#### Sample records for method numerical examples

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

CERN Document Server

Ramm, Alexander G

2012-01-01

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

2. On some examples of pollutant transport problems solved numerically using the boundary element method

Science.gov (United States)

2018-03-01

A boundary element method (BEM) is obtained for solving a boundary value problem of homogeneous anisotropic media governed by diffusion-convection equation. The application of the BEM is shown for two particular pollutant transport problems of Tello river and Unhas lake in Makassar Indonesia. For the two particular problems a variety of the coefficients of diffusion and the velocity components are taken. The results show that the solutions vary as the parameters change. And this suggests that one has to be careful in measuring or determining the values of the parameters.

3. Numerical methods

CERN Document Server

Dahlquist, Germund

1974-01-01

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

4. 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

5. 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.

6. Projector Method: theory and examples

International Nuclear Information System (INIS)

Dahl, E.D.

1985-01-01

The Projector Method technique for numerically analyzing lattice gauge theories was developed to take advantage of certain simplifying features of gauge theory models. Starting from a very general notion of what the Projector Method is, the techniques are applied to several model problems. After these examples have traced the development of the actual algorithm from the general principles of the Projector Method, a direct comparison between the Projector and the Euclidean Monte Carlo is made, followed by a discussion of the application to Periodic Quantum Electrodynamics in two and three spatial dimensions. Some methods for improving the efficiency of the Projector in various circumstances are outlined. 10 refs., 7 figs

7. 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.)

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.

9. 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

10. 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 ...

11. 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...

12. Numerical methods for image registration

CERN Document Server

Modersitzki, Jan

2003-01-01

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

13. An example of numerical simulation in causal set dynamics

International Nuclear Information System (INIS)

Krugly, Alexey L; Tserkovnikov, Ivan A

2013-01-01

The model of a discrete pregeometry on a microscopic scale is an x-graph. This is a directed acyclic graph. An outdegree and an indegree of each vertex are not more than 2. The sets of vertices and edges of x-graph are particular cases of causal sets. The sequential growth of a graph is an addition of new vertices one by one. A simple stochastic algorithm of sequential growth of x-graph are considered. It is based on a random walk at the x-graph. The particles in this model must be self-organized repetitive structures. We introduce the method of search of such repetitive structures. It is based on a discrete Fourier transformation. An example of numerical simulation is introduced.

14. Numerical approaches towards life cycle interpretation five examples

NARCIS (Netherlands)

Heijungs, R.; Kleijn, R.

2001-01-01

The ISO-standard for LCA distinguishes four phases, of which the last one, the interpretation, is the least elaborated. It can be regarded as containing procedural steps (like a completeness check) as well as numerical steps (like a sensitivity check). This paper provides five examples of techniques

15. A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

KAUST Repository

Osman, Hossam Omar; Salama, Amgad; Sun, Shuyu; Bao, Kai

2012-01-01

It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.

16. A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

KAUST Repository

Osman, Hossam Omar

2012-06-17

It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.

17. 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...

18. 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.

19. Numerical methods for hyperbolic differential functional problems

Directory of Open Access Journals (Sweden)

Roman Ciarski

2008-01-01

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

20. [Effects decomposition in mediation analysis: a numerical example].

Science.gov (United States)

Zugna, Daniela; Richiardi, Lorenzo

2018-01-01

Mediation analysis aims to decompose the total effect of the exposure on the outcome into a direct effect (unmediated) and an indirect effect (mediated by a mediator). When the interest also lies on understanding whether the exposure effect differs in different sub-groups of study population or under different scenarios, the mediation analysis needs to be integrated with interaction analysis. In this setting it is necessary to decompose the total effect not only into two components, the direct and indirect effects, but other two components linked to interaction. The interaction between the exposure and the mediator in their effect on the outcome could indeed act through the effect of the exposure on the mediator or through the mediator when the mediator is not totally explained by the exposure. We describe options for decomposition, proposed in literature, of the total effect and we illustrate them through a hypothetical example of the effect of age at diagnosis of cancer on survival, mediated and unmediated by the therapeutical approach, and a numerical example.

1. 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...

2. 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.

3. Numerical methods and analysis of multiscale problems

CERN Document Server

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.

