)

    Zhang Guihe; Duan Yuangang; Xu Xiao; Chen Rong

    2013-01-01

    This paper presents a quick and accuracy thermal stress calculation method, the Green's Function Method, which is a combination of finite element method and numerical algorithm method. Thermal stress calculation of Safe Injection Nozzle of Reactor Coolant Line of PWR plant is performed with Green's function method for heatup and cooldown thermal transients as a demonstration example, and the result is compared with finite element method to verify the rationality and accuracy of this method. The advantage and disadvantage of the Green's function method and the finite element method are also compared. (authors)

  8. 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

  9. 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 cro...

  10. 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.

  11. 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)

  12. An introduction to the application of relaxation method in numerical weather prediction

    International Nuclear Information System (INIS)

    Aquino, E.M.

    1984-11-01

    This paper is intended for workers in the field of numerical weather prediction to acquire experience and gain insight on the use of the relaxation method. Two approaches were carried out, one by explaining the method using hand calculations as applied to a given problem and the second one was the discussion of how the calculations could be carried out on a digital computer. (author)

  13. A Method for Calculating the Mean Orbits of Meteor Streams

    Science.gov (United States)

    Voloshchuk, Yu. I.; Kashcheev, B. L.

    An examination of the published catalogs of orbits of meteor streams and of a large number of works devoted to the selection of streams, their analysis and interpretation, showed that elements of stream orbits are calculated, as a rule, as arithmetical (sometimes, weighed) sample means. On the basis of these means, a search for parent bodies, a study of the evolution of swarms generating these streams, an analysis of one-dimensional and multidimensional distributions of these elements, etc., are performed. We show that systematic errors in the estimates of elements of the mean orbits are present in each of the catalogs. These errors are caused by the formal averaging of orbital elements over the sample, while ignoring the fact that they represent not only correlated, but dependent quantities, with nonlinear, in most cases, interrelations between them. Numerous examples are given of such inaccuracies, in particular, the cases where the "mean orbit of the stream" recorded by ground-based techniques does not cross the Earth's orbit. We suggest the computation algorithm, in which the averaging over the sample is carried out at the initial stage of the calculation of the mean orbit, and only for the variables required for subsequent calculations. After this, the known astrometric formulas are used to sequentially calculate all other parameters of the stream, considered now as a standard orbit. Variance analysis is used to estimate the errors in orbital elements of the streams, in the case that their orbits are obtained by averaging the orbital elements of meteoroids forming the stream, without taking into account their interdependence. The results obtained in this analysis indicate the behavior of systematic errors in the elements of orbits of meteor streams. As an example, the effect of the incorrect computation method on the distribution of elements of the stream orbits close to the orbits of asteroids of the Apollo, Aten, and Amor groups (AAA asteroids) is examined.

  14. Transportation channels calculation method in MATLAB

    International Nuclear Information System (INIS)

    Averyanov, G.P.; Budkin, V.A.; Dmitrieva, V.V.; Osadchuk, I.O.; Bashmakov, Yu.A.

    2014-01-01

    Output devices and charged particles transport channels are necessary components of any modern particle accelerator. They differ both in sizes and in terms of focusing elements depending on particle accelerator type and its destination. A package of transport line designing codes for magnet optical channels in MATLAB environment is presented in this report. Charged particles dynamics in a focusing channel can be studied easily by means of the matrix technique. MATLAB usage is convenient because its information objects are matrixes. MATLAB allows the use the modular principle to build the software package. Program blocks are small in size and easy to use. They can be executed separately or commonly. A set of codes has a user-friendly interface. Transport channel construction consists of focusing lenses (doublets and triplets). The main of the magneto-optical channel parameters are total length and lens position and parameters of the output beam in the phase space (channel acceptance, beam emittance - beam transverse dimensions, particles divergence and image stigmaticity). Choice of the channel operation parameters is based on the conditions for satisfying mutually competing demands. And therefore the channel parameters calculation is carried out by using the search engine optimization techniques.

  15. Domain decomposition methods for core calculations using the MINOS solver

    International Nuclear Information System (INIS)

    Guerin, P.; Baudron, A. M.; Lautard, J. J.

    2007-01-01

    Cell by cell homogenized transport calculations of an entire nuclear reactor core are currently too expensive for industrial applications, even if a simplified transport (SPn) approximation is used. In order to take advantage of parallel computers, we propose here two domain decomposition methods using the mixed dual finite element solver MINOS. The first one is a modal synthesis method on overlapping sub-domains: several Eigenmodes solutions of a local problem on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second one is an iterative method based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, we solve the problem on each sub-domain with the interface conditions given by the solutions on the close sub-domains estimated at the previous iteration. For these two methods, we give numerical results which demonstrate their accuracy and their efficiency for the diffusion model on realistic 2D and 3D cores. (authors)

  16. 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...

  17. 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.

  18. Two numerical methods for mean-field games

    KAUST Repository

    Gomes, Diogo A.

    2016-01-01

    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.

  19. 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

  20. 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...

  1. Numerical methods design, analysis, and computer implementation of algorithms

    CERN Document Server

    Greenbaum, Anne

    2012-01-01

    Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book a...

  2. Numerical method for two phase flow with a unstable interface

    International Nuclear Information System (INIS)

    Glimm, J.; Marchesin, D.; McBryan, O.

    1981-01-01

    The random choice method is used to compute the oil-water interface for two dimensional porous media equations. The equations used are a pair of coupled equations; the (elliptic) pressure equation and the (hyperbolic) saturation equation. The equations do not include the dispersive capillary pressure term and the computation does not introduce numerical diffusion. The method resolves saturation discontinuities sharply. The main conclusion of this paper is that the random choice is a correct numerical procedure for this problem even in the highly fingered case. Two methods of inducing fingers are considered: deterministically, through choice of Cauchy data and heterogeneity, through maximizing the randomness of the random choice method

  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. 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

  5. Acceleration and parallelization calculation of EFEN-SP_3 method

    International Nuclear Information System (INIS)

    Yang Wen; Zheng Youqi; Wu Hongchun; Cao Liangzhi; Li Yunzhao

    2013-01-01

    Due to the fact that the exponential function expansion nodal-SP_3 (EFEN-SP_3) method needs further improvement in computational efficiency to routinely carry out PWR whole core pin-by-pin calculation, the coarse mesh acceleration and spatial parallelization were investigated in this paper. The coarse mesh acceleration was built by considering discontinuity factor on each coarse mesh interface and preserving neutron balance within each coarse mesh in space, angle and energy. The spatial parallelization based on MPI was implemented by guaranteeing load balancing and minimizing communications cost to fully take advantage of the modern computing and storage abilities. Numerical results based on a commercial nuclear power reactor demonstrate an speedup ratio of about 40 for the coarse mesh acceleration and a parallel efficiency of higher than 60% with 40 CPUs for the spatial parallelization. With these two improvements, the EFEN code can complete a PWR whole core pin-by-pin calculation with 289 × 289 × 218 meshes and 4 energy groups within 100 s by using 48 CPUs (2.40 GHz frequency). (authors)

  6. Calculation of residual stresses by means of a 3D numerical weld simulation

    International Nuclear Information System (INIS)

    Nicak, Tomas; Huemmer, Matthias

    2008-01-01

    The numerical weld simulation has developed very fast in recent years. The problem complexity has increased from simple 2D models to full 3D models, which can describe the entire welding process more realistically. As recent research projects indicate, a quantitative assessment of the residual stresses by means of a 3D analysis is possible. The structure integrity can be assessed based on the weld simulation results superimposed with the operating load. Moreover, to support the qualification of welded components parametric studies for optimization of the residual stress distribution in the weld region can be performed. In this paper a full 3D numerical weld simulation for a man-hole drainage nozzle in a steam generator will be presented. The residual stresses are calculated by means of an uncoupled transient thermal and mechanical FE analysis. The paper will present a robust procedure allowing reasonable predictions of the residual stresses for complex structures in industrial practice. (authors)

  7. New efficient methods for calculating watersheds

    International Nuclear Information System (INIS)

    Fehr, E; Andrade, J S Jr; Herrmann, H J; Kadau, D; Moukarzel, C F; Da Cunha, S D; Da Silva, L R; Oliveira, E A

    2009-01-01

    We present an advanced algorithm for the determination of watershed lines on digital elevation models (DEMs) which is based on the iterative application of invasion percolation (IP). The main advantage of our method over previously proposed ones is that it has a sub-linear time-complexity. This enables us to process systems comprising up to 10 8 sites in a few CPU seconds. Using our algorithm we are able to demonstrate, convincingly and with high accuracy, the fractal character of watershed lines. We find the fractal dimension of watersheds to be D f = 1.211 ± 0.001 for artificial landscapes, D f = 1.10 ± 0.01 for the Alps and D f = 1.11 ± 0.01 for the Himalayas

  8. A numerical method for transient gas-liquid two-phase flow using a general curvilinear coordinate system. 1. Governing equations and numerical method

    International Nuclear Information System (INIS)

    Tomiyama, Akio; Matsuoka, Toshiyuki.

