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)

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.

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

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.

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.

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.

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)

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)

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...

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.

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.)

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.

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.

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.

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.

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

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

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.)

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)

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.)

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

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

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

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

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

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

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.

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)

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.

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....

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.

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)

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)

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

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)

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)

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

A simple and rational numerical method of two-phase flow with volume-junction model. 2. The numerical method for general condition of two-phase flow in non-equilibrium states

International Nuclear Information System (INIS)

Okazaki, Motoaki

1997-11-01

In the previous report, the usefulness of a new numerical method to achieve a rigorous numerical calculation using a simple explicit method with the volume-junction model was presented with the verification calculation for the depressurization of a saturated two-phase mixture. In this report, on the basis of solution method above, a numerical method for general condition of two-phase flow in non-equilibrium states is presented. In general condition of two-phase flow, the combinations of saturated and non-saturated conditions of each phase are considered in the each flow of volume and junction. Numerical evaluation programs are separately prepared for each combination of flow condition. Several numerical calculations of various kinds of non-equilibrium two-phase flow are made to examine the validity of the numerical method. Calculated results showed that the thermodynamic states obtained in different solution schemes were consistent with each other. In the first scheme, the states are determined by using the steam table as a function of pressure and specific enthalpy which are obtained as the solutions of simultaneous equations. In the second scheme, density and specific enthalpy of each phase are directly calculated by using conservation equations of mass and enthalpy of each phase, respectively. Further, no accumulation of error in mass and energy was found. As for the specific enthalpy, two cases of using energy equations for the volume are examined. The first case uses total energy conservation equation and the second case uses the type of the first law of thermodynamics. The results of both cases agreed well. (author)

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....

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...

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

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)

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.

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.

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

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.

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

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

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

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....

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)

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

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)

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.

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)

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

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

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.

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.)

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

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

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.

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...

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...

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.

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

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.

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)

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.)

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.

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

Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method

International Nuclear Information System (INIS)

Onishi, Yuki; Takiyasu, Jumpei; Amaya, Kenji; Yakuwa, Hiroshi; Hayabusa, Keisuke

2012-01-01

Highlights: ► A novel numerical method to analyze time dependent localized corrosion is developed. ► It takes electromigration, mass diffusion, chemical reactions, and moving boundaries. ► Our method perfectly satisfies the conservation of mass and electroneutrality. ► The behavior of typical crevice corrosion is successfully simulated. ► Both verification and validation of our method are carried out. - Abstract: A novel numerical method for time-dependent localized corrosion analysis is presented. Electromigration, mass diffusion, chemical reactions, and moving boundaries are considered in the numerical simulation of localized corrosion of engineering alloys in an underwater environment. Our method combines the finite volume method (FVM) and the voxel method. The FVM is adopted in the corrosion rate calculation so that the conservation of mass is satisfied. A newly developed decoupled algorithm with a projection method is introduced in the FVM to decouple the multiphysics problem into the electrostatic, mass transport, and chemical reaction analyses with electroneutrality maintained. The polarization curves for the corroding metal are used as boundary conditions for the metal surfaces to calculate the corrosion rates. The voxel method is adopted in updating the moving boundaries of cavities without remeshing and mesh-to-mesh solution mapping. Some modifications of the standard voxel method, which represents the boundaries as zigzag-shaped surfaces, are introduced to generate smooth surfaces. Our method successfully reproduces the numerical and experimental results of a capillary electrophoresis problem. Furthermore, the numerical results are qualitatively consistent with the experimental results for several examples of crevice corrosion.

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)

Conjugate-gradient optimization method for orbital-free density functional calculations.

Science.gov (United States)

Jiang, Hong; Yang, Weitao

2004-08-01

Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent extended Thomas-Fermi problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster Na216 with a local pseudopotential demonstrate that the method is accurate and efficient. (c) 2004 American Institute of Physics.

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

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.

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

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

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

Science.gov (United States)

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

2014-03-01

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

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

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

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.

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.

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.

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

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.

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)

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

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...

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-02-27

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

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

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

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.

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.

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.)

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

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...

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)

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

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*

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.

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.)

An approximate method to calculate ionization of LTE and non-LTE plasma

International Nuclear Information System (INIS)

Zhang Jun; Gu Peijun

1987-01-01

When matter, especially high Z element, is heated to high temperature, it will be ionized many times. The degree of ionization has a strong effect on many plasma properties. So an approximate method to calculate the mean ionization degree is needed for solving many practical problems. An analytical expression which is convenient for the approximate numerical calculation is given by fitting it to the scaling law and numerical results of the ionization potential of Thomas-Fermi statistical model. In LTE case, the ionization degree of Au calculated by using the approximate method is in agreement with that of the average ion model. By extending the approximate method to non-LTE case, the ionization degree of Au is similarly calculated according to Corona model and Collision-Radiatoin model(C-R). The results of Corona model agree with the published data quite well, while the results of C-R approach those of Corona model as the density is reduced and approach those of LTE as the density is increased. Finally, all approximately calculated results of ionization degree of Au and the comparision of them are given in figures and tables

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...

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)

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.

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

Numerical solution of the Navier-Stokes equations by discontinuous Galerkin method

Science.gov (United States)

Krasnov, M. M.; Kuchugov, P. A.; E Ladonkina, M.; E Lutsky, A.; Tishkin, V. F.

2017-02-01

Detailed unstructured grids and numerical methods of high accuracy are frequently used in the numerical simulation of gasdynamic flows in areas with complex geometry. Galerkin method with discontinuous basis functions or Discontinuous Galerkin Method (DGM) works well in dealing with such problems. This approach offers a number of advantages inherent to both finite-element and finite-difference approximations. Moreover, the present paper shows that DGM schemes can be viewed as Godunov method extension to piecewise-polynomial functions. As is known, DGM involves significant computational complexity, and this brings up the question of ensuring the most effective use of all the computational capacity available. In order to speed up the calculations, operator programming method has been applied while creating the computational module. This approach makes possible compact encoding of mathematical formulas and facilitates the porting of programs to parallel architectures, such as NVidia CUDA and Intel Xeon Phi. With the software package, based on DGM, numerical simulations of supersonic flow past solid bodies has been carried out. The numerical results are in good agreement with the experimental ones.

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.

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...

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.

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.

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.

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.

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.

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

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

Application of Numerical Integration and Data Fusion in Unit Vector Method

Science.gov (United States)

Zhang, J.

2012-01-01

The Unit Vector Method (UVM) is a series of orbit determination methods which are designed by Purple Mountain Observatory (PMO) and have been applied extensively. It gets the conditional equations for different kinds of data by projecting the basic equation to different unit vectors, and it suits for weighted process for different kinds of data. The high-precision data can play a major role in orbit determination, and accuracy of orbit determination is improved obviously. The improved UVM (PUVM2) promoted the UVM from initial orbit determination to orbit improvement, and unified the initial orbit determination and orbit improvement dynamically. The precision and efficiency are improved further. In this thesis, further research work has been done based on the UVM: Firstly, for the improvement of methods and techniques for observation, the types and decision of the observational data are improved substantially, it is also asked to improve the decision of orbit determination. The analytical perturbation can not meet the requirement. So, the numerical integration for calculating the perturbation has been introduced into the UVM. The accuracy of dynamical model suits for the accuracy of the real data, and the condition equations of UVM are modified accordingly. The accuracy of orbit determination is improved further. Secondly, data fusion method has been introduced into the UVM. The convergence mechanism and the defect of weighted strategy have been made clear in original UVM. The problem has been solved in this method, the calculation of approximate state transition matrix is simplified and the weighted strategy has been improved for the data with different dimension and different precision. Results of orbit determination of simulation and real data show that the work of this thesis is effective: (1) After the numerical integration has been introduced into the UVM, the accuracy of orbit determination is improved obviously, and it suits for the high-accuracy data of

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.

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

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.

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

Evaluation of the Reference Numerical Parameters of the Monthly Method in ISO 13790 Considering S/V Ratio

Directory of Open Access Journals (Sweden)

Hee-Jeong Kwak

2015-01-01

Full Text Available Many studies have investigated the accuracy of the numerical parameters in the application of the quasi steady-state calculation method. The aim of this study is to derive the reference numerical parameters of the ISO 13790 monthly method by reflecting the surface-to-volume (S/V ratio and the characteristics of the structures. The calculation process was established, and the parameters necessary to derive the reference numerical parameters were calculated based on the input data prepared for the established calculation processes. The reference numerical parameters were then derived through regression analyses of the calculated parameters and the time constant. The parameters obtained from an apartment building and the parameters of the international standard were both applied to the Passive House Planning Package (PHPP and EnergyPlus programs, and the results were analyzed in order to evaluate the validity of the results. The analysis revealed that the calculation results based on the parameters derived from this study yielded lower error rates than those based on the default parameters in ISO 13790. However, the differences were shown to be negligible in the case of high heat capacity.

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

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.

Calculations of time-of-flight aberrations in practical electrostatic electron lenses using the differential algebraic method

International Nuclear Information System (INIS)

Kang, Yongfeng; Zhao, Jingyi; Tang, Tiantong

2013-01-01

The high order time-of-flight (TOF) aberrations in a practical electrostatic electron lens are calculated using the differential algebraic (DA) method. The electrostatic fields of the electrostatic lens, which are calculated by the FEM methods, are in the form of discrete arrays. Thus, the proposed DA method is applicable for engineering designs, and programs are written to compute up to fifth order TOF aberrations of practical electrostatic electron lenses. An example is given, and TOF aberrations up to the fifth order are calculated. It is proven that the numerical results for the electrostatic fields in the form of discrete arrays have a good accuracy compared with the theoretical solutions. The accuracy is limited only by the accuracy of the numerical computation of the fields and the numerical computation algorithms for interpolation and integration. Finally, a practical electrostatic electron lens is analysed and discussed as an example.

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.

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

International Nuclear Information System (INIS)

Abdel Krim, M.S.

2001-01-01

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

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.

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

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

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…

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.

A new method for calculation of majority carrier compensation in photovoltaics

International Nuclear Information System (INIS)

Zhang Rumin; Liu Peng; Liu Dijun; Su Guobin

2015-01-01

In thin film solar cells, the semiconductor materials usually contain multiple impurity/defect states as donor or acceptor dopants. The local charge neutrality (LCN) condition determines the equilibrium Fermi (EF) level and concentration of electrons and holes. However, the equation of LCN is a transcendental equation of EF. It is impossible to find its analytical solution and we can only solve it by graphic or numerical method. A simple approximate graphic method (GM) used for estimation of majority carrier compensation of semiconductors with multiple donors and acceptors was proposed by Chin. By introducing the concept of ranking the dopants and the wrapping step function, dopants concentration and Fermi level could be obtained easily. In this paper, we analyze the graphic method and propose a new numeric graphic method (NGM) based on GM. In addition, comparison of NGM with NM and analytics of the accuracy of GM are presented. With numerical calculation, some procedures of GM extending the application of GM are improved. (paper)

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

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

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

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

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.

Numerical solution of stiff burnup equation with short half lived nuclides by the Krylov subspace method

International Nuclear Information System (INIS)

Yamamoto, Akio; Tatsumi, Masahiro; Sugimura, Naoki

2007-01-01

The Krylov subspace method is applied to solve nuclide burnup equations used for lattice physics calculations. The Krylov method is an efficient approach for solving ordinary differential equations with stiff nature such as the nuclide burnup with short lived nuclides. Some mathematical fundamentals of the Krylov subspace method and its application to burnup equations are discussed. Verification calculations are carried out in a PWR pin-cell geometry with UO 2 fuel. A detailed burnup chain that includes 193 fission products and 28 heavy nuclides is used in the verification calculations. Shortest half life found in the present burnup chain is approximately 30 s ( 106 Rh). Therefore, conventional methods (e.g., the Taylor series expansion with scaling and squaring) tend to require longer computation time due to numerical stiffness. Comparison with other numerical methods (e.g., the 4-th order Runge-Kutta-Gill) reveals that the Krylov subspace method can provide accurate solution for a detailed burnup chain used in the present study with short computation time. (author)

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

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

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.