4. Numerical computer methods part E

CERN Document Server

Johnson, Michael L

2004-01-01

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

5. Numerical methods in matrix computations

CERN Document Server

Björck, Åke

2015-01-01

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

6. Spectral methods in numerical plasma simulation

International Nuclear Information System (INIS)

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

1989-01-01

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

7. 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...

8. Uranium prospection methods illustrated with examples

International Nuclear Information System (INIS)

Valsardieu, C.

1985-01-01

Uranium exploration methods are briefly reviewed: aerial (radiometric, spectrometric), surface (mapping, radiometric, geophysical, geochemical), sub-surface (well logging, boring) and mining methods in the different steps of a mine project: preliminary studies, general prospecting, detailed prospecting deposit area and deposit estimation. Choice of methods depends strongly on geographic and geologic environment. Three examples are given concerning: an intragranitic deposit Limousin (France), a deposit spatially related to a discordance Athabasca (Canada) and a sedimentary deposit Manyingee (Western Australia) [fr

9. Strongly correlated systems numerical methods

CERN Document Server

Mancini, Ferdinando

2013-01-01

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

10. Methods for enhancing numerical integration

International Nuclear Information System (INIS)

Doncker, Elise de

2003-01-01

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

11. Upscaling of permeability field of fractured rock system: Numerical examples

KAUST Repository

Bao, K.; Salama, Amgad; Sun, S.

2012-01-01

When the permeability field of a given porous medium domain is heterogeneous by the existence of randomly distributed fractures such that numerical investigation becomes cumbersome, another level of upscaling may be required. That is such complex permeability field could be relaxed (i.e., smoothed) by constructing an effective permeability field. The effective permeability field is an approximation to the real permeability field that preserves certain quantities and provides an overall acceptable description of the flow field. In this work, the effective permeability for a fractured rock system is obtained for different coarsening scenarios starting from very coarse mesh all the way towards the fine mesh simulation. In all these scenarios, the effective permeability as well as the pressure at each cell is obtained. The total flux at the exit boundary is calculated in all these cases, and very good agreement is obtained.

12. Numerical methods in dynamic fracture mechanics

International Nuclear Information System (INIS)

Beskos, D.E.

1987-01-01

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

13. Two numerical methods for mean-field games

KAUST Repository

Gomes, Diogo A.

2016-01-09

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

14. Two numerical methods for mean-field games

KAUST Repository

Gomes, Diogo A.

2016-01-01

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

15. 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.)

16. 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)

17. Development of numerical methods for reactive transport

International Nuclear Information System (INIS)

Bouillard, N.

2006-12-01

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

18. Numerical methods used in simulation

International Nuclear Information System (INIS)

Caseau, Paul; Perrin, Michel; Planchard, Jacques

1978-01-01

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

19. Numerical methods in simulation of resistance welding

DEFF Research Database (Denmark)

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

2015-01-01

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

20. Numerical computer methods part D

CERN Document Server

Johnson, Michael L

2004-01-01

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

1. 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

2. Isogeometric methods for numerical simulation

CERN Document Server

Bordas, Stéphane

2015-01-01

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

3. Excel spreadsheet in teaching numerical methods

Science.gov (United States)

Djamila, Harimi

2017-09-01

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

4. 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.

5. 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.

6. 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...

7. 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...

8. 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

9. 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

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

Directory of Open Access Journals (Sweden)

Changqing Yang

2012-01-01

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

11. 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.

12. 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...

13. 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

14. A numerical method for resonance integral calculations

International Nuclear Information System (INIS)

Tanbay, Tayfun; Ozgener, Bilge

2013-01-01

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

15. 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.)

16. Direct design of LPV feedback controllers: technical details and numerical examples

OpenAIRE

Novara, Carlo

2014-01-01

The paper contains technical details of recent results developed by the author, regarding the design of LPV controllers directly from experimental data. Two numerical examples are also presented, about control of the Duffing oscillator and control of a two-degree-of-freedom manipulator.

17. Mixed Methods Sampling: A Typology with Examples

Science.gov (United States)

Teddlie, Charles; Yu, Fen

2007-01-01

This article presents a discussion of mixed methods (MM) sampling techniques. MM sampling involves combining well-established qualitative and quantitative techniques in creative ways to answer research questions posed by MM research designs. Several issues germane to MM sampling are presented including the differences between probability and…

18. Hybrid numerical calculation method for bend waveguides

OpenAIRE

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

2017-01-01

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

19. 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.