    1995-01-01

    A simple numerical method for solving a transient incompressible two-fluid model was proposed in the present study. A general curvilinear coordinate system was adopted in this method for predicting transient flows in practical engineering devices. The simplicity of the present method is due to the fact that the field equations and constitutive equations were expressed in a tensor form in the general curvilinear coordinate system. When a conventional rectangular mesh is adopted in a calculation, the method reduces to a numerical method for a Cartesian coordinate system. As an example, the present method was applied to transient air-water bubbly flow in a vertical U-tube. It was confirmed that the effects of centrifugal and gravitational forces on the phase distribution in the U-tube were reasonably predicted. (author)

  9. EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY

    Energy Technology Data Exchange (ETDEWEB)

    FRANCOIS, MARIANNE M. [Los Alamos National Laboratory; DENDY, EDWARD D. [Los Alamos National Laboratory; LOWRIE, ROBERT B. [Los Alamos National Laboratory; LIVESCU, DANIEL [Los Alamos National Laboratory; STEINKAMP, MICHAEL J. [Los Alamos National Laboratory

    2007-01-11

    The authors compare the effects of different numerical schemes for the advection and material interface treatments on the single-mode Rayleigh-Taylor instability, using the RAGE hydro-code. The interface growth and its surface density (interfacial area) versus time are investigated. The surface density metric shows to be better suited to characterize the difference in the flow, than the conventional interface growth metric. They have found that Van Leer's limiter combined to no interface treatment leads to the largest surface area. Finally, to quantify the difference between the numerical methods they have estimated the numerical viscosity in the linear-regime at different scales.

  10. Time dependent AN neutron transport calculations in finite media using a numerical inverse Laplace transform technique

    International Nuclear Information System (INIS)

    Ganapol, B.D.; Sumini, M.

    1990-01-01

    The time dependent space second order discrete form of the monokinetic transport equation is given an analytical solution, within the Laplace transform domain. Th A n dynamic model is presented and the general resolution procedure is worked out. The solution in the time domain is then obtained through the application of a numerical transform inversion technique. The justification of the research relies in the need to produce reliable and physically meaningful transport benchmarks for dynamic calculations. The paper is concluded by a few results followed by some physical comments

  11. Numerical methods for axisymmetric and 3D nonlinear beams

    Science.gov (United States)

    Pinton, Gianmarco F.; Trahey, Gregg E.

    2005-04-01

    Time domain algorithms that solve the Khokhlov--Zabolotzskaya--Kuznetsov (KZK) equation are described and implemented. This equation represents the propagation of finite amplitude sound beams in a homogenous thermoviscous fluid for axisymmetric and fully three dimensional geometries. In the numerical solution each of the terms is considered separately and the numerical methods are compared with known solutions. First and second order operator splitting are used to combine the separate terms in the KZK equation and their convergence is examined.

  12. 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

  13. 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

  14. Theory and numerical calculation of the acoustic field exerted by eddy-current forces

    Energy Technology Data Exchange (ETDEWEB)

    Kawashima, K.

    1976-01-01

    The equations for calculating the acoustic field produced within a nonmagnetic metal by interaction of eddy currents with a static magnetic field were obtained on the assumptions (1) an ultrasonic wave is generated by the electromagentic force through classical and macroscopic phenomena; (2) the electric, magnetic, and elastic properties of the metal are linear, isotropic, and homogeneous throughout the metal, which occupies semi-infinite space; (3) the whole system is axially symmetric; and (4) eddy currents and elastic waves show a steady-state sinusoidal variation. The acoustic field produced by a specific electromagnetic ultrasonic transducer with axial symmetry was calculated numerically, and the results showed a well-defined ultrasonic wave beam, which was narrower than had been expected from the size of the transducer. (auth)

  15. Comparison of turbulence models for numerical calculation of airflow in an annex 20 room

    DEFF Research Database (Denmark)

    Voigt, Lars P. K.

    2000-01-01

    The report deals with 2-D numerical calculation of room airflow in an isothermal annex 20 room. The report documents the ability of the flow solver EllipSys2D to give results in good agreement with measurements for the specified test case. The flow solver is a finite volume code solving the Reyno.......Applying theory for a two-dimensional wall jet, measurements are compared with calculated values of the turbulent kinetic energy....... the Reynolds Averaged Navier Stokes equations.Five two-equation turbulence models were tested. These are the standard k-epsilon model, the low-Reynolds number k-epison model by Launder & Sharma, the k-omega model by Wilcox, the k-omega baseline (BSL) model by Menter and the k-omega Shear Stress Transport (SST...

  16. An implicit second order numerical method for two-fluid models

    International Nuclear Information System (INIS)

    Toumi, I.

    1995-01-01

    We present an implicit upwind numerical method for a six equation two-fluid model based on a linearized Riemann solver. The construction of this approximate Riemann solver uses an extension of Roe's scheme. Extension to second order accurate method is achieved using a piecewise linear approximation of the solution and a slope limiter method. For advancing in time, a linearized implicit integrating step is used. In practice this new numerical method has proved to be stable and capable of generating accurate non-oscillating solutions for two-phase flow calculations. The scheme was applied both to shock tube problems and to standard tests for two-fluid codes. (author)

  17. 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....

  18. Valve cam design using numerical step-by-step method

    OpenAIRE

    Vasilyev, Aleksandr; Bakhracheva, Yuliya; Kabore, Ousman; Zelenskiy, Yuriy

    2014-01-01

    This article studies the numerical step-by-step method of cam profile design. The results of the study are used for designing the internal combustion engine valve gear. This method allows to profile the peak efficiency of cams in view of many restrictions, connected with valve gear serviceability and reliability.

  19. 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…

  20. 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

  1. 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.

  2. 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

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

    KAUST Repository

    Happola, Juho

    2017-01-01

    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.

  4. 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.

  5. Quantum Monte Carlo diagonalization method as a variational calculation

    International Nuclear Information System (INIS)

    Mizusaki, Takahiro; Otsuka, Takaharu; Honma, Michio.

    1997-01-01

    A stochastic method for performing large-scale shell model calculations is presented, which utilizes the auxiliary field Monte Carlo technique and diagonalization method. This method overcomes the limitation of the conventional shell model diagonalization and can extremely widen the feasibility of shell model calculations with realistic interactions for spectroscopic study of nuclear structure. (author)

  6. Multi-instantons and exact results II: specific cases, higher-order effects, and numerical calculations

    International Nuclear Information System (INIS)

    Zinn-Justin, Jean; Jentschura, Ulrich D.