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.

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...

Microstructure-based numerical modeling method for effective permittivity of ceramic/polymer composites

Science.gov (United States)

Jylhä, Liisi; Honkamo, Johanna; Jantunen, Heli; Sihvola, Ari

2005-05-01

Effective permittivity was modeled and measured for composites that consist of up to 35vol% of titanium dioxide powder dispersed in a continuous epoxy matrix. The study demonstrates a method that enables fast and accurate numerical modeling of the effective permittivity values of ceramic/polymer composites. The model requires electrostatic Monte Carlo simulations, where randomly oriented homogeneous prism-shaped inclusions occupy random positions in the background phase. The computation cost of solving the electrostatic problem by a finite-element code is decreased by the use of an averaging method where the same simulated sample is solved three times with orthogonal field directions. This helps to minimize the artificial anisotropy that results from the pseudorandomness inherent in the limited computational domains. All the required parameters for numerical simulations are calculated from the lattice structure of titanium dioxide. The results show a very good agreement between the measured and numerically calculated effective permittivities. When the prisms are approximated by oblate spheroids with the corresponding axial ratio, a fairly good prediction for the effective permittivity of the mixture can be achieved with the use of an advanced analytical mixing formula.

Comparison between the Gauss' law method and the zero current method to calculate multi-species ionic diffusion in saturated uncharged porous materials

DEFF Research Database (Denmark)

Johannesson, Björn

2010-01-01

There exist, mainly, two different continuum approaches to calculate transient multi species ionic diffusion. One of them is based on explicitly assuming a zero current in the diffusing mixture together with an introduction of a streaming electrical potential in the constitutive equations...... of the coupled set of equation in favor of the staggering approach. A one step truly implicit time stepping scheme is adopted together with an implementation of a modified Newton-Raphson iterational scheme for search of equilibrium at each considered time step calculation. Results from the zero current case...... difference of the two types of potentials, that is, the streaming electrical potential and the electrical field is carefully examined. A novel numerical method based on the finite element approach is established for the zero current method case. The proposed numerical method uses the direct calculation...

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)

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.

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....

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.

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)

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)

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

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.)

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)

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

International Nuclear Information System (INIS)

Wang, F.; Gantenbein, F.

1995-01-01

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

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)

A Gaussian quadrature method for total energy analysis in electronic state calculations

Science.gov (United States)

Fukushima, Kimichika

This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article showed that, for diatomic molecules such as CO and FeO, elliptic coordinates efficiently achieved high numerical integral accuracy even with a numerical basis set including transition metal atomic orbitals. This article will generalize straightforward details for multiatomic systems with direct integrals in each decomposed elliptic coordinate determined from the nuclear positions of picked-up atom pairs. Sample calculations were performed for the molecules O3 and H2O. This article will also try to present, in another coordinate, a numerical integral by partially using the Becke's decomposition published in 1988, but without the Becke's fuzzy cell generated by the polynomials of internuclear distance between the pair atoms. Instead, simple nuclear weights comprising exponential functions around nuclei are used. The one-center integral is performed with a Gaussian quadrature pack in a spherical coordinate, included in the author's original program in around 1980. As for this decomposition into one-center integrals, sample calculations are carried out for Li2.

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.

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

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.

Analytical and numerical calculation of magnetic field distribution in the slotted air-gap of tangential surface permanent-magnet motors

Directory of Open Access Journals (Sweden)

Boughrara Kamel

2009-01-01

Full Text Available This paper deals with the analytical and numerical analysis of the flux density distribution in the slotted air gap of permanent magnet motors with surface mounted tangentially magnetized permanent magnets. Two methods for magnetostatic field calculations are developed. The first one is an analytical method in which the effect of stator slots is taken into account by modulating the magnetic field distribution by the complex relative air gap permeance. The second one is a numerical method using 2-D finite element analysis with consideration of Dirichlet and anti-periodicity (periodicity boundary conditions and Lagrange Multipliers for simulation of movement. The results obtained by the analytical method are compared to the results of finite-element analysis.

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

Accurate treatment of material interface dynamics in the calculation of one-dimensional two-phase flows by the integral method of characteristics

International Nuclear Information System (INIS)

Shin, Y.W.; Wiedermann, A.H.

1984-01-01

Accurate numerical methods for treating the junction and boundary conditions needed in the transient two-phase flows of a piping network were published earlier by us; the same methods are used to formulate the treatment of the material interface as a moving boundary. The method formulated is used in a computer program to calculate sample problems designed to test the numerical methods as to their ability and the accuracy limits for calculation of the transient two-phase flows in the piping network downstream of a PWR pressurizer. Independent exact analytical solutions for the sample problems are used as the basis of a critical evaluation of the proposed numerical methods. The evaluation revealed that the proposed boundary scheme indeed generates very accurate numerical results. However, in some extreme flow conditions, numerical difficulties were experienced that eventually led to numerical instability. This paper discusses further a special technique to overcome the difficulty

Numerical simulation of electromagnetic wave propagation using time domain meshless method

International Nuclear Information System (INIS)

Ikuno, Soichiro; Fujita, Yoshihisa; Itoh, Taku; Nakata, Susumu; Nakamura, Hiroaki; Kamitani, Atsushi

2012-01-01

The electromagnetic wave propagation in various shaped wave guide is simulated by using meshless time domain method (MTDM). Generally, Finite Differential Time Domain (FDTD) method is applied for electromagnetic wave propagation simulation. However, the numerical domain should be divided into rectangle meshes if FDTD method is applied for the simulation. On the other hand, the node disposition of MTDM can easily describe the structure of arbitrary shaped wave guide. This is the large advantage of the meshless time domain method. The results of computations show that the damping rate is stably calculated in case with R < 0.03, where R denotes a support radius of the weight function for the shape function. And the results indicate that the support radius R of the weight functions should be selected small, and monomials must be used for calculating the shape functions. (author)

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

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.

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.

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

Thermal protection system gap analysis using a loosely coupled fluid-structural thermal numerical method

Science.gov (United States)

Huang, Jie; Li, Piao; Yao, Weixing

2018-05-01

A loosely coupled fluid-structural thermal numerical method is introduced for the thermal protection system (TPS) gap thermal control analysis in this paper. The aerodynamic heating and structural thermal are analyzed by computational fluid dynamics (CFD) and numerical heat transfer (NHT) methods respectively. An interpolation algorithm based on the control surface is adopted for the data exchanges on the coupled surface. In order to verify the analysis precision of the loosely coupled method, a circular tube example was analyzed, and the wall temperature agrees well with the test result. TPS gap thermal control performance was studied by the loosely coupled method successfully. The gap heat flux is mainly distributed in the small region at the top of the gap which is the high temperature region. Besides, TPS gap temperature and the power of the active cooling system (CCS) calculated by the traditional uncoupled method are higher than that calculated by the coupled method obviously. The reason is that the uncoupled method doesn't consider the coupled effect between the aerodynamic heating and structural thermal, however the coupled method considers it, so TPS gap thermal control performance can be analyzed more accurately by the coupled method.

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.

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

International Nuclear Information System (INIS)

Xu, Yuenong; Smooke, M.D.

1993-01-01

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

Performance of some numerical Laplace inversion methods on American put option formula

Science.gov (United States)

Octaviano, I.; Yuniar, A. R.; Anisa, L.; Surjanto, S. D.; Putri, E. R. M.

2018-03-01

Numerical inversion approaches of Laplace transform is used to obtain a semianalytic solution. Some of the mathematical inversion methods such as Durbin-Crump, Widder, and Papoulis can be used to calculate American put options through the optimal exercise price in the Laplace space. The comparison of methods on some simple functions is aimed to know the accuracy and parameters which used in the calculation of American put options. The result obtained is the performance of each method regarding accuracy and computational speed. The Durbin-Crump method has an average error relative of 2.006e-004 with computational speed of 0.04871 seconds, the Widder method has an average error relative of 0.0048 with computational speed of 3.100181 seconds, and the Papoulis method has an average error relative of 9.8558e-004 with computational speed of 0.020793 seconds.

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

Numerical method to optimize the polar-azimuthal orientation of infrared superconducting-nanowire single-photon detectors.

Science.gov (United States)

Csete, Mária; Sipos, Áron; Najafi, Faraz; Hu, Xiaolong; Berggren, Karl K

2011-11-01

A finite-element method for calculating the illumination-dependence of absorption in three-dimensional nanostructures is presented based on the radio frequency module of the Comsol Multiphysics software package (Comsol AB). This method is capable of numerically determining the optical response and near-field distribution of subwavelength periodic structures as a function of illumination orientations specified by polar angle, φ, and azimuthal angle, γ. The method was applied to determine the illumination-angle-dependent absorptance in cavity-based superconducting-nanowire single-photon detector (SNSPD) designs. Niobium-nitride stripes based on dimensions of conventional SNSPDs and integrated with ~ quarter-wavelength hydrogen-silsesquioxane-filled nano-optical cavity and covered by a thin gold film acting as a reflector were illuminated from below by p-polarized light in this study. The numerical results were compared to results from complementary transfer-matrix-method calculations on composite layers made of analogous film-stacks. This comparison helped to uncover the optical phenomena contributing to the appearance of extrema in the optical response. This paper presents an approach to optimizing the absorptance of different sensing and detecting devices via simultaneous numerical optimization of the polar and azimuthal illumination angles. © 2011 Optical Society of America

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1997-12-31

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

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

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.

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)

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

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)

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

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...

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.

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

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.

Calculation of seismic response of a flexible rotor by complex modal method, 1

International Nuclear Information System (INIS)

Azuma, Takao; Saito, Shinobu

1984-01-01

In rotary machines, at the time of earthquakes, whether the rotating part and stationary part touch or whether the bearings and seals are damaged or not are problems. In order to examine these problems, it is necessary to analyze the seismic response of a rotary shaft or sometimes a casing system. But the conventional analysis methods are unsatisfactory. Accordingly, in the case of a general shaft system supported with slide bearings and on which gyro effect acts, complex modal method must be used. This calculation method is explained in detail in the book of Lancaster, however, when this method is applied to the seismic response of rotary shafts, the calculation time is considerably different according to the method of final integration. In this study, good results were obtained when the method which did not depend on numerical integration was attempted. The equation of motion and its solution, the displacement vector of a foundation, the verification of the calculation program and the example of calculating the seismic response of two coupled rotor shafts are reported. (Kako, I.)

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.

Time-independent lattice Boltzmann method calculation of hydrodynamic interactions between two particles

Science.gov (United States)

Ding, E. J.

2015-06-01

The time-independent lattice Boltzmann algorithm (TILBA) is developed to calculate the hydrodynamic interactions between two particles in a Stokes flow. The TILBA is distinguished from the traditional lattice Boltzmann method in that a background matrix (BGM) is generated prior to the calculation. The BGM, once prepared, can be reused for calculations for different scenarios, and the computational cost for each such calculation will be significantly reduced. The advantage of the TILBA is that it is easy to code and can be applied to any particle shape without complicated implementation, and the computational cost is independent of the shape of the particle. The TILBA is validated and shown to be accurate by comparing calculation results obtained from the TILBA to analytical or numerical solutions for certain problems.