20. Numerical methods in electron magnetic resonance

International Nuclear Information System (INIS)

Soernes, A.R.

1998-01-01

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

1. Numerical methods in electron magnetic resonance

Energy Technology Data Exchange (ETDEWEB)

Soernes, A.R

1998-07-01

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

2. Numerical methods in nuclear engineering. Part 1

International Nuclear Information System (INIS)

Phillips, G.J.

1983-08-01

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

3. A hybrid numerical method for orbit correction

International Nuclear Information System (INIS)

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

1997-09-01

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

4. Conservative numerical methods for solitary wave interactions

Energy Technology Data Exchange (ETDEWEB)

2003-07-18

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

5. 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.

6. 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.

7. Numerical methods for differential equations and applications

International Nuclear Information System (INIS)

Ixaru, L.G.

1984-01-01

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

8. 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...

9. Intelligent numerical methods applications to fractional calculus

CERN Document Server

Anastassiou, George A

2016-01-01

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

10. 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

11. Partial differential equations with numerical methods

CERN Document Server

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.

12. Numerical method for the nonlinear Fokker-Planck equation

International Nuclear Information System (INIS)

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

1997-01-01

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

13. 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

14. Numerical methods for coupled fracture problems

Science.gov (United States)

Viesca, Robert C.; Garagash, Dmitry I.

2018-04-01

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

15. Selection of robust methods. Numerical examples and results

Czech Academy of Sciences Publication Activity Database

Víšek, Jan Ámos

2005-01-01

Roč. 21, č. 11 (2005), s. 1-58 ISSN 1212-074X R&D Projects: GA ČR(CZ) GA402/03/0084 Institutional research plan: CEZ:AV0Z10750506 Keywords : robust regression * model selection * uniform consistency of M-estimators Subject RIV: BA - General Mathematics

16. RELAP-7 Numerical Stabilization: Entropy Viscosity Method

Energy Technology Data Exchange (ETDEWEB)

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

2014-06-01

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

17. On vortex loops and filaments: three examples of numerical predictions of flows containing vortices.

Science.gov (United States)

Krause, Egon

2003-01-01

Vortex motion plays a dominant role in many flow problems. This article aims at demonstrating some of the characteristic features of vortices with the aid of numerical solutions of the governing equations of fluid mechanics, the Navier-Stokes equations. Their discretized forms will first be reviewed briefly. Thereafter three problems of fluid flow involving vortex loops and filaments are discussed. In the first, the time-dependent motion and the mutual interaction of two colliding vortex rings are discussed, predicted in good agreement with experimental observations. The second example shows how vortex rings are generated, move, and interact with each other during the suction stroke in the cylinder of an automotive engine. The numerical results, validated with experimental data, suggest that vortex rings can be used to influence the spreading of the fuel droplets prior to ignition and reduce the fuel consumption. In the third example, it is shown that vortices can also occur in aerodynamic flows over delta wings at angle of attack as well as pipe flows: of particular interest for technical applications of these flows is the situation in which the vortex cores are destroyed, usually referred to as vortex breakdown or bursting. Although reliable breakdown criteria could not be established as yet, the numerical predictions obtained so far are found to agree well with the few experimental data available in the recent literature.

18. Two split cell numerical methods for solving 2-D non-equilibrium radiation transport equations

International Nuclear Information System (INIS)

Feng Tinggui

2004-11-01

Two numerically positive methods, the step characteristic integral method and subcell balance method, for solving radiative transfer equations on quadrilateral grids are presented. Numerical examples shows that the schemes presented are feasible on non-rectangle grid computation, and that the computing results by the schemes presented are comparative to that by the discrete ordinate diamond scheme on rectangle grid. (author)

19. Numerical methods for engine-airframe integration

International Nuclear Information System (INIS)

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

1986-01-01

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

20. 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

1. Nonlinear time series theory, methods and applications with R examples

CERN Document Server

Douc, Randal; Stoffer, David

2014-01-01

FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre

2. 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.

CERN Document Server

1991-01-01

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

4. Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Verner Method

Directory of Open Access Journals (Sweden)

T. Jayakumar

2015-01-01

Full Text Available In this paper we study the numerical methods for Fuzzy Differential equations by an application of the Runge-Kutta Verner method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.

5. Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method

Directory of Open Access Journals (Sweden)

De-Gang Wang

2012-01-01

Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.