    2004-01-01

    In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton contributions to the partition function, using the formalism introduced in the first part of the treatise [Ann. Phys. (N. Y.) (previous issue) (2004)]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific potential which bears an analogy with the Fokker-Planck equation. The latter potential has the peculiar property that the perturbation series for the ground-state energy vanishes to all orders and is thus formally convergent (the ground-state energy, however, is non-zero and positive). For the potentials (ii), (iii), and (iv), we calculate the perturbative B-function as well as the instanton A-function to fourth order in g. We also consider the double-well potential in detail, and present some higher-order analytic as well as numerical calculations to verify explicitly the related conjectures up to the order of three instantons. Strategies analogous to those outlined here could result in new conjectures for problems where our present understanding is more limited

  7. Roundtrip matrix method for calculating the leaky resonant modes of open nanophotonic structures

    DEFF Research Database (Denmark)

    de Lasson, Jakob Rosenkrantz; Kristensen, Philip Trøst; Mørk, Jesper

    2014-01-01

    We present a numerical method for calculating quasi-normal modes of open nanophotonic structures. The method is based on scattering matrices and a unity eigenvalue of the roundtrip matrix of an internal cavity, and we develop it in detail with electromagnetic fields expanded on Bloch modes...

  8. Assessment of chemical exposures: calculation methods for environmental professionals

    National Research Council Canada - National Science Library

    Daugherty, Jack E

    1997-01-01

    ... on by scientists, businessmen, and policymakers. Assessment of Chemical Exposures: Calculation Methods for Environmental Professionals addresses the expanding scope of exposure assessments in both the workplace and environment...

  9. 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

  10. 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)

  11. 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

  12. 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.

  13. Comparison of the methods for calculating the interfacial heat transfer coefficient in hot stamping

    International Nuclear Information System (INIS)

    Zhao, Kunmin; Wang, Bin; Chang, Ying; Tang, Xinghui; Yan, Jianwen

    2015-01-01

    This paper presents a hot stamping experimentation and three methods for calculating the Interfacial Heat Transfer Coefficient (IHTC) of 22MnB5 boron steel. Comparison of the calculation results shows an average error of 7.5% for the heat balance method, 3.7% for the Beck's nonlinear inverse estimation method (the Beck's method), and 10.3% for the finite-element-analysis-based optimization method (the FEA method). The Beck's method is a robust and accurate method for identifying the IHTC in hot stamping applications. The numerical simulation using the IHTC identified by the Beck's method can predict the temperature field with a high accuracy. - Highlights: • A theoretical formula was derived for direct calculation of IHTC. • The Beck's method is a robust and accurate method for identifying IHTC. • Finite element method can be used to identify an overall equivalent IHTC

  14. 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.

  15. 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

  16. Numerical Integration Methods for the Takagi-Taupin Equations for Crystals of Rectangular Cross Section

    International Nuclear Information System (INIS)

    Kolosov, S.I.; Punegov, V.I.

    2005-01-01

    Two independent methods for calculation of the rocking curves for laterally bounded crystals are developed. Numerical simulation of diffraction for crystals of different sizes is performed. The results obtained using the dynamical theory of diffraction are compared to those obtained in the kinematic approximation

  17. 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.

  18. Numerical simulation methods for wave propagation through optical waveguides

    International Nuclear Information System (INIS)

    Sharma, A.

    1993-01-01

    The simulation of the field propagation through waveguides requires numerical solutions of the Helmholtz equation. For this purpose a method based on the principle of orthogonal collocation was recently developed. The method is also applicable to nonlinear pulse propagation through optical fibers. Some of the salient features of this method and its application to both linear and nonlinear wave propagation through optical waveguides are discussed in this report. 51 refs, 8 figs, 2 tabs

  19. 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

  20. NUMERICAL WITHOUT ITERATION METHOD OF MODELING OF ELECTROMECHANICAL PROCESSES IN ASYNCHRONOUS ENGINES

    Directory of Open Access Journals (Sweden)

    D. G. Patalakh

    2018-02-01

    Full Text Available Purpose. Development of calculation of electromagnetic and electromechanic transients is in asynchronous engines without iterations. Methodology. Numeral methods of integration of usual differential equations, programming. Findings. As the system of equations, describing the dynamics of asynchronous engine, contents the products of rotor and stator currents and product of rotation frequency of rotor and currents, so this system is nonlinear one. The numeral solution of nonlinear differential equations supposes an iteration process on every step of integration. Time-continuing and badly converging iteration process may be the reason of calculation slowing. The improvement of numeral method by the way of an iteration process removing is offered. As result the modeling time is reduced. The improved numeral method is applied for integration of differential equations, describing the dynamics of asynchronous engine. Originality. The improvement of numeral method allowing to execute numeral integrations of differential equations containing product of functions is offered, that allows to avoid an iteration process on every step of integration and shorten modeling time. Practical value. On the basis of the offered methodology the universal program of modeling of electromechanics processes in asynchronous engines could be developed as taking advantage on fast-acting.

  1. 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)

  2. Comments on Simplified Calculation Method for Fire Exposed Concrete Columns

    DEFF Research Database (Denmark)

    Hertz, Kristian Dahl

    1998-01-01

    The author has developed new simplified calculation methods for fire exposed columns. Methods, which are found In ENV 1992-1-2 chapter 4.3 and in proposal for Danish code of Practise DS411 chapter 9. In the present supporting document the methods are derived and 50 eccentrically loaded fire expos...... columns are calculated and compared to results of full-scale tests. Furthermore 500 columns are calculated in order to present each test result related to a variation of the calculation in time of fire resistance....

  3. Numerical Exact Ab Initio Four-Nucleon Scattering Calculations: from Dream to Reality

    Science.gov (United States)

    Fonseca, A. C.; Deltuva, A.

    2017-03-01

    In the present manuscript we review the work of the last ten years on the pursuit to obtain numerical exact solutions of the four-nucleon scattering problem using the most advanced force models that fit two nucleon data up to pion production threshold with a χ ^2 per data point approximately one, together with the Coulomb interaction between protons; three- and four-nucleon forces are also included in the framework of a meson exchange potential model where NN couples to NΔ. Failure to describe the world data on four-nucleon scattering observables in the framework of a non relativistic scattering approach falls necessarily on the force models one uses. Four-nucleon observables pose very clear challenges, particular in the low energy region where there are a number of resonances whose position and width needs to be dynamically generated by the nucleon-nucleon (NN) interactions one uses. In addition, our calculations constitute the most advance piece of work where observables for all four-nucleon reactions involving isospin I=0, I=0 coupled to I=1 and isospin I=1 initial states are calculated at energies both below and above breakup threshold. We also present a very extensive comparison between calculated results and data for cross sections and spin observables. Therefore the present work reveals both the shortcomings and successes of some of the present NN force models in describing four-nucleon data and serve as a benchmark for future developments.

  4. Comparison of two numerical modelling codes for hydraulic and transport calculations in the near-field

    International Nuclear Information System (INIS)

    Kalin, J.; Petkovsek, B.; Montarnal, Ph.; Genty, A.; Deville, E.; Krivic, J.; Ratej, J.

    2011-01-01

    In the past years the Slovenian Performance Analysis/Safety Assessment team has performed many generic studies for the future Slovenian low and intermediate level waste repository, most recently a Special Safety Analysis for the Krsko site. The modelling approach was to split the problem into three parts: near-field (detailed model of the repository), far-field (i.e., geosphere) and biosphere. In the Special Safety Analysis the code used to perform the near-field calculations was Hydrus2D. Recently the team has begun a cooperation with the French Commisariat al'Energie Atomique/Saclay (CEA/Saclay) and, as a part of this cooperation, began investigations into using the Alliances numerical platform for near-field calculations in order to compare the overall approach and calculated results. The article presents the comparison between these two codes for a silo-type repository that was considered in the Special Safety Analysis. The physical layout and characteristics of the repository are presented and a hydraulic and transport model of the repository is developed and implemented in Alliances. Some analysis of sensitivity to mesh fineness and to simulation timestep has been preformed and is also presented. The compared quantity is the output flux of radionuclides on the boundary of the model. Finally the results from Hydrus2D and Alliances are compared and the differences and similarities are commented.