A new Tone's method in APOLLO3® and its application to fast and thermal reactor calculations

Directory of Open Access Journals (Sweden)

Li Mao

2017-09-01

Full Text Available This paper presents a newly developed resonance self-shielding method based on Tone's method in APOLLO3® for fast and thermal reactor calculations. The new method is based on simplified models, the narrow resonance approximation for the slowing down source and Tone's approximation for group collision probability matrix. It utilizes mathematical probability tables as quadrature formulas in calculating effective cross-sections. Numerical results for the ZPPR drawer calculations in 1,968 groups show that, in the case of the double-column fuel drawer, Tone's method gives equivalent precision to the subgroup method while markedly reducing the total number of collision probability matrix calculations and hence the central processing unit time. In the case of a single-column fuel drawer with the presence of a uranium metal material, Tone's method obtains less precise results than those of the subgroup method due to less precise heterogeneous–homogeneous equivalence. The same options are also applied to PWR UOX, MOX, and Gd cells using the SHEM 361-group library, with the objective of analyzing whether this energy mesh might be suitable for the application of this methodology to thermal systems. The numerical results show that comparable precision is reached with both Tone's and the subgroup methods, with the satisfactory representation of intrapellet spatial effects.

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

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

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

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.)

Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

Energy Technology Data Exchange (ETDEWEB)

Cobb, J.W.

1995-02-01

There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

Numerical Estimation Method for the NonStationary Thrust of Pulsejet Ejector Nozzle

Directory of Open Access Journals (Sweden)

A. Yu. Mikushkin

2016-01-01

Full Text Available The article considers a calculation method for the non-stationary thrust of pulsejet ejector nozzle that is based on detonation combustion of gaseous fuel.To determine initial distributions of the thermodynamic parameters inside the detonation tube was carried out a rapid analysis based on x-t-diagrams of motion of glowing combustion products. For this purpose, the section with transparent walls was connected to the outlet of the tube to register the movement of products of combustion.Based on obtained images and gas-dynamic and thermodynamic equations the velocity distribution of the combustion products, its density, pressure and temperature required for numerical analysis were calculated. The world literature presents data on distribution of parameters, however they are given only for direct initiation of detonation at the closed end and for chemically "frozen" gas composition. The article presents the interpolation methods of parameters measured at the temperatures of 2500-2800K.Estimation of the thermodynamic parameters is based on the Chapman-Jouguet theory that the speed of the combustion products directly behind the detonation wave front with respect to the wave front is equal to the speed of sound of these products at a given point. The method of minimizing enthalpy of the final thermodynamic state was used to calculate the equilibrium parameters. Thus, a software package «IVTANTHERMO», which is a database of thermodynamic properties of many individual substances in a wide temperature range, was used.An integral thrust was numerically calculated according to the ejector nozzle surface. We solved the Navier-Stokes equations using the finite-difference Roe scheme of the second order. The combustion products were considered both as an inert mixture with "frozen" composition and as a mixture in chemical equilibrium with the changing temperature. The comparison with experimental results was made.The above method can be used for rapid

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.

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.

Sensitivity analysis of numerical solutions for environmental fluid problems

International Nuclear Information System (INIS)

Tanaka, Nobuatsu; Motoyama, Yasunori

2003-01-01

In this study, we present a new numerical method to quantitatively analyze the error of numerical solutions by using the sensitivity analysis. If a reference case of typical parameters is one calculated with the method, no additional calculation is required to estimate the results of the other numerical parameters such as more detailed solutions. Furthermore, we can estimate the strict solution from the sensitivity analysis results and can quantitatively evaluate the reliability of the numerical solution by calculating the numerical error. (author)

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

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

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

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)

A two-dimensional discontinuous heterogeneous finite element method for neutron transport calculations

International Nuclear Information System (INIS)

Masiello, E.; Sanchez, R.

2007-01-01

A discontinuous heterogeneous finite element method is presented and discussed. The method is intended for realistic numerical pin-by-pin lattice calculations when an exact representation of the geometric shape of the pins is made without need for homogenization. The method keeps the advantages of conventional discrete ordinate methods, such as fast execution together with the possibility to deal with a large number of spatial meshes, while minimizing the need for geometric modeling. It also provides a complete factorization in space, angle, and energy for the discretized matrices and minimizes, thus, storage requirements. An angular multigrid acceleration technique has also been developed to speed up the rate of convergence of the inner iterations. A particular aspect of this acceleration is the introduction of boundary restriction and prolongation operators that minimize oscillatory behavior and enhance positivity. Numerical tests are presented that show the high precision of the method and the efficiency of the angular multigrid acceleration. (authors)

Research for developing precise tsunami evaluation methods. Probabilistic tsunami hazard analysis/numerical simulation method with dispersion and wave breaking

International Nuclear Information System (INIS)

2007-01-01

The present report introduces main results of investigations on precise tsunami evaluation methods, which were carried out from the viewpoint of safety evaluation for nuclear power facilities and deliberated by the Tsunami Evaluation Subcommittee. A framework for the probabilistic tsunami hazard analysis (PTHA) based on logic tree is proposed and calculation on the Pacific side of northeastern Japan is performed as a case study. Tsunami motions with dispersion and wave breaking were investigated both experimentally and numerically. The numerical simulation method is verified for its practicability by applying to a historical tsunami. Tsunami force is also investigated and formulae of tsunami pressure acting on breakwaters and on building due to inundating tsunami are proposed. (author)

A New Numerical Method for Z2 Topological Insulators with Strong Disorder

Science.gov (United States)

Akagi, Yutaka; Katsura, Hosho; Koma, Tohru

2017-12-01

We propose a new method to numerically compute the Z2 indices for disordered topological insulators in Kitaev's periodic table. All of the Z2 indices are derived from the index formulae which are expressed in terms of a pair of projections introduced by Avron, Seiler, and Simon. For a given pair of projections, the corresponding index is determined by the spectrum of the difference between the two projections. This difference exhibits remarkable and useful properties, as it is compact and has a supersymmetric structure in the spectrum. These properties enable highly efficient numerical calculation of the indices of disordered topological insulators. The method, which we propose, is demonstrated for the Bernevig-Hughes-Zhang and Wilson-Dirac models whose topological phases are characterized by a Z2 index in two and three dimensions, respectively.

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

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

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

Theories, Methods and Numerical Technology of Sheet Metal Cold and Hot Forming Analysis, Simulation and Engineering Applications

CERN Document Server

Hu, Ping; Liu, Li-zhong; Zhu, Yi-guo

2013-01-01

Over the last 15 years, the application of innovative steel concepts in the automotive industry has increased steadily. Numerical simulation technology of hot forming of high-strength steel allows engineers to modify the formability of hot forming steel metals and to optimize die design schemes. Theories, Methods and Numerical Technology of Sheet Metal Cold and Hot Forming focuses on hot and cold forming theories, numerical methods, relative simulation and experiment techniques for high-strength steel forming and die design in the automobile industry. Theories, Methods and Numerical Technology of Sheet Metal Cold and Hot Forming introduces the general theories of cold forming, then expands upon advanced hot forming theories and simulation methods, including: • the forming process, • constitutive equations, • hot boundary constraint treatment, and • hot forming equipment and experiments. Various calculation methods of cold and hot forming, based on the authors’ experience in commercial CAE software f...

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

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

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...

Probabilistic numerics and uncertainty in computations.

Science.gov (United States)

Hennig, Philipp; Osborne, Michael A; Girolami, Mark

2015-07-08

We deliver a call to arms for probabilistic numerical methods : algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

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

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

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

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

Activity in the fronto-parietal network indicates numerical inductive reasoning beyond calculation: An fMRI study combined with a cognitive model.

Science.gov (United States)

Liang, Peipeng; Jia, Xiuqin; Taatgen, Niels A; Borst, Jelmer P; Li, Kuncheng

2016-05-19

Numerical inductive reasoning refers to the process of identifying and extrapolating the rule involved in numeric materials. It is associated with calculation, and shares the common activation of the fronto-parietal regions with calculation, which suggests that numerical inductive reasoning may correspond to a general calculation process. However, compared with calculation, rule identification is critical and unique to reasoning. Previous studies have established the central role of the fronto-parietal network for relational integration during rule identification in numerical inductive reasoning. The current question of interest is whether numerical inductive reasoning exclusively corresponds to calculation or operates beyond calculation, and whether it is possible to distinguish between them based on the activity pattern in the fronto-parietal network. To directly address this issue, three types of problems were created: numerical inductive reasoning, calculation, and perceptual judgment. Our results showed that the fronto-parietal network was more active in numerical inductive reasoning which requires more exchanges between intermediate representations and long-term declarative knowledge during rule identification. These results survived even after controlling for the covariates of response time and error rate. A computational cognitive model was developed using the cognitive architecture ACT-R to account for the behavioral results and brain activity in the fronto-parietal network.

Numerical simulation of subwoofer array congurations using the Finite Element Method

Directory of Open Access Journals (Sweden)

Xavier Banyuls-Juan

2017-08-01

Full Text Available Teaching in the Master of Acoustic Engineering includes contents that require the modeling of acoustic systems of two types: simple systems through analytical theory and complex models using simulation techniques. In the present work, we describe an example of complex acoustic sources modeling using the finite element method: subwoofer sound radiation in different configurations. Numerical simulations in the frequency domain can calculate the radiation pattern of systems that do not have a simple analytical solution.

Numerical Analysis of Indoor Sound Quality Evaluation Using Finite Element Method

Directory of Open Access Journals (Sweden)

Yu-Tuan Chou

2013-01-01

Full Text Available Indoors sound field distribution is important to Room Acoustics, but the field suffers numerous problems, for example, multipath propagation and scattering owing to sound absorption by furniture and other aspects of décor. Generally, an ideal interior space must have a sound field with clear quality. This provides both the speaker and the listener with a pleasant conversational environment. This investigation uses the Finite Element Method to assess the acoustic distribution based on the indoor space and chamber volume. In this situation, a fixed sound source at different frequencies is used to simulate the acoustic characteristics of the indoor space. This method considers the furniture and decoration sound absorbing material and thus different sound absorption coefficients and configurations. The preliminary numerical simulation provides a method that can forecast the distribution of sound in an indoor room in complex situations. Consequently, it is possible to arrange interior furnishings and appliances to optimize acoustic distribution and environmental friendliness. Additionally, the analytical results can also be used to calculate the Reverberation Time and speech intelligibility for specified indoor space.

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.

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

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.

A study on calculation method for mechanical impedance of air spring

International Nuclear Information System (INIS)

Changgeng, Shuai; Penghui, Li; Rustighi, Emiliano

2016-01-01

This paper proposes an approximate analytic method of obtaining the mechanical impedance of air spring. The sound pressure distribution in cylindrical air spring is calculated based on the linear air wave theory. The influences of different boundary conditions on the acoustic pressure field distribution in cylindrical air spring are analysed. A 1-order ordinary differential matrix equation for the state vector of revolutionary shells under internal pressure is derived based on the non-moment theory of elastic thin shell. Referring to the transfer matrix method, a kind of expanded homogeneous capacity high precision integration method is introduced to solve the non-homogeneous matrix differential equation. Combined the solved stress field of shell with the calculated sound pressure field in air spring under the displacement harmonic excitation, the approximate analytical expression of the input and transfer mechanical impedance for the air spring can be achieved. The numerical simulation with the Comsol Multiphysics software verifies the correctness of theoretical analysis result. (paper)

Numerical modeling method on the movement of water flow and suspended solids in two-dimensional sedimentation tanks in the wastewater treatment plant.

Science.gov (United States)

Zeng, Guang-Ming; Jiang, Yi-Min; Qin, Xiao-Sheng; Huang, Guo-He; Li, Jian-Bing

2003-01-01

Taking the distributing calculation of velocity and concentration as an example, the paper established a series of governing equations by the vorticity-stream function method, and dispersed the equations by the finite differencing method. After figuring out the distribution field of velocity, the paper also calculated the concentration distribution in sedimentation tank by using the two-dimensional concentration transport equation. The validity and feasibility of the numerical method was verified through comparing with experimental data. Furthermore, the paper carried out a tentative exploration into the application of numerical simulation of sedimentation tanks.