6. 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)

7. 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)

8. 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

9. Numerical method of identification of an unknown source term in a heat equation

Directory of Open Access Journals (Sweden)

Fatullayev Afet Golayo?lu

2002-01-01

Full Text Available A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

10. CEMRACS 2010: Numerical methods for fusion

International Nuclear Information System (INIS)

2011-01-01

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

11. Numerical spin tracking in a synchrotron computer code Spink: Examples (RHIC)

International Nuclear Information System (INIS)

Luccio, A.

1995-01-01

In the course of acceleration of polarized protons in a synchrotron, many depolarizing resonances are encountered. They are classified in two categories: Intrinsic resonances that depend on the lattice structure of the ring and arise from the coupling of betatron oscillations with horizontal magnetic fields, and imperfection resonances caused by orbit distortions due to field errors. In general, the spectrum of resonances vs spin tune Gγ(G = 1.7928, the proton gyromagnetic anomaly, and y the proton relativistic energy ratio) for a given lattice tune ν, or vs ν for a given Gγ, contains a multitude of lines with various amplitudes or resonance strengths. The depolarization due to the resonance lines can be studied by numerically tracking protons with spin in a model accelerator. Tracking will allow one to check the strength of resonances, to study the effects of devices like Siberian Snakes, to find safe lattice tune regions where to operate, and finally to study in detail the operation of special devices such as Spin Flippers. A few computer codes exist that calculate resonance strengths E k and perform tracking, for proton and electron machines. Most relevant to our work for the AGS and RHIC machines are the programs Depol and Snake. Depol, calculates the E k 's by Fourier analysis. The input to Depol is the output of a machine model code, such as Synch or Mad, containing all details of the lattice. Snake, does the tracking, starting from a synthetic machine, that contains a certain number of periods, of FODO cells, of Siberian snakes, etc. We believed the complexities of machines like the AGS or RHIC could not be adequately represented by Snake. Then, we decided to write a new code, Spink, that combines some of the features of Depol and Snake. I.E., Spink reads a Mad output like Depol and tracks as Snake does. The structure of the code and examples for RHIC are described in the following

12. Survey of numerical methods for compressible fluids

Energy Technology Data Exchange (ETDEWEB)

Sod, G A

1977-06-01

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

13. Numerical methods in physical and economic sciences

International Nuclear Information System (INIS)

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

1974-01-01

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

14. Numerical method for solving linear Fredholm fuzzy integral equations of the second kind

Energy Technology Data Exchange (ETDEWEB)

Abbasbandy, S. [Department of Mathematics, Imam Khomeini International University, P.O. Box 288, Ghazvin 34194 (Iran, Islamic Republic of)]. E-mail: saeid@abbasbandy.com; Babolian, E. [Faculty of Mathematical Sciences and Computer Engineering, Teacher Training University, Tehran 15618 (Iran, Islamic Republic of); Alavi, M. [Department of Mathematics, Arak Branch, Islamic Azad University, Arak 38135 (Iran, Islamic Republic of)

2007-01-15

In this paper we use parametric form of fuzzy number and convert a linear fuzzy Fredholm integral equation to two linear system of integral equation of the second kind in crisp case. We can use one of the numerical method such as Nystrom and find the approximation solution of the system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equations of the second kind. The proposed method is illustrated by solving some numerical examples.

15. Quantum dynamic imaging theoretical and numerical methods

CERN Document Server

Ivanov, Misha

2011-01-01

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

16. Numerical modeling of isothermal compositional grading by convex splitting methods

KAUST Repository

Li, Yiteng

2017-04-09

In this paper, an isothermal compositional grading process is simulated based on convex splitting methods with the Peng-Robinson equation of state. We first present a new form of gravity/chemical equilibrium condition by minimizing the total energy which consists of Helmholtz free energy and gravitational potential energy, and incorporating Lagrange multipliers for mass conservation. The time-independent equilibrium equations are transformed into a system of transient equations as our solution strategy. It is proved our time-marching scheme is unconditionally energy stable by the semi-implicit convex splitting method in which the convex part of Helmholtz free energy and its derivative are treated implicitly and the concave parts are treated explicitly. With relaxation factor controlling Newton iteration, our method is able to converge to a solution with satisfactory accuracy if a good initial estimate of mole compositions is provided. More importantly, it helps us automatically split the unstable single phase into two phases, determine the existence of gas-oil contact (GOC) and locate its position if GOC does exist. A number of numerical examples are presented to show the performance of our method.