  5. Comparison of two numerical modelling codes for hydraulic and transport calculations in the near-field

    Energy Technology Data Exchange (ETDEWEB)

    Kalin, J., E-mail: jan.kalin@zag.s [Slovenian National Building and Civil Engineering Institute, Dimiceva 12, SI-1000 Ljubljana (Slovenia); Petkovsek, B., E-mail: borut.petkovsek@zag.s [Slovenian National Building and Civil Engineering Institute, Dimiceva 12, SI-1000 Ljubljana (Slovenia); Montarnal, Ph., E-mail: philippe.montarnal@cea.f [CEA/Saclay, DM2S/SFME/LSET, Gif-sur-Yvette, 91191 cedex (France); Genty, A., E-mail: alain.genty@cea.f [CEA/Saclay, DM2S/SFME/LSET, Gif-sur-Yvette, 91191 cedex (France); Deville, E., E-mail: estelle.deville@cea.f [CEA/Saclay, DM2S/SFME/LSET, Gif-sur-Yvette, 91191 cedex (France); Krivic, J., E-mail: jure.krivic@geo-zs.s [Geological Survey of Slovenia, Dimiceva 14, SI-1000 Ljubljana (Slovenia); Ratej, J., E-mail: joze.ratej@geo-zs.s [Geological Survey of Slovenia, Dimiceva 14, SI-1000 Ljubljana (Slovenia)

    2011-04-15

    In the past years the Slovenian Performance Analysis/Safety Assessment team has performed many generic studies for the future Slovenian low and intermediate level waste repository, most recently a Special Safety Analysis for the Krsko site. The modelling approach was to split the problem into three parts: near-field (detailed model of the repository), far-field (i.e., geosphere) and biosphere. In the Special Safety Analysis the code used to perform the near-field calculations was Hydrus2D. Recently the team has begun a cooperation with the French Commisariat al'Energie Atomique/Saclay (CEA/Saclay) and, as a part of this cooperation, began investigations into using the Alliances numerical platform for near-field calculations in order to compare the overall approach and calculated results. The article presents the comparison between these two codes for a silo-type repository that was considered in the Special Safety Analysis. The physical layout and characteristics of the repository are presented and a hydraulic and transport model of the repository is developed and implemented in Alliances. Some analysis of sensitivity to mesh fineness and to simulation timestep has been preformed and is also presented. The compared quantity is the output flux of radionuclides on the boundary of the model. Finally the results from Hydrus2D and Alliances are compared and the differences and similarities are commented.

  6. 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

  7. Mixed first- and second-order transport method using domain decomposition techniques for reactor core calculations

    International Nuclear Information System (INIS)

    Girardi, E.; Ruggieri, J.M.

    2003-01-01

    The aim of this paper is to present the last developments made on a domain decomposition method applied to reactor core calculations. In this method, two kind of balance equation with two different numerical methods dealing with two different unknowns are coupled. In the first part the two balance transport equations (first order and second order one) are presented with the corresponding following numerical methods: Variational Nodal Method and Discrete Ordinate Nodal Method. In the second part, the Multi-Method/Multi-Domain algorithm is introduced by applying the Schwarz domain decomposition to the multigroup eigenvalue problem of the transport equation. The resulting algorithm is then provided. The projection operators used to coupled the two methods are detailed in the last part of the paper. Finally some preliminary numerical applications on benchmarks are given showing encouraging results. (authors)

  8. 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

  9. Research on GPU-accelerated algorithm in 3D finite difference neutron diffusion calculation method

    International Nuclear Information System (INIS)

    Xu Qi; Yu Ganglin; Wang Kan; Sun Jialong

    2014-01-01

    In this paper, the adaptability of the neutron diffusion numerical algorithm on GPUs was studied, and a GPU-accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. The IAEA 3D PWR benchmark problem was calculated in the numerical test. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. (authors)

  10. 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

  11. Method of characteristics - Based sensitivity calculations for international PWR benchmark

    International Nuclear Information System (INIS)

    Suslov, I. R.; Tormyshev, I. V.; Komlev, O. G.

    2013-01-01

    Method to calculate sensitivity of fractional-linear neutron flux functionals to transport equation coefficients is proposed. Implementation of the method on the basis of MOC code MCCG3D is developed. Sensitivity calculations for fission intensity for international PWR benchmark are performed. (authors)

  12. 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

  13. Manual method for dose calculation in gynecologic brachytherapy

    International Nuclear Information System (INIS)

    Vianello, Elizabeth A.; Almeida, Carlos E. de; Biaggio, Maria F. de

    1998-01-01

    This paper describes a manual method for dose calculation in brachytherapy of gynecological tumors, which allows the calculation of the doses at any plane or point of clinical interest. This method uses basic principles of vectorial algebra and the simulating orthogonal films taken from the patient with the applicators and dummy sources in place. The results obtained with method were compared with the values calculated with the values calculated with the treatment planning system model Theraplan and the agreement was better than 5% in most cases. The critical points associated with the final accuracy of the proposed method is related to the quality of the image and the appropriate selection of the magnification factors. This method is strongly recommended to the radiation oncology centers where are no treatment planning systems available and the dose calculations are manually done. (author)

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

    International Nuclear Information System (INIS)

    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

  15. 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.

  16. The Davidson Method as an alternative to power iterations for criticality calculations

    International Nuclear Information System (INIS)

    Subramanian, C.; Van Criekingen, S.; Heuveline, V.; Nataf, F.; Have, P.

    2011-01-01

    The Davidson method is implemented within the neutron transport core solver parafish to solve k-eigenvalue criticality transport problems. The parafish solver is based on domain decomposition, uses spherical harmonics (P_N method) for angular discretization, and nonconforming finite elements for spatial discretization. The Davidson method is compared to the traditional power iteration method in that context. Encouraging numerical results are obtained with both sequential and parallel calculations. (author)

  17. 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.

  18. 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)

  19. A Broyden numerical Kutta condition for an unsteady panel method

    International Nuclear Information System (INIS)

    Liu, P.; Bose, N.; Colbourne, B.

    2003-01-01

    In panel methods, numerical Kutta conditions are applied in order to ensure that pressure differences between the surfaces at the trailing edges of lifting surface elements are close to zero. Previous numerical Kutta conditions for 3-D panel methods have focused on use of the Newton-Raphson iterative procedure. For extreme unsteady motions, such as for oscillating hydrofoils or for a propeller behind a blockage, the Newton-Raphson procedure can have severe convergence difficulties. The Broyden iteration, a modified Newton-Raphson iteration procedure, is applied here to obtain improved convergence behavior. Using the Broyden iteration increases the reliability, robustness and in many cases computing efficiency for unsteady, multi-body interactive flows. This method was tested in a time domain code for an ice class propeller in both open water flow and during interaction with a nearby ice blockage. Predictions showed that the method was effective in these extreme flows. (author)

  20. Analytic and numerical calculations of quantum synchrotron spectra from relativistic electron distributions

    International Nuclear Information System (INIS)

    Brainerd, J.J.; Petrosian, V.

    1987-01-01

    Calculations are performed numerically and analytically of synchrotron spectra for thermal and power-law electron distributions using the single-particle synchrotron power spectrum derived from quantum electrodynamics. It is found that the photon energy at which quantum effects appear is proportional to temperature and independent of field strength for thermal spectra; quantum effects introduce an exponential roll-off away from the classical spectra. For power law spectra, the photon energy at which quantum effects appear is inversely proportional to the magnetic field strength; quantum effects produce a steeper power law than is found classically. The results are compared with spectra derived from the classical power spectrum with an energy cutoff ensuring conservation of energy. It is found that an energy cutoff is generally an inadequate approximation of quantum effects for low photon energies and for thermal spectra, but gives reasonable results for high-energy emission from power-law electron distributions. 17 references

  1. Characterization of BPM pickup designs for the HESR rate at FAIR using simulations and numerical calculations

    Energy Technology Data Exchange (ETDEWEB)

    Halama, Arthur; Kamerdzhiev, Vsevolod; Boehme, Christian; Srinivasan, Sudharsan [Forschungszentrum Juelich, IKP-4 (Germany)

    2016-07-01

    The institute of Nuclear Physics 4(IKP-4) of the Research Center Juelich (FZJ) is in charge of building and commissioning the High Energy Storage Ring (HESR) within the international Facility for Antiproton and Ion Research (FAIR) at Darmstadt. Simulations and numerical calculations were performed to characterize the initial beam position pickup design. Capacitive couplings of the electrodes and the behavior of the electrical equivalent circuit were investigated. This made room for changes to the design and performance increase. A prototype of the BPM pickup was constructed and tested on a dedicated test bench. Preliminary results will be presented. In order to gain higher signal levels and higher sensitivity, another suggested design was characterized as well and put into comparison.