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.

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

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.)

Reliability-Based Stability Analysis of Rock Slopes Using Numerical Analysis and Response Surface Method

Science.gov (United States)

Dadashzadeh, N.; Duzgun, H. S. B.; Yesiloglu-Gultekin, N.

2017-08-01

While advanced numerical techniques in slope stability analysis are successfully used in deterministic studies, they have so far found limited use in probabilistic analyses due to their high computation cost. The first-order reliability method (FORM) is one of the most efficient probabilistic techniques to perform probabilistic stability analysis by considering the associated uncertainties in the analysis parameters. However, it is not possible to directly use FORM in numerical slope stability evaluations as it requires definition of a limit state performance function. In this study, an integrated methodology for probabilistic numerical modeling of rock slope stability is proposed. The methodology is based on response surface method, where FORM is used to develop an explicit performance function from the results of numerical simulations. The implementation of the proposed methodology is performed by considering a large potential rock wedge in Sumela Monastery, Turkey. The accuracy of the developed performance function to truly represent the limit state surface is evaluated by monitoring the slope behavior. The calculated probability of failure is compared with Monte Carlo simulation (MCS) method. The proposed methodology is found to be 72% more efficient than MCS, while the accuracy is decreased with an error of 24%.

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

Energy Technology Data Exchange (ETDEWEB)

Manohara, S. R.; Hanagodimath, S. M.; Gerward, L. [Department of Physics, Gulbarga University, Gulbarga, Karnataka 585 106 (India); Department of Physics, Technical University of Denmark, Lyngby DK-2800 (Denmark)

2009-01-15

The effective atomic numbers Z{sub 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{sub eff} is given a new meaning by using a modern database of photon interaction cross sections (WinXCom). The results of the two methods are compared and discussed. It is shown that for all biomolecules the direct method gives larger values of Z{sub eff} than the interpolation method, in particular at low energies (1-100 keV) At medium energies (0.1-5 MeV), Z{sub eff} for both methods is about constant and equal to the mean atomic number of the material. Wherever possible, the calculated values of Z{sub eff} are compared with experimental data.

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

International Nuclear Information System (INIS)

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

2009-01-01

The effective atomic numbers Z eff of some fatty acids and amino acids have been calculated by two numerical methods, a direct method and an interpolation method, in the energy range of 1 keV-20 MeV. The notion of Z eff is given a new meaning by using a modern database of photon interaction cross sections (WinXCom). The results of the two methods are compared and discussed. It is shown that for all biomolecules the direct method gives larger values of Z eff than the interpolation method, in particular at low energies (1-100 keV) At medium energies (0.1-5 MeV), Z eff for both methods is about constant and equal to the mean atomic number of the material. Wherever possible, the calculated values of Z eff are compared with experimental data.

Activity in the fronto-parietal network indicates numerical inductive reasoning beyond calculation : An fMRI study combined with a cognitive model

NARCIS (Netherlands)

Liang, Peipeng; Jia, Xiuqin; Taatgen, Niels A; Borst, Jelmer P; Li, Kuncheng

2016-01-01

Numerical inductive reasoning refers to the process of identifying and extrapolating the rule involved in numeric materials. It is associated with calculation, and shares the common activation of the fronto-parietal regions with calculation, which suggests that numerical inductive reasoning may

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

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.

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

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.)

On Calculation Methods and Results for Straight Cylindrical Roller Bearing Deflection, Stiffness, and Stress

Science.gov (United States)

Krantz, Timothy L.

2011-01-01

The purpose of this study was to assess some calculation methods for quantifying the relationships of bearing geometry, material properties, load, deflection, stiffness, and stress. The scope of the work was limited to two-dimensional modeling of straight cylindrical roller bearings. Preparations for studies of dynamic response of bearings with damaged surfaces motivated this work. Studies were selected to exercise and build confidence in the numerical tools. Three calculation methods were used in this work. Two of the methods were numerical solutions of the Hertz contact approach. The third method used was a combined finite element surface integral method. Example calculations were done for a single roller loaded between an inner and outer raceway for code verification. Next, a bearing with 13 rollers and all-steel construction was used as an example to do additional code verification, including an assessment of the leading order of accuracy of the finite element and surface integral method. Results from that study show that the method is at least first-order accurate. Those results also show that the contact grid refinement has a more significant influence on precision as compared to the finite element grid refinement. To explore the influence of material properties, the 13-roller bearing was modeled as made from Nitinol 60, a material with very different properties from steel and showing some potential for bearing applications. The codes were exercised to compare contact areas and stress levels for steel and Nitinol 60 bearings operating at equivalent power density. As a step toward modeling the dynamic response of bearings having surface damage, static analyses were completed to simulate a bearing with a spall or similar damage.

Stability, accuracy and numerical diffusion analysis of nodal expansion method for steady convection diffusion equation

International Nuclear Information System (INIS)

Zhou, Xiafeng; Guo, Jiong; Li, Fu

2015-01-01

Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of

Stability, accuracy and numerical diffusion analysis of nodal expansion method for steady convection diffusion equation

Energy Technology Data Exchange (ETDEWEB)

Zhou, Xiafeng, E-mail: zhou-xf11@mails.tsinghua.edu.cn; Guo, Jiong, E-mail: guojiong12@tsinghua.edu.cn; Li, Fu, E-mail: lifu@tsinghua.edu.cn

2015-12-15

Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of

Fast calculation method of computer-generated hologram using a depth camera with point cloud gridding

Science.gov (United States)

Zhao, Yu; Shi, Chen-Xiao; Kwon, Ki-Chul; Piao, Yan-Ling; Piao, Mei-Lan; Kim, Nam

2018-03-01

We propose a fast calculation method for a computer-generated hologram (CGH) of real objects that uses a point cloud gridding method. The depth information of the scene is acquired using a depth camera and the point cloud model is reconstructed virtually. Because each point of the point cloud is distributed precisely to the exact coordinates of each layer, each point of the point cloud can be classified into grids according to its depth. A diffraction calculation is performed on the grids using a fast Fourier transform (FFT) to obtain a CGH. The computational complexity is reduced dramatically in comparison with conventional methods. The feasibility of the proposed method was confirmed by numerical and optical experiments.

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)

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.

NUMERICAL SIMULATION OF ELECTRICAL IMPEDANCE TOMOGRAPHY PROBLEM AND STUDY OF APPROACH BASED ON FINITE VOLUME METHOD

Directory of Open Access Journals (Sweden)

Ye. S. Sherina

2014-01-01

Full Text Available This research has been aimed to carry out a study of peculiarities that arise in a numerical simulation of the electrical impedance tomography (EIT problem. Static EIT image reconstruction is sensitive to a measurement noise and approximation error. A special consideration has been given to reducing of the approximation error, which originates from numerical implementation drawbacks. This paper presents in detail two numerical approaches for solving EIT forward problem. The finite volume method (FVM on unstructured triangular mesh is introduced. In order to compare this approach, the finite element (FEM based forward solver was implemented, which has gained the most popularity among researchers. The calculated potential distribution with the assumed initial conductivity distribution has been compared to the analytical solution of a test Neumann boundary problem and to the results of problem simulation by means of ANSYS FLUENT commercial software. Two approaches to linearized EIT image reconstruction are discussed. Reconstruction of the conductivity distribution is an ill-posed problem, typically requiring a large amount of computation and resolved by minimization techniques. The objective function to be minimized is constructed of measured voltage and calculated boundary voltage on the electrodes. A classical modified Newton type iterative method and the stochastic differential evolution method are employed. A software package has been developed for the problem under investigation. Numerical tests were conducted on simulated data. The obtained results could be helpful to researches tackling the hardware and software issues for medical applications of EIT.

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

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.

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

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

Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics

International Nuclear Information System (INIS)

Beyer, Florian; Daszuta, Boris; Frauendiener, Jörg; Whale, Ben

2014-01-01

Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through the use of integer spin-weighted spherical harmonics, we present a method which allows for the implementation of arbitrary tensorial evolution equations. Our method combines two numerical techniques that were originally developed with different applications in mind. The first is Huffenberger and Wandelt’s spectral decomposition algorithm to perform the mapping from physical to spectral space. The second is the application of Luscombe and Luban’s method, to convert numerically divergent linear recursions into stable nonlinear recursions, to the calculation of reduced Wigner d-functions. We give a detailed discussion of the theory and numerical implementation of our algorithm. The properties of our method are investigated by solving the scalar and vectorial advection equation on the sphere, as well as the 2 + 1 Maxwell equations on a deformed sphere. (paper)

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

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.

New Systematic CFD Methods to Calculate Static and Single Dynamic Stability Derivatives of Aircraft

Directory of Open Access Journals (Sweden)

Bai-gang Mi

2017-01-01

Full Text Available Several new systematic methods for high fidelity and reliability calculation of static and single dynamic derivatives are proposed in this paper. Angle of attack step response is used to obtain static derivative directly; then translation acceleration dynamic derivative and rotary dynamic derivative can be calculated by employing the step response motion of rate of the angle of attack and unsteady motion of pitching angular velocity step response, respectively. Longitudinal stability derivative calculations of SACCON UCAV are taken as test cases for validation. Numerical results of all cases achieve good agreement with reference values or experiments data from wind tunnel, which indicate that the proposed methods can be considered as new tools in the process of design and production of advanced aircrafts for their high efficiency and precision.

Beam shape coefficients calculation for an elliptical Gaussian beam with 1-dimensional quadrature and localized approximation methods

Science.gov (United States)

Wang, Wei; Shen, Jianqi

2018-06-01

The use of a shaped beam for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively. Numerical techniques for evaluating the BSCs of a shaped beam, such as the quadrature, the localized approximation (LA), the integral localized approximation (ILA) methods, have been developed within the framework of generalized Lorenz-Mie theory (GLMT). The quadrature methods usually employ the 2-/3-dimensional integrations. In this work, the expressions of the BSCs for an elliptical Gaussian beam (EGB) are simplified into the 1-dimensional integral so as to speed up the numerical computation. Numerical results of BSCs are used to reconstruct the beam field and the fidelity of the reconstructed field to the given beam field is estimated. It is demonstrated that the proposed method is much faster than the 2-dimensional integrations and it can acquire more accurate results than the LA method. Limitations of the quadrature method and also the LA method in the numerical calculation are analyzed in detail.

Physical models and numerical methods of the reactor dynamic computer program RETRAN

International Nuclear Information System (INIS)

Kamelander, G.; Woloch, F.; Sdouz, G.; Koinig, H.

1984-03-01

This report describes the physical models and the numerical methods of the reactor dynamic code RETRAN simulating reactivity transients in Light-Water-Reactors. The neutron-physical part of RETRAN bases on the two-group-diffusion equations which are solved by discretization similar to the TWIGL-method. An exponential transformation is applied and the inner iterations are accelerated by a coarse-mesh-rebalancing procedure. The thermo-hydraulic model approximates the equation of state by a built-in steam-water-table and disposes of options for the calculation of heat-conduction coefficients and heat transfer coefficients. (Author) [de

Summation of Parquet diagrams as an ab initio method in nuclear structure calculations

International Nuclear Information System (INIS)

Bergli, Elise; Hjorth-Jensen, Morten

2011-01-01

Research highlights: → We present a Green's function based approach for doing ab initio nuclear structure calculations. → In particular the sum the subset of so-called Parquet diagrams. → Applying the theory to a simple but realistic model, results in good agreement with other ab initio methods. → This opens up for ab initio calculations for medium-heavy nuclei. - Abstract: In this work we discuss the summation of the Parquet class of diagrams within Green's function theory as a possible framework for ab initio nuclear structure calculations. The theory is presented and some numerical details are discussed, in particular the approximations employed. We apply the Parquet method to a simple model, and compare our results with those from an exact solution. The main conclusion is that even at the level of approximation presented here, the results shows good agreement with other comparable ab initio approaches.