17. Multiple predictor smoothing methods for sensitivity analysis: Example results

International Nuclear Information System (INIS)

Storlie, Curtis B.; Helton, Jon C.

2008-01-01

The use of multiple predictor smoothing methods in sampling-based sensitivity analyses of complex models is investigated. Specifically, sensitivity analysis procedures based on smoothing methods employing the stepwise application of the following nonparametric regression techniques are described in the first part of this presentation: (i) locally weighted regression (LOESS), (ii) additive models, (iii) projection pursuit regression, and (iv) recursive partitioning regression. In this, the second and concluding part of the presentation, the indicated procedures are illustrated with both simple test problems and results from a performance assessment for a radioactive waste disposal facility (i.e., the Waste Isolation Pilot Plant). As shown by the example illustrations, the use of smoothing procedures based on nonparametric regression techniques can yield more informative sensitivity analysis results than can be obtained with more traditional sensitivity analysis procedures based on linear regression, rank regression or quadratic regression when nonlinear relationships between model inputs and model predictions are present

18. A higher order numerical method for time fractional partial differential equations with nonsmooth data

Science.gov (United States)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

19. Numerical method improvement for a subchannel code

Energy Technology Data Exchange (ETDEWEB)

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

2016-07-15

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

20. 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...

1. Numerical Methods for Partial Differential Equations.

Science.gov (United States)

1984-01-09

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

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

CERN Document Server

Zhang, Zhongqiang

2017-01-01

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

3. Numerical simulation of GEW equation using RBF collocation method

Directory of Open Access Journals (Sweden)

Hamid Panahipour

2012-08-01

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

4. Balancing of linkages and robot manipulators advanced methods with illustrative examples

CERN Document Server

Arakelian, Vigen

2015-01-01

In this book advanced balancing methods for planar and spatial linkages, hand operated and automatic robot manipulators are presented. It is organized into three main parts and eight chapters. The main parts are the introduction to balancing, the balancing of linkages and the balancing of robot manipulators. The review of state-of-the-art literature including more than 500 references discloses particularities of shaking force/moment balancing and gravity compensation methods. Then new methods for balancing of linkages are considered. Methods provided in the second part of the book deal with the partial and complete shaking force/moment balancing of various linkages. A new field for balancing methods applications is the design of mechanical systems for fast manipulation. Special attention is given to the shaking force/moment balancing of robot manipulators. Gravity balancing methods are also discussed. The suggested balancing methods are illustrated by numerous examples.

5. A New Method to Solve Numeric Solution of Nonlinear Dynamic System

Directory of Open Access Journals (Sweden)

Min Hu

2016-01-01

Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.

6. Numerical Methods for Bayesian Inverse Problems

KAUST Repository

Ernst, Oliver

2014-01-06

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

7. Numerical Methods for Bayesian Inverse Problems

KAUST Repository

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

2014-01-01

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

8. Dating method by fission tracks: some Brazilian examples

International Nuclear Information System (INIS)

1996-01-01

The Fission Track method (TF) complements the dating of a interval of tectonic events occurred in low temperatures not detected by another radiometric methods. In the South part of Craton of Sao Francisco the dating of apatites of archaean rocks produced ages TF between 900 and 500 Ma, reflecting the progressive acting of the Brazilian margin mobile belts in the archaean craton areas. Apatite of some igneous and metamorphic rocks of the Braziliana age, in the Faixa Ribeira segment, between the Rio de Janeiro and Salvador cities, produced TF ages between 140 and 80 Ma. The basaltic and alkaline volcanism related to the Atlantic Ocean opening dated from this interval. The TF dating in apatites of the continental margin rocks allowed to date the event. In the Cabo Frio region (Southeastern part of Rio de Janeiro State), titanite and apatite of the Transamazonic orthognaisses produced TF dates between 190 and 80 to 40 Ma. The age around 190 Ma date previously the rift formation precursor of the South Atlantic Ocean opening, while the ages between 80 and 40 Ma were related to the alkaline rocks intrusion. The examples mentioned demonstrate the event diversity which may be dated by the Fission Tracks method, mainly in the craton area and margin belts study

9. 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

10. 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.