  2. 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

  3. Workshop on Numerical Methods for Ordinary Differential Equations

    CERN Document Server

    Gear, Charles; Russo, Elvira

    1989-01-01

    Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.

  4. 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

  5. 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.

  6. Numerical

    Directory of Open Access Journals (Sweden)

    M. Boumaza

    2015-07-01

    Full Text Available Transient convection heat transfer is of fundamental interest in many industrial and environmental situations, as well as in electronic devices and security of energy systems. Transient fluid flow problems are among the more difficult to analyze and yet are very often encountered in modern day technology. The main objective of this research project is to carry out a theoretical and numerical analysis of transient convective heat transfer in vertical flows, when the thermal field is due to different kinds of variation, in time and space of some boundary conditions, such as wall temperature or wall heat flux. This is achieved by the development of a mathematical model and its resolution by suitable numerical methods, as well as performing various sensitivity analyses. These objectives are achieved through a theoretical investigation of the effects of wall and fluid axial conduction, physical properties and heat capacity of the pipe wall on the transient downward mixed convection in a circular duct experiencing a sudden change in the applied heat flux on the outside surface of a central zone.

  7. Numerical calculation models of the elastoplastic response of a structure under seismic action

    International Nuclear Information System (INIS)

    Edjtemai, Nima.

    1982-06-01

    Two digital calculation models developed in this work have made it possible to analyze the exact dynamic behaviour of ductile structures with one or several degrees of liberty, during earthquakes. With the first model, response spectra were built in the linear and non-linear fields for different absorption and ductility values and two types of seismic accelerograms. The comparative study of these spectra made it possible to check the validity of certain hypotheses suggested for the construction of elastoplastic spectra from corresponding linear spectra. A simplified method of non-linear seismic calculation based on the modal analysis and the spectra of elastoplastic response was then applied to structures with a varying number of degrees of liberty. The results obtained in this manner were compared with those provided by an exact calculation provided by the second digital model developed by us [fr

  8. A New Thermodynamic Calculation Method for Binary Alloys: Part I: Statistical Calculation of Excess Functions

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    The improved form of calculation formula for the activities of the components in binary liquids and solid alloys has been derived based on the free volume theory considering excess entropy and Miedema's model for calculating the formation heat of binary alloys. A calculation method of excess thermodynamic functions for binary alloys, the formulas of integral molar excess properties and partial molar excess properties for solid ordered or disordered binary alloys have been developed. The calculated results are in good agreement with the experimental values.

  9. 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...

  10. BOKASUN: A fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

    Science.gov (United States)

    Caffo, Michele; Czyż, Henryk; Gunia, Michał; Remiddi, Ettore

    2009-03-01

    We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations. Program summaryProgram title: BOKASUN Catalogue identifier: AECG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9404 No. of bytes in distributed program, including test data, etc.: 104 123 Distribution format: tar.gz Programming language: FORTRAN77 Computer: Any computer with a Fortran compiler accepting FORTRAN77 standard. Tested on various PC's with LINUX Operating system: LINUX RAM: 120 kbytes Classification: 4.4 Nature of problem: Any integral arising in the evaluation of the two-loop sunrise Feynman diagram can be expressed in terms of a given set of Master Integrals, which should be calculated numerically. The program provides a fast and precise evaluation method of the Master Integrals for arbitrary (but not vanishing) masses and arbitrary value of the external momentum. Solution method: The integrals depend on three internal masses and the external momentum squared p. The method is a combination of an accelerated expansion in 1/p in its (pretty large!) region of fast convergence and of a Runge-Kutta numerical solution of a system of linear differential equations. Running time: To obtain 4 Master Integrals on PC with 2 GHz processor it takes 3 μs for series expansion with pre-calculated coefficients, 80 μs for series expansion without pre-calculated coefficients, from a few seconds up to a few minutes for Runge-Kutta method (depending

  11. 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

  12. Hybrid RANS-LES using high order numerical methods

    Science.gov (United States)

    Henry de Frahan, Marc; Yellapantula, Shashank; Vijayakumar, Ganesh; Knaus, Robert; Sprague, Michael

    2017-11-01

    Understanding the impact of wind turbine wake dynamics on downstream turbines is particularly important for the design of efficient wind farms. Due to their tractable computational cost, hybrid RANS/LES models are an attractive framework for simulating separation flows such as the wake dynamics behind a wind turbine. High-order numerical methods can be computationally efficient and provide increased accuracy in simulating complex flows. In the context of LES, high-order numerical methods have shown some success in predictions of turbulent flows. However, the specifics of hybrid RANS-LES models, including the transition region between both modeling frameworks, pose unique challenges for high-order numerical methods. In this work, we study the effect of increasing the order of accuracy of the numerical scheme in simulations of canonical turbulent flows using RANS, LES, and hybrid RANS-LES models. We describe the interactions between filtering, model transition, and order of accuracy and their effect on turbulence quantities such as kinetic energy spectra, boundary layer evolution, and dissipation rate. This work was funded by the U.S. Department of Energy, Exascale Computing Project, under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory.

  13. Hamming method for solving the delayed neutron precursor concentration for reactivity calculation

    International Nuclear Information System (INIS)

    Díaz, Daniel Suescún; Ospina, Juan Felipe Flórez; Sarasty, Jesús Andrés Rodríguez

    2012-01-01

    Highlights: ► We present a new formulation to calculate the reactivity using the Hamming method. ► This method shows better accuracy than existing methods for reactivity calculation. ► The reactivity is calculated without limitation of the nuclear power form. ► The method can be implemented in reactivity meters with time step of up to 0.1 s. - Abstract: We propose a new method for numerically solving the inverse point kinetic equation for a nuclear reactor using the Hamming method, without requiring the nuclear power history and without using the Laplace transform. This new method converges with accuracy of order h 5 , where h is the step in the computation time. The procedure is validated for different forms of the nuclear power and with different time steps. The results indicate that this method has a better accuracy and lower computational effort compared with other conventional methods that use the nuclear power history.

  14. 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....

  15. A finite element method for SSI time history calculation

    International Nuclear Information System (INIS)

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

    1989-01-01

    The method which is proposed is based on a finite element modelization 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 is presented, then applications are 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 are described

  16. 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

  17. 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

  18. 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)

  19. Numerical calculation on infrared characteristics of the special vehicle exhaust system

    Science.gov (United States)

    Feng, Yun-song; Li, Xiao-xia; Jin, Wei

    2017-10-01

    For mastery of infrared radiation characteristics and flow field of the special vehicle exhaust system, first, a physical model of the special vehicle exhaust system is established with the Gambit, and the mathematical model of flow field is determined. Secondly, software Fluent6.3 is used to simulated the 3-D exterior flow field of the special vehicle exhaust system, and the datum of flow field, such as temperature, pressure and density, are obtained. Thirdly, based on the plume temperature, the special vehicle exhaust space is divided. The exhaust is equivalent to a gray-body. A calculating model of the vehicle exhaust infrared radiation is established, and the exhaust infrared radiation characteristics are calculated by the software MATLAB, then the spatial distribution curves are drawn. Finally, the numerical results are analyzing, and the basic laws of the special vehicle exhaust infrared radiation are explored. The results show that with the increase of the engine speed, the temperature of the exhaust pipe wall of the special vehicle increases, and the temperature and pressure of the exhaust gas flow field increase, which leads to the enhancement of the infrared radiation intensity

  20. Comparison of numerical models for calculating dispersion from accidental releases of pollutants

    Energy Technology Data Exchange (ETDEWEB)

    Pepper, D W [Savannah River Lab., Aiken, SC; Cooper, R E; Baker, A J

    1982-01-01

    A modular, data-based system approach has been developed to facilitate computational simulation of multi-dimensional pollutant dispersion in atmospheric, steam, estuary, and groundwater applications. This system is used to assess effects of accidental releases of pollutants to the environment. Model sophistication ranges from simple statistical to complex three-dimensional numerical methods. The system used specifies desired degree of model sophistication from a terminal. The model used depends on the particular type of problem being solved, and on a basis of merit related to computer cost. The results of prediction for several model problems are presented.