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

High order aberrations calculation of a hexapole corrector using a differential algebra method

Energy Technology Data Exchange (ETDEWEB)

Kang, Yongfeng, E-mail: yfkang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Zhao, Jingyi, E-mail: jingyi.zhao@foxmail.com [School of Science, Chang’an University, Xi’an 710064 (China); Tang, Tiantong [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China)

2017-02-21

A differential algebraic (DA) method is proved as an unusual and effective tool in numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. In this paper, the differential algebra (DA) method has been employed to compute the high order aberrations up to the fifth order of a practical hexapole corrector including round lenses and hexapole lenses. The program has been developed and tested as well. The electro-magnetic fields of arbitrary point are obtained by local analytic expressions, then field potentials are transformed into new forms which can be operated in the DA calculation. In this paper, the geometric and chromatic aberrations up to fifth order of a practical hexapole corrector system are calculated by the developed program.

Depth compensating calculation method of computer-generated holograms using symmetry and similarity of zone plates

Science.gov (United States)

Wei, Hui; Gong, Guanghong; Li, Ni

2017-10-01

Computer-generated hologram (CGH) is a promising 3D display technology while it is challenged by heavy computation load and vast memory requirement. To solve these problems, a depth compensating CGH calculation method based on symmetry and similarity of zone plates is proposed and implemented on graphics processing unit (GPU). An improved LUT method is put forward to compute the distances between object points and hologram pixels in the XY direction. The concept of depth compensating factor is defined and used for calculating the holograms of points with different depth positions instead of layer-based methods. The proposed method is suitable for arbitrary sampling objects with lower memory usage and higher computational efficiency compared to other CGH methods. The effectiveness of the proposed method is validated by numerical and optical experiments.

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

Comparative analysis of nodal and edge finite element method for numerical analysis of 3-D magnetostatic systems

International Nuclear Information System (INIS)

Mintchev, Pavel; Dimitrov, Marin; Balinov, Stoimen

2002-01-01

The possibilities for applying the Finite Element Method (FEM) with gauged magnetic vector potential and the Edge Element Method (EEM) for three-dimensional numerical analysis of magnetostatic systems are analyzed. It is established that the EEM ensures sufficient accuracy for engineering calculations but in some cases its use results in bad convergence. The use of the FEM with gauged magnetic vector potential instead of the EEM is recommended for preliminary calculations of devices with complex geometry and large air gaps between the ferromagnetic parts. (Author)

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

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

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...

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.)

Intercomparison of analysis methods for seismically isolated nuclear structures. Part 1: Advanced test data and numerical methods. Working material

International Nuclear Information System (INIS)

1993-01-01

The purpose of the meeting was to review proposed contributions from CRP participating organizations to discuss in detail the experimental data on seismic isolators, to review the numerical methods for the analysis of the seismic isolators, and to perform a first comparison of the calculation results. The aim of the CRP was to validate the reliable numerical methods used for both detailed evaluation of dynamic behaviour of isolation devices and isolated nuclear structures of different nuclear power plant types. The full maturity of seismic isolation for nuclear applications was stressed, as well as the excellent behaviour of isolated structures during the recent earthquakes in Japan and the USA. Participants from Italy, USA, Japan, Russian federation, Republic of Korea, United Kingdom, India and European Commission have presented overview papers on the present programs and their status of contribution to the CRP

Intercomparison of analysis methods for seismically isolated nuclear structures. Part 1: Advanced test data and numerical methods. Working material

Energy Technology Data Exchange (ETDEWEB)

NONE

1993-07-01

The purpose of the meeting was to review proposed contributions from CRP participating organizations to discuss in detail the experimental data on seismic isolators, to review the numerical methods for the analysis of the seismic isolators, and to perform a first comparison of the calculation results. The aim of the CRP was to validate the reliable numerical methods used for both detailed evaluation of dynamic behaviour of isolation devices and isolated nuclear structures of different nuclear power plant types. The full maturity of seismic isolation for nuclear applications was stressed, as well as the excellent behaviour of isolated structures during the recent earthquakes in Japan and the USA. Participants from Italy, USA, Japan, Russian federation, Republic of Korea, United Kingdom, India and European Commission have presented overview papers on the present programs and their status of contribution to the CRP.

A revised method to calculate the concentration time integral of atmospheric pollutants

International Nuclear Information System (INIS)

Voelz, E.; Schultz, H.

1980-01-01

It is possible to calculate the spreading of a plume in the atmosphere under nonstationary and nonhomogeneous conditions by introducing the ''particle-in-cell'' method (PIC). This is a numerical method by which the transport of and the diffusion in the plume is reproduced in such a way, that particles representing the concentration are moved time step-wise in restricted regions (cells) and separately with the advection velocity and the diffusion velocity. This has a systematical advantage over the steady state Gaussian plume model usually used. The fixed-point concentration time integral is calculated directly instead of being substituted by the locally integrated concentration at a constant time as is done in the Gaussian model. In this way inaccuracies due to the above mentioned computational techniques may be avoided for short-time emissions, as may be seen by the fact that both integrals do not lead to the same results. Also the PIC method enables one to consider the height-dependent wind speed and its variations while the Gaussian model can be used only with averaged wind data. The concentration time integral calculated by the PIC method results in higher maximum values in shorter distances to the source. This is an effect often observed in measurements. (author)

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...

Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation

International Nuclear Information System (INIS)

Kawamoto, Yosuke; Chiba, Go; Tsuji, Masashi; Narabayashi, Tadashi

2015-01-01

Highlights: • We propose a new numerical solution of matrix exponential in burn-up depletion calculations. • The depletion calculation with extremely short half-lived nuclides can be done numerically stable with this method. • The computational time is shorter than the other conventional methods. - Abstract: Nuclear fuel burn-up depletion calculations are essential to compute the nuclear fuel composition transition. In the burn-up calculations, the matrix exponential method has been widely used. In the present paper, we propose a new numerical solution of the matrix exponential, a Mini-Max Polynomial Approximation (MMPA) method. This method is numerically stable for burn-up matrices with extremely short half-lived nuclides as the Chebyshev Rational Approximation Method (CRAM), and it has several advantages over CRAM. We also propose a multi-step calculation, a computational time reduction scheme of the MMPA method, which can perform simultaneously burn-up calculations with several time periods. The applicability of these methods has been theoretically and numerically proved for general burn-up matrices. The numerical verification has been performed, and it has been shown that these methods have high precision equivalent to CRAM

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

KAUST Repository

Lin, Longyuan

2013-12-17

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 are used to describe the nucleation rate and the droplet growth, respectively. The conservation of the liquid phase is described by a finite number of moments of the size distribution function. The moment equations are then combined with the Euler equations and are solved by the finite-volume method. The numerical method is first validated by comparing its prediction with experimental results from the literature. The effects of nitrogen condensation on hypersonic nozzle flows are then numerically examined. The parameters at the nozzle exit under the conditions of condensation and no-condensation are evaluated. For the condensation case, the static pressure, the static temperature, and the amount of condensed fluid at the nozzle exit decrease with the increase of the total temperature. Compared with the no-condensation case, both the static pressure and temperature at the nozzle exit increase, and the Mach number decreases due to the nitrogen condensation. It is also indicated that preheating the nitrogen gas is necessary to avoid the nitrogen condensation even for a hypersonic nozzle with a Mach number of 5 operating at room temperatures. © 2013 Springer-Verlag Berlin Heidelberg.

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.

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.

Calculated Low-Speed Steady and Time-Dependent Aerodynamic Derivatives for Some Airfoils Using a Discrete Vortex Method

Science.gov (United States)

Riley, Donald R.

2015-01-01

This paper contains a collection of some results of four individual studies presenting calculated numerical values for airfoil aerodynamic stability derivatives in unseparated inviscid incompressible flow due separately to angle-of-attack, pitch rate, flap deflection, and airfoil camber using a discrete vortex method. Both steady conditions and oscillatory motion were considered. Variables include the number of vortices representing the airfoil, the pitch axis / moment center chordwise location, flap chord to airfoil chord ratio, and circular or parabolic arc camber. Comparisons with some experimental and other theoretical information are included. The calculated aerodynamic numerical results obtained using a limited number of vortices provided in each study compared favorably with thin airfoil theory predictions. Of particular interest are those aerodynamic results calculated herein (such as induced drag) that are not readily available elsewhere.

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

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

Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations

International Nuclear Information System (INIS)

Yamamoto, Akio

2005-01-01

This paper proposes a new acceleration method for neutron transport calculations: the generalized coarse-mesh rebalance (GCMR) method. The GCMR method is a unified scheme of the traditional coarse-mesh rebalance (CMR) and the coarse-mesh finite difference (CMFD) acceleration methods. Namely, by using an appropriate acceleration factor, formulation of the GCMR method becomes identical to that of the CMR or CMFD method. This also indicates that the convergence property of the GCMR method can be controlled by the acceleration factor since the convergence properties of the CMR and CMFD methods are generally different. In order to evaluate the convergence property of the GCMR method, a linearized Fourier analysis was carried out for a one-group homogeneous medium, and the results clarified the relationship between the acceleration factor and the spectral radius. It was also shown that the spectral radius of the GCMR method is smaller than those of the CMR and CMFD methods. Furthermore, the Fourier analysis showed that when an appropriate acceleration factor was used, the spectral radius of the GCMR method did not exceed unity in this study, which was in contrast to the results of the CMR or the CMFD method. Application of the GCMR method to practical calculations will be easy when the CMFD acceleration is already adopted in a transport code. By multiplying a suitable acceleration factor to a coefficient (D FD ) of a finite difference formulation, one can improve the numerical instability of the CMFD acceleration method

Integral method for the calculation of Hawking radiation in dispersive media. I. Symmetric asymptotics

Science.gov (United States)

Robertson, Scott; Leonhardt, Ulf

2014-11-01

Hawking radiation has become experimentally testable thanks to the many analog systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion and give rise to a numerically soluble and stable ordinary differential equation only if the rest-frame dispersion relation Ω2(k ) is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.

Efficient Method for Calculating the Composite Stiffness of Parabolic Leaf Springs with Variable Stiffness for Vehicle Rear Suspension

Directory of Open Access Journals (Sweden)

Wen-ku Shi

2016-01-01

Full Text Available The composite stiffness of parabolic leaf springs with variable stiffness is difficult to calculate using traditional integral equations. Numerical integration or FEA may be used but will require computer-aided software and long calculation times. An efficient method for calculating the composite stiffness of parabolic leaf springs with variable stiffness is developed and evaluated to reduce the complexity of calculation and shorten the calculation time. A simplified model for double-leaf springs with variable stiffness is built, and a composite stiffness calculation method for the model is derived using displacement superposition and material deformation continuity. The proposed method can be applied on triple-leaf and multileaf springs. The accuracy of the calculation method is verified by the rig test and FEA analysis. Finally, several parameters that should be considered during the design process of springs are discussed. The rig test and FEA analytical results indicate that the calculated results are acceptable. The proposed method can provide guidance for the design and production of parabolic leaf springs with variable stiffness. The composite stiffness of the leaf spring can be calculated quickly and accurately when the basic parameters of the leaf spring are known.

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...