  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. 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.

  3. A method of paralleling computer calculation for two-dimensional kinetic plasma model

    International Nuclear Information System (INIS)

    Brazhnik, V.A.; Demchenko, V.V.; Dem'yanov, V.G.; D'yakov, V.E.; Ol'shanskij, V.V.; Panchenko, V.I.

    1987-01-01

    A method for parallel computer calculation and OSIRIS program complex realizing it and designed for numerical plasma simulation by the macroparticle method are described. The calculation can be carried out either with one or simultaneously with two computers BESM-6, that is provided by some package of interacting programs functioning in every computer. Program interaction in every computer is based on event techniques realized in OS DISPAK. Parallel computer calculation with two BESM-6 computers allows to accelerate the computation 1.5 times

  4. 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

  5. Numerical Calculation of Effect of Elastic Deformation on Aerodynamic Characteristics of a Rocket

    OpenAIRE

    Abbas, Laith K.; Chen, Dongyang; Rui, Xiaoting

    2014-01-01

    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 ver...

  6. Comparison of calculational methods for EBT reactor nucleonics

    International Nuclear Information System (INIS)

    Henninger, R.J.; Seed, T.J.; Soran, P.D.; Dudziak, D.J.

    1980-01-01

    Nucleonic calculations for a preliminary conceptual design of the first wall/blanket/shield/coil assembly for an EBT reactor are described. Two-dimensional Monte Carlo, and one- and two-dimensional discrete-ordinates calculations are compared. Good agreement for the calculated values of tritium breeding and nuclear heating is seen. We find that the three methods are all useful and complementary as a design of this type evolves

  7. 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

  8. 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.)

  9. Numerical analysis for multi-group neutron-diffusion equation using Radial Point Interpolation Method (RPIM)

    International Nuclear Information System (INIS)

    Kim, Kyung-O; Jeong, Hae Sun; Jo, Daeseong

    2017-01-01

    Highlights: • Employing the Radial Point Interpolation Method (RPIM) in numerical analysis of multi-group neutron-diffusion equation. • Establishing mathematical formation of modified multi-group neutron-diffusion equation by RPIM. • Performing the numerical analysis for 2D critical problem. - Abstract: A mesh-free method is introduced to overcome the drawbacks (e.g., mesh generation and connectivity definition between the meshes) of mesh-based (nodal) methods such as the finite-element method and finite-difference method. In particular, the Point Interpolation Method (PIM) using a radial basis function is employed in the numerical analysis for the multi-group neutron-diffusion equation. The benchmark calculations are performed for the 2D homogeneous and heterogeneous problems, and the Multiquadrics (MQ) and Gaussian (EXP) functions are employed to analyze the effect of the radial basis function on the numerical solution. Additionally, the effect of the dimensionless shape parameter in those functions on the calculation accuracy is evaluated. According to the results, the radial PIM (RPIM) can provide a highly accurate solution for the multiplication eigenvalue and the neutron flux distribution, and the numerical solution with the MQ radial basis function exhibits the stable accuracy with respect to the reference solutions compared with the other solution. The dimensionless shape parameter directly affects the calculation accuracy and computing time. Values between 1.87 and 3.0 for the benchmark problems considered in this study lead to the most accurate solution. The difference between the analytical and numerical results for the neutron flux is significantly increased in the edge of the problem geometry, even though the maximum difference is lower than 4%. This phenomenon seems to arise from the derivative boundary condition at (x,0) and (0,y) positions, and it may be necessary to introduce additional strategy (e.g., the method using fictitious points and

  10. 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)

  11. A GPU-based calculation using the three-dimensional FDTD method for electromagnetic field analysis.

    Science.gov (United States)

    Nagaoka, Tomoaki; Watanabe, Soichi

    2010-01-01

    Numerical simulations with the numerical human model using the finite-difference time domain (FDTD) method have recently been performed frequently in a number of fields in biomedical engineering. However, the FDTD calculation runs too slowly. We focus, therefore, on general purpose programming on the graphics processing unit (GPGPU). The three-dimensional FDTD method was implemented on the GPU using Compute Unified Device Architecture (CUDA). In this study, we used the NVIDIA Tesla C1060 as a GPGPU board. The performance of the GPU is evaluated in comparison with the performance of a conventional CPU and a vector supercomputer. The results indicate that three-dimensional FDTD calculations using a GPU can significantly reduce run time in comparison with that using a conventional CPU, even a native GPU implementation of the three-dimensional FDTD method, while the GPU/CPU speed ratio varies with the calculation domain and thread block size.

  12. Quantum mechanical methods for calculation of force constants

    International Nuclear Information System (INIS)

    Mullally, D.J.

    1985-01-01

    The focus of this thesis is upon the calculation of force constants; i.e., the second derivatives of the potential energy with respect to nuclear displacements. This information is useful for the calculation of molecular vibrational modes and frequencies. In addition, it may be used for the location and characterization of equilibrium and transition state geometries. The methods presented may also be applied to the calculation of electric polarizabilities and infrared and Raman vibrational intensities. Two approaches to this problem are studied and evaluated: finite difference methods and analytical techniques. The most suitable method depends on the type and level of theory used to calculate the electronic wave function. Double point displacement finite differencing is often required for accurate calculation of the force constant matrix. These calculations require energy and gradient calculations on both sides of the geometry of interest. In order to speed up these calculations, a novel method is presented that uses geometry dependent information about the wavefunction. A detailed derivation for the analytical evaluation of force constants with a complete active space multiconfiguration self consistent field wave function is presented

  13. New method for calculation of integral characteristics of thermal plumes

    DEFF Research Database (Denmark)

    Zukowska, Daria; Popiolek, Zbigniew; Melikov, Arsen Krikor

    2008-01-01

    A method for calculation of integral characteristics of thermal plumes is proposed. The method allows for determination of the integral parameters of plumes based on speed measurements performed with omnidirectional low velocity thermoanemometers. The method includes a procedure for calculation...... of the directional velocity (upward component of the mean velocity). The method is applied for determination of the characteristics of an asymmetric thermal plume generated by a sitting person. The method was validated in full-scale experiments in a climatic chamber with a thermal manikin as a simulator of a sitting...

  14. The pseudo-harmonics method applied to depletion calculation

    International Nuclear Information System (INIS)

    Silva, F.C. da; Amaral, J.A.C.; Thome, Z.D.

    1989-01-01

    In this paper, a new method for performing depletion calculations, based on the use of the Pseudo-Harmonics perturbation method, was developed. The fuel burnup was considered as a global perturbation and the multigroup difusion equations were rewriten in such a way as to treat the soluble boron concentration as the eigenvalue. By doing this, the critical boron concentration can be obtained by a perturbation method. A test of the new method was performed for a H 2 O-colled, D 2 O-moderated reactor. Comparison with direct calculation showed that this method is very accurate and efficient. (author) [pt

  15. Development of the numerical method for liquid metal magnetohydrodynamics (I). Investigation of the method and development of the 2D method

    International Nuclear Information System (INIS)

    Ohira, H.; Ara, K.

    2002-11-01

    Advanced electromagnetic components are investigated in Feasibility Studies on Commercialized FR Cycle System to apply to the main cooling systems of Liquid Metal Fast Reactor. Although a lot of experiments and numerical analysis were carried out on both high Reynolds numbers and high magnetic Reynolds numbers, the complex phenomena could not be evaluated in detail. As the first step of the development of the numerical methods for the liquid metal magnetohydrodynamics, we investigated numerical methods that could be applied to the electromagnetic components with both complex structures and high magnetic turbulent field. As a result, we selected GSMAC (Generalized-Simplified MArker and Cell) method for calculating the liquid metal fluid dynamics because it could be easily applied to the complex flow field. We also selected the vector-FEM for calculating the magnetic field of the large components because the method had no interaction procedure. In the high magnetic turbulent field, the dynamic-SGS models would be also a promising model for the good estimation, because it could calculate the field directly without any experimental constant. In order to verify the GSMAC and the vector-FEM, we developed the 2D numerical models and calculated the magnetohydrodynamics in the large electromagnetic pump. It was estimated from these results that the methods were basically reasonable, because the calculated pressure differences had the similar tendencies to the experimental ones. (author)

  16. Preliminary analysis of four numerical models for calculating the mesoscale transport of Kr-85

    Energy Technology Data Exchange (ETDEWEB)

    Pepper, D W; Cooper, R E [Du Pont de Nemours (E.I.) and Co., Aiken, SC (USA). Savannah River Lab.

    1983-01-01

    A performance study of four numerical algorithms for multi-dimensional advection-diffusion prediction on mesoscale grids has been made. Dispersion from point and distributed sources and a simulation of a continuous source are compared with analytical solutions to assess relative accuracy. Model predictions are then compared with actual measurements of Kr-85 emitted from the Savannah River Plant (SRP). The particle-in-cell and method of moments algorithms exhibit superior accuracy in modeling single source releases. For modeling distributed sources, algorithms based on the pseudospectral and finite element interpolation concepts exhibit comparable accuracy. The method of moments is felt to be the best overall performer, although all the models appear to be relatively close in accuracy.

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

    Directory of Open Access Journals (Sweden)

    Takashi Tanaka

    2014-06-01

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

  18. 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)

  19. Numerical renormalization group method for entanglement negativity at finite temperature

    Science.gov (United States)

    Shim, Jeongmin; Sim, H.-S.; Lee, Seung-Sup B.

    2018-04-01

    We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contributes to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.

  20. 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

  1. 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)

  2. Uniqueness and numerical methods in inverse obstacle scattering

    International Nuclear Information System (INIS)

    Kress, Rainer

    2007-01-01

    The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for incident plane waves. We will review some classical and some recent results and draw attention to open problems. In the second part we will survey on numerical methods for solving inverse obstacle scattering problems. Roughly speaking, these methods can be classified into three groups. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods, Landweber iterations or conjugate gradient methods for its solution. Decomposition methods, in principle, separate the inverse scattering problem into an ill-posed linear problem to reconstruct the scattered wave from its far field and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling methods. These are based on the numerical evaluation of criteria in terms of indicator functions that decide whether a point lies inside or outside the scatterer. The tutorial will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages

  3. 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.

  4. Statistics of Monte Carlo methods used in radiation transport calculation

    International Nuclear Information System (INIS)

    Datta, D.

    2009-01-01

    Radiation transport calculation can be carried out by using either deterministic or statistical methods. Radiation transport calculation based on statistical methods is basic theme of the Monte Carlo methods. The aim of this lecture is to describe the fundamental statistics required to build the foundations of Monte Carlo technique for radiation transport calculation. Lecture note is organized in the following way. Section (1) will describe the introduction of Basic Monte Carlo and its classification towards the respective field. Section (2) will describe the random sampling methods, a key component of Monte Carlo radiation transport calculation, Section (3) will provide the statistical uncertainty of Monte Carlo estimates, Section (4) will describe in brief the importance of variance reduction techniques while sampling particles such as photon, or neutron in the process of radiation transport

  5. Comparison study on cell calculation method of fast reactor

    International Nuclear Information System (INIS)

    Chiba, Gou

    2002-10-01

    Effective cross sections obtained by cell calculations are used in core calculations in current deterministic methods. Therefore, it is important to calculate the effective cross sections accurately and several methods have been proposed. In this study, some of the methods are compared to each other using a continuous energy Monte Carlo method as a reference. The result shows that the table look-up method used in Japan Nuclear Cycle Development Institute (JNC) sometimes has a difference over 10% in effective microscopic cross sections and be inferior to the sub-group method. The problem was overcome by introducing a new nuclear constant system developed in JNC, in which the ultra free energy group library is used. The system can also deal with resonance interaction effects between nuclides which are not able to be considered by other methods. In addition, a new method was proposed to calculate effective cross section accurately for power reactor fuel subassembly where the new nuclear constant system cannot be applied. This method uses the sub-group method and the ultra fine energy group collision probability method. The microscopic effective cross sections obtained by this method agree with the reference values within 5% difference. (author)

  6. Calculation of radiation effects in solids by direct numerical solution of the adjoint transport equation

    International Nuclear Information System (INIS)

    Matthes, W.K.

    1998-01-01

    The 'adjoint transport equation in its integro-differential form' is derived for the radiation damage produced by atoms injected into solids. We reduce it to the one-dimensional form and prepare it for a numerical solution by: --discretizing the continuous variables energy, space and direction, --replacing the partial differential quotients by finite differences and --evaluating the collision integral by a double sum. By a proper manipulation of this double sum the adjoint transport equation turns into a (very large) set of linear equations with tridiagonal matrix which can be solved by a special (simple and fast) algorithm. The solution of this set of linear equations contains complete information on a specified damage type (e.g. the energy deposited in a volume V) in terms of the function D(i,E,c,x) which gives the damage produced by all particles generated in a cascade initiated by a particle of type i starting at x with energy E in direction c. It is essential to remark that one calculation gives the damage function D for the complete ranges of the variables {i,E,c and x} (for numerical reasons of course on grid-points in the {E,c,x}-space). This is most useful to applications where a general source-distribution S(i,E,c,x) of particles is given by the experimental setup (e.g. beam-window and and target in proton accelerator work. The beam-protons along their path through the window--or target material generate recoil atoms by elastic collisions or nuclear reactions. These recoil atoms form the particle source S). The total damage produced then is eventually given by: D = (Σ)i ∫ ∫ ∫ S(i, E, c, x)*D(i, E, c, x)*dE*dc*dx A Fortran-77 program running on a PC-486 was written for the overall procedure and applied to some problems

  7. Numerical method for the unsteady potential flow about pitching airfoils

    International Nuclear Information System (INIS)

    Parrouffe, J.-M.; Paraschivoiu, I.

    1985-01-01

    This paper presents a numerical method for the unsteady potential flow about an aerodynamic profile and in its wake. This study has many applications such as airplane wings and propellers, guide vanes, subcavitant hydrofoils and wind turbine blades. Typical of such nonstationary configurations is the rotor of the Darrieus vertical-axis wind turbine whose blades are exposed to cyclic aerodynamic loads in the operating state

  8. Numerical Verification Methods for Spherical $t$-Designs

    OpenAIRE

    Chen, Xiaojun

    2009-01-01

    The construction of spherical $t$-designs with $(t+1)^2$ points on the unit sphere $S^2$ in $\\mathbb{R}^3$ can be reformulated as an underdetermined system of nonlinear equations. This system is highly nonlinear and involves the evaluation of a degree $t$ polynomial in $(t+1)^4$ arguments. This paper reviews numerical verification methods using the Brouwer fixed point theorem and Krawczyk interval operator for solutions of the underdetermined system of nonlinear equations...