Some robust numerical methods for flow and transport in porous media; Quelques methodes numeriques robustes pour l'ecoulement et le transport en milieu poreux

Energy Technology Data Exchange (ETDEWEB)

Sboui, A

2007-01-15

The aim of this thesis is to model and develop numerical tools adapted to study underground water flow and the propagation of pollutants in a porous medium. The main motivation of this work is a benchmark from GDR Momas and ANDRA to simulate the 3-D propagation of radionuclides around a deep disposal of nuclear waste. Firstly, we construct a new mixed finite elements method suitable for general hexahedral meshes. Convergence of the method is proved and shown in numerical experiments. Secondly, we present a method of time discretization for the advection equation which allows for the use of different time steps in different sub-domains in order to take into account of strong heterogeneities. Finally a numerical method for the calculation of the transport of contaminants is proposed. The techniques above were implemented in a 3-D code and simulation results are shown on the 3-D far field benchmark from GDR Momas and ANDRA. (author)

Isochronous Cyclotron Closed Equilibrium Orbit Calculation Program Description

CERN Document Server

Kian, I N; Tarashkevich, R

2003-01-01

The Equilibrium Orbit Research Program - EORP, written in C++ with the use of Visual C++ is described. The program is intended for the calculation of the particle rotation frequency and particle kinetic energy in the closed equilibrium orbits of an isochronous cyclotron, where the closed equilibrium orbits are described through the radius and particle momentum angle: r_{eo}(\\theta) and \\varphi_{p}(\\theta). The program algorithm was developed on the basis of articles, lecture notes and original analytic calculations. The results of calculations by the EORP were checked and confirmed by using the results of calculations by the numerical methods. The discrepancies between the EORP results and the numerical method results for the calculations of the particle rotation frequency and particle kinetic energy are within the limits of \\pm1\\cdot10^{-4}. The EORP results and the numerical method results for the calculations of r_{eo}(\\theta) and \\varphi_{p}(\\theta) practically coincide. All this proves the accuracy of ca...

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

Numerical approach to one-loop integrals

International Nuclear Information System (INIS)

Fujimoto, Junpei; Shimizu, Yoshimitsu; Kato, Kiyoshi; Oyanagi, Yoshio.

1992-01-01

Two numerical methods are proposed for the calculation of one-loop scalar integrals. In the first method, the singularity is cancelled by the symmetrization of the integrand and the integration is done by a Monte-Carlo method. In the second one, after the transform of the integrand into a standard form, the integral is reduced into a regular numerical integral. These methods provide us practical tools to evaluate one-loop Feynman diagrams with desired numerical accuracy. They are extended to the integral with numerator and the treatment of the one-loop virtual correction to the cross section is also presented. (author)

Calculation of nuclear reactivity using the generalised Adams-Bashforth-Moulton predictor corrector method

Energy Technology Data Exchange (ETDEWEB)

Suescun-Diaz, Daniel [Surcolombiana Univ., Neiva (Colombia). Groupo de Fisica Teorica; Narvaez-Paredes, Mauricio [Javeriana Univ., Cali (Colombia). Groupo de Matematica y Estadistica Aplicada Pontificia; Lozano-Parada, Jamie H. [Univ. del Valle, Cali (Colombia). Dept. de Ingenieria

2016-03-15

In this paper, the generalisation of the 4th-order Adams-Bashforth-Moulton predictor-corrector method is proposed to numerically solve the point kinetic equations of the nuclear reactivity calculations without using the nuclear power history. Due to the nature of the point kinetic equations, different predictor modifiers are used in order improve the precision of the approximations obtained. The results obtained with the prediction formulas and generalised corrections improve the precision when compared with previous methods and are valid for various forms of nuclear power and different time steps.

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

New recording methods and electromechanical analysis; Nouvelles methodes d'enregistrement et de depouillement electromecanique des numerations de particules

Energy Technology Data Exchange (ETDEWEB)

Meunier, R; Bonpas, M; Legrand, J P [Commissariat a l' Energie Atomique, Saclay(France). Centre d' Etudes Nucleaires

1954-07-01

The measurement that the most often occurs in nuclear physics are of the numerations of pulses representing the transit of a particle in a detector that can be a Geiger counter, a photomultiplier or a pulse chamber. We studied and constructed an electromagnetic recorder who permits to get automatically and without calculation: 1) the activity of a radioelement according to the time; 2) the curve of decrease of a radioelement and its period; 3) any curves of growth or decrease; 4) the activity, at any instant, of a neutron detector; 5) the neutron densities ratios in several points by the method of the detectors. (M.B.) [French] Les mesures qui se presentent le plus souvent en physique nucleaire sont des numerations d'impulsions representant le passage d'une particule dans un detecteur qui peut etre un compteur de Geiger, un photomultiplicateur ou une chambre a impulsions. Nous avons etudie et construit un enregistreur electromagnetique qui permet d'obtenir automatiquement et sans calcul: 1) l'activite d'un radioelement en fonction du temps; 2) la courbe de decroissance d'un radioelement et sa periode; 3) des courbes quelconques de croissance ou de decroissance; 4) l'activite, rapportee a un instant quelconque, d'un detecteur de neutrons; 5) les rapports des densites de neutrons en plusieurs points par la methode des detecteurs. (M.B.)

Applications of Laplace transform methods to airfoil motion and stability calculations

Science.gov (United States)

Edwards, J. W.

1979-01-01

This paper reviews the development of generalized unsteady aerodynamic theory and presents a derivation of the generalized Possio integral equation. Numerical calculations resolve questions concerning subsonic indicial lift functions and demonstrate the generation of Kutta waves at high values of reduced frequency, subsonic Mach number, or both. The use of rational function approximations of unsteady aerodynamic loads in aeroelastic stability calculations is reviewed, and a reformulation of the matrix Pade approximation technique is given. Numerical examples of flutter boundary calculations for a wing which is to be flight tested are given. Finally, a simplified aerodynamic model of transonic flow is used to study the stability of an airfoil exposed to supersonic and subsonic flow regions.

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

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...

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...

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.

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.

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.

Numerical analysis of transport phenomena in Y-Ba-Cu-O melt during growth of superconducting crystal Y123 by Czochralski method

Science.gov (United States)

Szmyd, J. S.; Suzuki, K.

2003-10-01

In 1993, at the Superconductivity Research Laboratory (SRL), International Superconductivity Technology Centre (ISTEC), in Tokyo, continuous growth of large single crystals of YBa 2Cu 3O 7- x (Y123) was achieved by the application of a modified Czochralski method. This paper presents the numerical computations of the flow, thermal and Y concentration fields in the Ba-Cu-O melt for Y123 single crystal growth by this modified method. The finite volume method was used to calculate the fluid flow, heat transfer and yttrium distribution in the melt with staggered numerical grid. The flow in the melt was modelled as an incompressible Newtonian and Boussinesque fluid. Calculations are presented for a combined flow regime of buoyancy-driven natural convection and crystal-rotation-driven forced convection.

A new numerical modelling method for deformation behaviour of metallic porous materials using X-ray computed microtomography

Energy Technology Data Exchange (ETDEWEB)

Doroszko, M., E-mail: m.doroszko@pb.edu.pl; Seweryn, A., E-mail: a.seweryn@pb.edu.pl

2017-03-24

Microtomographic devices have limited imaging accuracy and are often insufficient for proper mapping of small details of real objects (e.g. elements of material mesostructures). This paper describes a new method developed to compensate the effect of X-ray computed microtomography (micro-CT) inaccuracy in numerical modelling of the deformation process of porous sintered 316 L steel. The method involves modification of microtomographic images where the pore shapes are separated. The modification consists of the reconstruction of fissures and small pores omitted by micro-CT scanning due to the limited accuracy of the measuring device. It enables proper modelling of the tensile deformation process of porous materials. In addition, the proposed approach is compared to methods described in the available literature. As a result of numerical calculations, stress and strain distributions were obtained in deformed sintered 316 L steel. Based on the results, macroscopic stress-strain curves were received. Maximum principal stress distributions obtained by the proposed calculation model, indicated specific locations, where the stress reached a critical value, and fracture initiation occurred. These are bridges with small cross sections and notches in the shape of pores. Based on calculation results, the influence of the deformation mechanism of the material porous mesostructures on their properties at the macroscale is described.

A new numerical modelling method for deformation behaviour of metallic porous materials using X-ray computed microtomography

International Nuclear Information System (INIS)

Doroszko, M.; Seweryn, A.

2017-01-01

Microtomographic devices have limited imaging accuracy and are often insufficient for proper mapping of small details of real objects (e.g. elements of material mesostructures). This paper describes a new method developed to compensate the effect of X-ray computed microtomography (micro-CT) inaccuracy in numerical modelling of the deformation process of porous sintered 316 L steel. The method involves modification of microtomographic images where the pore shapes are separated. The modification consists of the reconstruction of fissures and small pores omitted by micro-CT scanning due to the limited accuracy of the measuring device. It enables proper modelling of the tensile deformation process of porous materials. In addition, the proposed approach is compared to methods described in the available literature. As a result of numerical calculations, stress and strain distributions were obtained in deformed sintered 316 L steel. Based on the results, macroscopic stress-strain curves were received. Maximum principal stress distributions obtained by the proposed calculation model, indicated specific locations, where the stress reached a critical value, and fracture initiation occurred. These are bridges with small cross sections and notches in the shape of pores. Based on calculation results, the influence of the deformation mechanism of the material porous mesostructures on their properties at the macroscale is described.

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)

On determination of microphone response and other parameters by a hybrid experimental and numerical method

DEFF Research Database (Denmark)

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

2008-01-01

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 distributions can be used together with a numerical formulation such as the Boundary Element Method for estimating the microphone response and other parameters...... such as the acoustic centres. In this work, a hybrid method is presented. The velocity distributions of condenser Laboratory Standard microphones were measured using a laser vibrometer. This measured velocity distribution was used for estimating the microphone responses and parameters. The agreement with experimental......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...

A direct hybrid SN method for slab-geometry lattice calculations

International Nuclear Information System (INIS)

Silva, Davi J.M.; Barros, Ricardo C.; Zani, Jose H.

2011-01-01

In this work we describe a hybrid direct method for calculating the thermal disadvantage factor and the neutron flux distribution in fuel-moderator lattices. For the mathematical model, we use the one-speed slab-geometry discrete ordinates (S N ) transport equation with linearly anisotropic scattering. The basic idea is to use higher order angular quadrature set in the highly absorbing fuel region (S NF ) and lower order angular quadrature set in the diffusive moderator region (S NM ) , i.e., N F > N M . We apply special continuity conditions based on the equivalence of the S N and P N-1 equations, which characterize the hybrid model. Numerical results to a typical model problem are given to illustrate the accuracy and the efficiency of the offered hybrid method. (author)

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.

Isochronous cyclotron closed equilibrium orbit calculation program description

International Nuclear Information System (INIS)

Kiyan, I.N.; Vorozhtsov, S.B.; Tarashkevich, R.

2003-01-01

The Equilibrium Orbit Research Program - EORP, written in C++ with the use of Visual C++ is described. The program is intended for the calculation of the particle rotation frequency and particle kinetic energy in the closed equilibrium orbits of an isochronous cyclotron, where the closed equilibrium orbits are described through the radius and particle momentum angle: r eo (θ) and φ p (θ). The program algorithm was developed on the basis of articles, lecture notes and original analytic calculations. The results of calculations by the EORP were checked and confirmed by using the results of calculations by the numerical methods. The discrepancies between the EORP results and the numerical method results for the calculations of the particle rotation frequency and particle kinetic energy are within the limits of ±1·10 -4 . The EORP results and the numerical method results for the calculations of r eo (θ) and φ p (θ) practically coincide. All this proves the accuracy of calculations by the EORP for the isochronous cyclotrons with the azimuthally varied fields. As is evident from the results of calculations, the program can be used for the calculations of both straight - sector and spiral-sector isochronous cyclotrons. (author)

Application of the variational method for calculation of neutron spectra and group constants - Master thesis

International Nuclear Information System (INIS)

Milosevic, M.

1979-01-01

One-dimensional variational method for cylindrical configuration was applied for calculating group constants, together with effects of elastic slowing down, anisotropic elastic scattering, inelastic scattering, heterogeneous resonance absorption with the aim to include the presence of a number of different isotopes and effects of neutron leakage from the reactor core. Neutron flux shape P 3 and adjoint function are proposed in order to enable calculation of smaller size reactors and inclusion of heterogeneity effects by cell calculations. Microscopic multigroup constants were prepared based on the UKNDL data library. Analytical-numerical approach was applied for solving the equations of the P 3 approximation to obtain neutron flux moments and adjoint functions

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.

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)

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...

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

DEFF Research Database (Denmark)

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

2008-01-01

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

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)

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.

Calculated Low-Speed Steady and Time-Dependent Aerodynamic Derivatives for Several Different Wings Using a Discrete Vortex Method

Science.gov (United States)

Riley, Donald R.

2016-01-01

Calculated numerical values for some aerodynamic terms and stability Derivatives for several different wings in unseparated inviscid incompressible flow were made using a discrete vortex method involving a limited number of horseshoe vortices. Both longitudinal and lateral-directional derivatives were calculated for steady conditions as well as for sinusoidal oscillatory motions. Variables included the number of vortices used and the rotation axis/moment center chordwise location. Frequencies considered were limited to the range of interest to vehicle dynamic stability (kb <.24 ). Comparisons of some calculated numerical results with experimental wind-tunnel measurements were in reasonable agreement in the low angle-of-attack range considering the differences existing between the mathematical representation and experimental wind-tunnel models tested. Of particular interest was the presence of induced drag for the oscillatory condition.

Some robust numerical methods for flow and transport in porous media; Quelques methodes numeriques robustes pour l'ecoulement et le transport en milieu poreux

Energy Technology Data Exchange (ETDEWEB)

Sboui, A

2007-01-15

The aim of this thesis is to model and develop numerical tools adapted to study underground water flow and the propagation of pollutants in a porous medium. The main motivation of this work is a benchmark from GDR Momas and ANDRA to simulate the 3-D propagation of radionuclides around a deep disposal of nuclear waste. Firstly, we construct a new mixed finite elements method suitable for general hexahedral meshes. Convergence of the method is proved and shown in numerical experiments. Secondly, we present a method of time discretization for the advection equation which allows for the use of different time steps in different sub-domains in order to take into account of strong heterogeneities. Finally a numerical method for the calculation of the transport of contaminants is proposed. The techniques above were implemented in a 3-D code and simulation results are shown on the 3-D far field benchmark from GDR Momas and ANDRA. (author)

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 ...

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

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...

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.

Use of exact albedo conditions in numerical methods for one-dimensional one-speed discrete ordinates eigenvalue problems

International Nuclear Information System (INIS)

Abreu, M.P. de

1994-01-01

The use of exact albedo boundary conditions in numerical methods applied to one-dimensional one-speed discrete ordinates (S n ) eigenvalue problems for nuclear reactor global calculations is described. An albedo operator that treats the reflector region around a nuclear reactor core implicitly is described and exactly was derived. To illustrate the method's efficiency and accuracy, it was used conventional linear diamond method with the albedo option to solve typical model problems. (author)

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.

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.

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

Explicit appropriate basis function method for numerical solution of stiff systems

International Nuclear Information System (INIS)

Chen, Wenzhen; Xiao, Hongguang; Li, Haofeng; Chen, Ling

2015-01-01

Highlights: • An explicit numerical method called the appropriate basis function method is presented. • The method differs from the power series method for obtaining approximate numerical solutions. • Two cases show the method is fit for linear and nonlinear stiff systems. • The method is very simple and effective for most of differential equation systems. - Abstract: In this paper, an explicit numerical method, called the appropriate basis function method, is presented. The explicit appropriate basis function method differs from the power series method because it employs an appropriate basis function such as the exponential function, or periodic function, other than a polynomial, to obtain approximate numerical solutions. The method is successful and effective for the numerical solution of the first order ordinary differential equations. Two examples are presented to show the ability of the method for dealing with linear and nonlinear systems of differential equations

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...

Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

Directory of Open Access Journals (Sweden)

Aydin Secer

2013-01-01

Full Text Available An efficient solution algorithm for sinc-Galerkin method has been presented for obtaining numerical solution of PDEs with Dirichlet-type boundary conditions by using Maple Computer Algebra System. The method is based on Whittaker cardinal function and uses approximating basis functions and their appropriate derivatives. In this work, PDEs have been converted to algebraic equation systems with new accurate explicit approximations of inner products without the need to calculate any numeric integrals. The solution of this system of algebraic equations has been reduced to the solution of a matrix equation system via Maple. The accuracy of the solutions has been compared with the exact solutions of the test problem. Computational results indicate that the technique presented in this study is valid for linear partial differential equations with various types of boundary conditions.

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)

Analysis of the two-fluid model and the drift-flux model for numerical calculation of two-phase flow

Energy Technology Data Exchange (ETDEWEB)

Munkejord, Svend Tollak

2006-05-11

This thesis analyses models for two-phase flows and methods for the numerical resolution of these models. It is therefore one contribution to the development of reliable design tools for multiphase applications. Such tools are needed and expected by engineers in a range of fields, including in the oil and gas industry. The approximate Riemann solver of Roe has been studied. Roe schemes for three different two-phase flow models have been implemented in the framework of a standard numerical algorithm for the solution of hyperbolic conservation laws. The schemes have been analysed by calculation of benchmark tests from the literature, and by comparison with each other. A Roe scheme for the four-equation one-pressure two-fluid model has been implemented, and a second-order extension based on wave decomposition and flux-difference splitting was shown to work well and to give improved results compared to the first-order scheme. The convergence properties of the scheme were tested on smooth and discontinuous solutions. A Roe scheme has been proposed for a five-equation two-pressure two-fluid model with pressure relaxation. The use of analogous numerical methods for the five-equation and four-equation models allowed for a direct comparison of a method with and without pressure relaxation. Numerical experiments demonstrated that the two approaches converged to the same results, but that the five-equation pressure-relaxation method was significantly more dissipative, particularly for contact discontinuities. Furthermore, even though the five-equation model with instantaneous pressure relaxation has real eigenvalues, the calculations showed that it produced oscillations for cases where the four-equation model had complex eigenvalues. A Roe scheme has been constructed for the drift-flux model with general closure laws. For the case of the Zuber-Findlay slip law describing bubbly flows, the Roe matrix is completely analytical. Hence the present Roe scheme is more efficient than

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.

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.

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.

The Numerical Welding Simulation - Developments and Validation of Simplified and Bead Lumping Methods

International Nuclear Information System (INIS)

Baup, Olivier

2001-01-01

The aim of this work was to study the TIG multipass welding process on stainless steel, by means of numerical methods and then to work out simplified and bead lumping methods in order to reduce adjusting and realisation times of these calculations. A simulation was used as reference for the validation of these methods; after the presentation of the test series having led to the option choices of this calculation (2D generalised plane strains, elastoplastic model with an isotropic hardening, hardening restoration due to high temperatures), various simplifications were tried on a plate geometry. These simplifications related various modelling points with a correct plastic flow representation in the plate. The use of a reduced number of thermal fields characterising the bead deposit and a low number of tensile curves allow to obtain interesting results, decreasing significantly the Computing times. In addition various lumping bead methods have been studied and concerning both the shape and the thermic of the macro-deposits. The macro-deposit shapes studied are in 'L', or in layer or they represent two beads one on top of the other. Among these three methods, only those using a few number of lumping beads gave bad results since thermo-mechanical history was deeply modified near and inside the weld. Thereafter, simplified methods have been applied to a tubular geometry. On this new geometry, experimental measurements were made during welding, which allow a validation of the reference calculation. Simplified and reference calculations gave approximately the same stress fields as found on plate geometry. Finally, in the last part of this document a procedure for automatic data setting permitting to reduce significantly the calculation phase preparation is presented. It has been applied to the calculation of thick pipe welding in 90 beads; the results are compared with a simplified simulation realised by Framatome and with experimental measurements. A bead by

New recording methods and electromechanical analysis; Nouvelles methodes d'enregistrement et de depouillement electromecanique des numerations de particules

Energy Technology Data Exchange (ETDEWEB)

Meunier, R.; Bonpas, M.; Legrand, J.P. [Commissariat a l' Energie Atomique, Saclay(France). Centre d' Etudes Nucleaires

1954-07-01

The measurement that the most often occurs in nuclear physics are of the numerations of pulses representing the transit of a particle in a detector that can be a Geiger counter, a photomultiplier or a pulse chamber. We studied and constructed an electromagnetic recorder who permits to get automatically and without calculation: 1) the activity of a radioelement according to the time; 2) the curve of decrease of a radioelement and its period; 3) any curves of growth or decrease; 4) the activity, at any instant, of a neutron detector; 5) the neutron densities ratios in several points by the method of the detectors. (M.B.) [French] Les mesures qui se presentent le plus souvent en physique nucleaire sont des numerations d'impulsions representant le passage d'une particule dans un detecteur qui peut etre un compteur de Geiger, un photomultiplicateur ou une chambre a impulsions. Nous avons etudie et construit un enregistreur electromagnetique qui permet d'obtenir automatiquement et sans calcul: 1) l'activite d'un radioelement en fonction du temps; 2) la courbe de decroissance d'un radioelement et sa periode; 3) des courbes quelconques de croissance ou de decroissance; 4) l'activite, rapportee a un instant quelconque, d'un detecteur de neutrons; 5) les rapports des densites de neutrons en plusieurs points par la methode des detecteurs. (M.B.)

The application of the large particles method of numerical modeling of the process of carbonic nanostructures synthesis in plasma

Science.gov (United States)

Abramov, G. V.; Gavrilov, A. N.

2018-03-01

The article deals with the numerical solution of the mathematical model of the particles motion and interaction in multicomponent plasma by the example of electric arc synthesis of carbon nanostructures. The high order of the particles and the number of their interactions requires a significant input of machine resources and time for calculations. Application of the large particles method makes it possible to reduce the amount of computation and the requirements for hardware resources without affecting the accuracy of numerical calculations. The use of technology of GPGPU parallel computing using the Nvidia CUDA technology allows organizing all General purpose computation on the basis of the graphical processor graphics card. The comparative analysis of different approaches to parallelization of computations to speed up calculations with the choice of the algorithm in which to calculate the accuracy of the solution shared memory is used. Numerical study of the influence of particles density in the macro particle on the motion parameters and the total number of particle collisions in the plasma for different modes of synthesis has been carried out. The rational range of the coherence coefficient of particle in the macro particle is computed.

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.

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.

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.

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

Development of Numerical Technique to Analyze the Flow Characteristics of Porous Media Using Lattice Boltzmann Method

Energy Technology Data Exchange (ETDEWEB)

Kim, Hyung Min [Kyonggi Univ., Suwon (Korea, Republic of)

2016-11-15

The performance of proton exchange membrane fuel cells (PEMFC) is strongly related to the water flow and accumulation in the gas diffusion layer (GDL) and catalyst layer. Understanding the behavior of fluid from the characteristics of the media is crucial for the improvement of the performance and design of the GDL. In this paper, a numerical method is proposed to calculate the design parameters of the GDL, i.e., permeability, tortuosity, and effective diffusivity. The fluid flow in a channel filled with randomly packed hard spheres is simulated to validate the method. The flow simulation was performed by lattice Boltzmann method with bounce back condition for the solid volume fraction in the porous media, with different values of porosities. Permeability, which affects the flow, was calculated from the average pressure drop and the velocity in the porous media. Tortuosity, calculated by the ratio the average path length of the randomly injected massless particles to the thickness of the porous media, and the resultant effective diffusivity were in good agreement with the theoretical model. The suggested method can be used to calculate the parameters of real GDL accurately without any modification.