  9. 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)

  10. Internal quality control of RIA with Tonks error calculation method

    International Nuclear Information System (INIS)

    Chen Xiaodong

    1996-01-01

    According to the methodology feature of RIA, an internal quality control chart with Tonks error calculation method which is suitable for RIA is designed. The quality control chart defines the value of the allowance error with normal reference range. The method has the simplicity of its performance and directly perceived through the senses. Taking the example of determining T 3 and T 4 , the calculation of allowance error, drawing of quality control chart and the analysis of result are introduced

  11. Hybrid TE-TM scheme for time domain numerical calculations of wakefields in structures with walls of finite conductivity

    Directory of Open Access Journals (Sweden)

    Andranik Tsakanian

    2012-05-01

    Full Text Available In particle accelerators a preferred direction, the direction of motion, is well defined. If in a numerical calculation the (numerical dispersion in this direction is suppressed, a quite coarse mesh and moderate computational resources can be used to reach accurate results even for extremely short electron bunches. Several approaches have been proposed in the past decades to reduce the accumulated dispersion error in wakefield calculations for perfectly conducting structures. In this paper we extend the TE/TM splitting algorithm to a new hybrid scheme that allows for wakefield calculations in structures with walls of finite conductivity. The conductive boundary is modeled by one-dimensional wires connected to each boundary cell. A good agreement of the numerical simulations with analytical results and other numerical approaches is obtained.

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

    Science.gov (United States)

    Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

    2015-08-01

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

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

    International Nuclear Information System (INIS)

    Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

    2015-01-01

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

  14. Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies

    Energy Technology Data Exchange (ETDEWEB)

    Safta, Cosmin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Najm, Habib N. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Phipps, Eric Todd [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2014-09-01

    Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.

  15. A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.

    Science.gov (United States)

    Ling, Hong; Luo, Ercang; Dai, Wei

    2006-12-22

    Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy.

  16. 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)

  17. A parallel orbital-updating based plane-wave basis method for electronic structure calculations

    International Nuclear Information System (INIS)

    Pan, Yan; Dai, Xiaoying; Gironcoli, Stefano de; Gong, Xin-Gao; Rignanese, Gian-Marco; Zhou, Aihui

    2017-01-01

    Highlights: • Propose three parallel orbital-updating based plane-wave basis methods for electronic structure calculations. • These new methods can avoid the generating of large scale eigenvalue problems and then reduce the computational cost. • These new methods allow for two-level parallelization which is particularly interesting for large scale parallelization. • Numerical experiments show that these new methods are reliable and efficient for large scale calculations on modern supercomputers. - Abstract: Motivated by the recently proposed parallel orbital-updating approach in real space method , we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue problems. In addition, we propose two new modified parallel orbital-updating methods. Compared to the traditional plane-wave methods, our methods allow for two-level parallelization, which is particularly interesting for large scale parallelization. Numerical experiments show that these new methods are more reliable and efficient for large scale calculations on modern supercomputers.

  18. 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.

  19. 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.

  20. 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.

  1. SELECT NUMERICAL METHODS FOR MODELING THE DYNAMICS SYSTEMS

    Directory of Open Access Journals (Sweden)

    Tetiana D. Panchenko

    2016-07-01

    Full Text Available The article deals with the creation of methodical support for mathematical modeling of dynamic processes in elements of the systems and complexes. As mathematical models ordinary differential equations have been used. The coefficients of the equations of the models can be nonlinear functions of the process. The projection-grid method is used as the main tool. It has been described iterative method algorithms taking into account the approximate solution prior to the first iteration and proposed adaptive control computing process. The original method of estimation error in the calculation solutions as well as for a given level of error of the technique solutions purpose adaptive method for solving configuration parameters is offered. A method for setting an adaptive method for solving the settings for a given level of error is given. The proposed method can be used for distributed computing.

  2. 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)

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

    Science.gov (United States)

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

    2015-05-01

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

  4. Numerical investigations on contactless methods for measuring critical current density in HTS: application of modified constitutive-relation method

    International Nuclear Information System (INIS)

    Kamitani, A.; Takayama, T.; Itoh, T.; Ikuno, S.

    2011-01-01

    A fast method is proposed for calculating the shielding current density in an HTS. The J-E constitutive relation is modified so as not to change the solution. A numerical code is developed on the basis of the proposed method. The permanent magnet method is successfully simulated by means of the code. A fast method has been proposed for calculating the shielding current density in a high-temperature superconducting thin film. An initial-boundary-value problem of the shielding current density cannot be always solved by means of the Runge-Kutta method even when an adaptive step-size control algorithm is incorporated to the method. In order to suppress an overflow in the algorithm, the J-E constitutive relation is modified so that its solution may satisfy the original constitutive relation. A numerical code for analyzing the shielding current density has been developed on the basis of this method and, as an application of the code, the permanent magnet method for measuring the critical current density has been investigated numerically.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. Validation of calculational methods for nuclear criticality safety - approved 1975

    International Nuclear Information System (INIS)

    Anon.

    1977-01-01

    The American National Standard for Nuclear Criticality Safety in Operations with Fissionable Materials Outside Reactors, N16.1-1975, states in 4.2.5: In the absence of directly applicable experimental measurements, the limits may be derived from calculations made by a method shown to be valid by comparison with experimental data, provided sufficient allowances are made for uncertainties in the data and in the calculations. There are many methods of calculation which vary widely in basis and form. Each has its place in the broad spectrum of problems encountered in the nuclear criticality safety field; however, the general procedure to be followed in establishing validity is common to all. The standard states the requirements for establishing the validity and area(s) of applicability of any calculational method used in assessing nuclear criticality safety

  11. 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)

  12. 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

  13. 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.

  14. Numerical calculation procedure for criticality parameters of the two-zone reflected reactor with flat central zone

    International Nuclear Information System (INIS)

    Bosevski, T.; Strugar, P.

    1966-10-01

    In determining the criticality parameters of a two-zone reactor with flat central zone one encounters a numerical problem requiring the solution of a system of two non-linear equations. To solve them the Newton method, which proved convenient, was used n this work. By comparing our results with those reported one obtains about 5% smaller values of both the radius of the flat zone and of the radial buckling of the outer zone. This discrepancy probably results from some approximations used in solving the same system of equations used in solving the same system of equations where the procedure form was applied, whereas the calculation time is by one order of magnitude smaller

  15. Phenomenology and numerical calculations of lean hydrogen-air premixed flame propagation in a turbulent flow

    International Nuclear Information System (INIS)

    Faix-Gantier, A.

    2001-12-01

    This thesis concerns the study of flame propagation in a turbulent flow of lean hydrogen-air mixtures. The aim is to precise the characteristics of propagation as well as combustion and turbulence models able to take into account the peculiarities of these mixtures. This research work is related to the prevention of fire hazards associated with accidental release of hydrogen within the reactor of a nuclear power plant. In a first part, the scales (the flame velocity and thickness) associated with the laminar flame propagation in hydrogen-air mixtures are studied. A specific attention is devoted to the intrinsic instability properties of such flames. Then, the turbulence scales potentially present within a reactor are estimated in order to allow for the determination of the regimes of combustion that might be present within the reactor and among which the flamelet regime appears to be conceivable. In a second part, starting with the analysis of the propagation properties of a mean reaction zone calculated with a flamelet model, we show that, with an adequate tuning of the parameter appearing in the mean reaction rate expression, it is possible to predict numerically the turbulent flame speeds available with the literature. (author)

  16. 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.

  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. 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.

  19. 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.

  20. Criticism of the OPW method for band structure calculations

    International Nuclear Information System (INIS)

    Lendi, K.

    1977-01-01

    The OPW method is associated with a general eigenvalue problem of type (A - lambda B) x vector = 0, in which the matrix B and in particular its lowest eigenvalue decide upon the stability of the solutions lambda and, therefore, upon the applicability of the method which may become very questionable for heavier substances. Analytical proofs as well as explicit numerical estimates for several solids are given [pt