Resampling Approach for Determination of the Method for Reference Interval Calculation in Clinical Laboratory Practice▿

Science.gov (United States)

Pavlov, Igor Y.; Wilson, Andrew R.; Delgado, Julio C.

2010-01-01

Reference intervals (RI) play a key role in clinical interpretation of laboratory test results. Numerous articles are devoted to analyzing and discussing various methods of RI determination. The two most widely used approaches are the parametric method, which assumes data normality, and a nonparametric, rank-based procedure. The decision about which method to use is usually made arbitrarily. The goal of this study was to demonstrate that using a resampling approach for the comparison of RI determination techniques could help researchers select the right procedure. Three methods of RI calculation—parametric, transformed parametric, and quantile-based bootstrapping—were applied to multiple random samples drawn from 81 values of complement factor B observations and from a computer-simulated normally distributed population. It was shown that differences in RI between legitimate methods could be up to 20% and even more. The transformed parametric method was found to be the best method for the calculation of RI of non-normally distributed factor B estimations, producing an unbiased RI and the lowest confidence limits and interquartile ranges. For a simulated Gaussian population, parametric calculations, as expected, were the best; quantile-based bootstrapping produced biased results at low sample sizes, and the transformed parametric method generated heavily biased RI. The resampling approach could help compare different RI calculation methods. An algorithm showing a resampling procedure for choosing the appropriate method for RI calculations is included. PMID:20554803

Composite magnetic refrigerants for an Ericsson cycle: New method of selection using a numerical approach

International Nuclear Information System (INIS)

Smaieli, A.; Chahine, R.

1997-01-01

The efficient operation of an Ericsson cycle requires the magnetic entropy change (AS) be constant as a function of temperature. To realize this condition using composite materials, a numerical method has been developed to determine the optimum proportions of the components. The Gd x Er 1-x (x = 0.69, 0.90) alloys have been used to investigate the validity of the numerical method. The values of ΔS have been determined from experimental magnetization curves of these alloys, in the 0.1-9 T magnetic field and the 200-290 K range. The calculations have led to the mass ratio y = 0.56 for the composite (Gd 0.90 Er 0.10 ) y (Gd 0.69 Er 0.31 ) 1-y . The ΔS of this composite is fairly constant in the 225-280 K range. To confirm this result, the magnetization curves of the composite material have been determined experimentally, and the corresponding ΔS was compared with the one predicted numerically. A good agreement was found proving the method's ability to properly determine the required fractions of the refrigerant's constituent materials

Calibration of a single hexagonal NaI(Tl) detector using a new numerical method based on the efficiency transfer method

Energy Technology Data Exchange (ETDEWEB)

Abbas, Mahmoud I., E-mail: mabbas@physicist.net [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Badawi, M.S. [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Ruskov, I.N. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia (Bulgaria); El-Khatib, A.M. [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Grozdanov, D.N. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia (Bulgaria); Thabet, A.A. [Department of Medical Equipment Technology, Faculty of Allied Medical Sciences, Pharos University in Alexandria (Egypt); Kopatch, Yu.N. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Gouda, M.M. [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Skoy, V.R. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)

2015-01-21

Gamma-ray detector systems are important instruments in a broad range of science and new setup are continually developing. The most recent step in the evolution of detectors for nuclear spectroscopy is the construction of large arrays of detectors of different forms (for example, conical, pentagonal, hexagonal, etc.) and sizes, where the performance and the efficiency can be increased. In this work, a new direct numerical method (NAM), in an integral form and based on the efficiency transfer (ET) method, is used to calculate the full-energy peak efficiency of a single hexagonal NaI(Tl) detector. The algorithms and the calculations of the effective solid angle ratios for a point (isotropic irradiating) gamma-source situated coaxially at different distances from the detector front-end surface, taking into account the attenuation of the gamma-rays in the detector's material, end-cap and the other materials in-between the gamma-source and the detector, are considered as the core of this (ET) method. The calculated full-energy peak efficiency values by the (NAM) are found to be in a good agreement with the measured experimental data.

Three dimensional numerical modeling for ground penetrating radar using finite difference time domain (FDTD) method; Jikan ryoiki yugen sabunho ni yoru chika radar no sanjigen suchi modeling

Energy Technology Data Exchange (ETDEWEB)

Sanada, Y; Ashida, Y; Sassa, K [Kyoto University, Kyoto (Japan)

1996-10-01

3-D numerical modeling by FDTD method was studied for ground penetrating radar. Radar radiates electromagnetic wave, and determines the existence and distance of objects by reflection wave. Ground penetrating radar uses the above functions for underground surveys, however, its resolution and velocity analysis accuracy are problems. In particular, propagation characteristics of electromagnetic wave in media such as heterogeneous and anisotropic soil and rock are essential. The behavior of electromagnetic wave in the ground could be precisely reproduced by 3-D numerical modeling using FDTD method. FDTD method makes precise analysis in time domain and electric and magnetic fields possible by sequentially calculating the difference equation of Maxwell`s equation. Because of the high calculation efficiency of FDTD method, more precise complicated analysis can be expected by using the latest advanced computers. The numerical model and calculation example are illustrated for surface type electromagnetic pulse ground penetrating radar assuming the survey of steel pipes of 1m deep. 4 refs., 3 figs., 1 tab.

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.

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.

Analytical-numerical method for treatment of turbulent diffusion of particles in the air

International Nuclear Information System (INIS)

Arsov, L.J.

1976-01-01

This work deals with the problem of air pollution around a stationary punctual source. For description of air pollution from a punctual source a mathematical model is suggested, and for calculation of effluents concentration an analytical-numerical algorithm is given. In addition to the analitical treatment the mathematical model is far more flexible and complete. Eddy diffusivity is represented by an arbitrary function, and an arbitrary wind velocity profile ahs been proposed. The apsorption of the ground is introduced through a variable apsorption coefficient, and the sedimentation through the mean velocity of deposition. To determine the movement of particles a parabolic equation of diffusion is used. The method has been tested through calculation of effluents concentration for different values of physical parameters

Mixed dual finite element methods for the numerical treatment of the diffusion equation in hexagonal geometry

International Nuclear Information System (INIS)

Schneider, D.

2001-01-01

The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P N approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)

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.

Numerical analysis of isothermal JET injection into a denser liquid pool using RD-MPS Method

Energy Technology Data Exchange (ETDEWEB)

Park, S. [KEPCO Nuclear Fuel, Daejeon (Korea, Republic of); Park, H. S. [POSTECH, Pohang (Korea, Republic of); Jeun, G. [Hanyang Univ., Seoul (Korea, Republic of)

2012-03-15

In this study, the rigid body dynamics coupled moving particle semi-implicit (RD-MPS) method was used to simulate a plunging liquid jet penetrating into a denser liquid pool. The phenomenon is related to fuel-coolant interactions (FCI) during severe accidents in nuclear power plants when coolant water is forcedly injected into a melt pool. A numerical particle method like MPS enables to simulate the complex multiphase flow in that significant deformation of fluids occurs due to its inherent grid less algorithm. However, the MPS method alone cannot continue the calculation for a long time as shown in the Ikea's work due to the large deformation of fluid surfaces and the difference in both liquid densities. In the RD-MPS method, the rigid body dynamics was coupled with the moving particle semi-implicit method to increase the overall stability of calculations and to calculate the multi-phase behavior of fluids. We performed two and three dimensional calculations to simulate jet penetration behaviors in a denser liquid pool, and the result was in good agreement with that of experiment. The simulation results suggested that the coupled model be useful in simulating dynamic interactions of multi-phase incompressible fluids as well as that the 3-D simulation for the plunging jet in a confined geometry predicted better agreement with experimental results than the 2-D simulation did.

Numerical analysis of isothermal JET injection into a denser liquid pool using RD-MPS Method

International Nuclear Information System (INIS)

Park, S.; Park, H. S.; Jeun, G.

2012-01-01

In this study, the rigid body dynamics coupled moving particle semi-implicit (RD-MPS) method was used to simulate a plunging liquid jet penetrating into a denser liquid pool. The phenomenon is related to fuel-coolant interactions (FCI) during severe accidents in nuclear power plants when coolant water is forcedly injected into a melt pool. A numerical particle method like MPS enables to simulate the complex multiphase flow in that significant deformation of fluids occurs due to its inherent grid less algorithm. However, the MPS method alone cannot continue the calculation for a long time as shown in the Ikea's work due to the large deformation of fluid surfaces and the difference in both liquid densities. In the RD-MPS method, the rigid body dynamics was coupled with the moving particle semi-implicit method to increase the overall stability of calculations and to calculate the multi-phase behavior of fluids. We performed two and three dimensional calculations to simulate jet penetration behaviors in a denser liquid pool, and the result was in good agreement with that of experiment. The simulation results suggested that the coupled model be useful in simulating dynamic interactions of multi-phase incompressible fluids as well as that the 3-D simulation for the plunging jet in a confined geometry predicted better agreement with experimental results than the 2-D simulation did

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

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

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.

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.

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

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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.

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.

Numerical methods in finance and economics a MATLAB-based introduction

CERN Document Server

Brandimarte, Paolo

2006-01-01

A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of financeThe use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications.The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions.Among this book''s most outstanding features is the...

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...

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...

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

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.

Simulation of X-ray topographs: a new method to calculate the diffracted field

International Nuclear Information System (INIS)

Carvalho, C.A.M.; Epelboin, Y.

1993-01-01

The precision of the numerical algorithms used to integrate the Takagi-Taupin equations has been in the past a severe limitation for the simulation of accurate topographs. The intensity, especially in the direct image of the defect, is underestimated. This has forbidden the use of the reciprocity theorem for the simulation of traverse and white-beam synchrotron topographs. A new algorithm is described, based on two different methods of expressing the partial-derivative equations, which permits a faster and more accurate calculation. (orig.)

Application of an analytical method for the field calculation in superconducting magnets

International Nuclear Information System (INIS)

Martinelli, G.; Morini, A.

1983-01-01

Superconducting magnets are taking on ever-growing importance due to their increasing prospects of utilization in electrical machines, nuclear fusion, MHD conversion and high-energy physics. These magnets are generally composed of cylindrical or saddle coils, while a ferromagnetic shield is generally situated outside them. This paper uses an analytical method for calculating the magnetic field at every point in a superconducting magnet composed of cylindrical or saddle coils. The method takes into account the real lengths and finite thickness of the coils as well as their radial and axial ferromagnetic shields, if present. The values and distribution of the flux density for some superconducting magnets of high dimensions and high magnetic field, composed of cylindrical or saddle coils, are also given. The results obtained with analytical method are compared with those obtained using numerical methods

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...

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.

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.

Numerical differentiation methods for the logarithmic derivative technique used in dielectric spectroscopy

Directory of Open Access Journals (Sweden)

Henrik Haspel

2010-06-01

Full Text Available In dielectric relaxation spectroscopy the conduction contribution often hampers the evaluation of dielectric spectra, especially in the low-frequency regime. In order to overcome this the logarithmic derivative technique could be used, where the calculation of the logarithmic derivative of the real part of the complex permittivity function is needed. Since broadband dielectric measurement provides discrete permittivity function, numerical differentiation has to be used. Applicability of the Savitzky-Golay convolution method in the derivative analysis is examined, and a detailed investigation of the influential parameters (frequency, spectrum resolution, peak shape is presented on synthetic dielectric data.

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

Numerical simulation of GEW equation using RBF collocation method

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