11. A difference quotient-numerical integration method for solving radiative transfer problems

International Nuclear Information System (INIS)

Ding Peizhu

1992-01-01

A difference quotient-numerical integration method is adopted to solve radiative transfer problems in an anisotropic scattering slab medium. By using the method, the radiative transfer problem is separated into a system of linear algebraic equations and the coefficient matrix of the system is a band matrix, so the method is very simple to evaluate on computer and to deduce formulae and easy to master for experimentalists. An example is evaluated and it is shown that the method is precise

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

Science.gov (United States)

Felbacq, Didier

2016-11-01

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

13. Introduction to numerical methods for time dependent differential equations

CERN Document Server

Kreiss, Heinz-Otto

2014-01-01

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

14. 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.)

15. 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

16. 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)

17. Numerical Study on Several Stabilized Finite Element Methods for the Steady Incompressible Flow Problem with Damping

Directory of Open Access Journals (Sweden)

Jilian Wu

2013-01-01

Full Text Available We discuss several stabilized finite element methods, which are penalty, regular, multiscale enrichment, and local Gauss integration method, for the steady incompressible flow problem with damping based on the lowest equal-order finite element space pair. Then we give the numerical comparisons between them in three numerical examples which show that the local Gauss integration method has good stability, efficiency, and accuracy properties and it is better than the others for the steady incompressible flow problem with damping on the whole. However, to our surprise, the regular method spends less CPU-time and has better accuracy properties by using Crout solver.

18. Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

Science.gov (United States)

Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye

2018-04-01

The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

19. 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

20. Comparative numerical solutions of stiff Ordinary differential equations using magnus series expansion method

Directory of Open Access Journals (Sweden)

SURE KÖME

2014-12-01

Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.

1. Hybrid numerical methods for multiscale simulations of subsurface biogeochemical processes

International Nuclear Information System (INIS)

Scheibe, T D; Tartakovsky, A M; Tartakovsky, D M; Redden, G D; Meakin, P

2007-01-01

Many subsurface flow and transport problems of importance today involve coupled non-linear flow, transport, and reaction in media exhibiting complex heterogeneity. In particular, problems involving biological mediation of reactions fall into this class of problems. Recent experimental research has revealed important details about the physical, chemical, and biological mechanisms involved in these processes at a variety of scales ranging from molecular to laboratory scales. However, it has not been practical or possible to translate detailed knowledge at small scales into reliable predictions of field-scale phenomena important for environmental management applications. A large assortment of numerical simulation tools have been developed, each with its own characteristic scale. Important examples include 1. molecular simulations (e.g., molecular dynamics); 2. simulation of microbial processes at the cell level (e.g., cellular automata or particle individual-based models); 3. pore-scale simulations (e.g., lattice-Boltzmann, pore network models, and discrete particle methods such as smoothed particle hydrodynamics); and 4. macroscopic continuum-scale simulations (e.g., traditional partial differential equations solved by finite difference or finite element methods). While many problems can be effectively addressed by one of these models at a single scale, some problems may require explicit integration of models across multiple scales. We are developing a hybrid multi-scale subsurface reactive transport modeling framework that integrates models with diverse representations of physics, chemistry and biology at different scales (sub-pore, pore and continuum). The modeling framework is being designed to take advantage of advanced computational technologies including parallel code components using the Common Component Architecture, parallel solvers, gridding, data and workflow management, and visualization. This paper describes the specific methods/codes being used at each

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

CERN Document Server

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

2009-01-01

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

3. 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.

4. 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

5. 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.

6. Exponential and Bessel fitting methods for the numerical solution of the Schroedinger equation

International Nuclear Information System (INIS)

Raptis, A.D.; Cash, J.R.

1987-01-01

A new method is developed for the numerical integration of the one dimensional radial Schroedinger equation. This method involves using different integration formulae in different parts of the range of integration rather than using the same integration formula throughout. Two new integration formulae are derived, one which integrates Bessel and Neumann functions exactly and another which exactly integrates certain exponential functions. It is shown that, for large r, these new formulae are much more accurate than standard integration methods for the Schroedinger equation. The benefit of using this new approach is demonstrated by considering some numerical examples based on the Lennard-Jones potential. (orig.)

7. 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...

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

Czech Academy of Sciences Publication Activity Database

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

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

9. Using crowdsourcing to evaluate published scientific literature: methods and example.

Directory of Open Access Journals (Sweden)

Andrew W Brown

Full Text Available Systematically evaluating scientific literature is a time consuming endeavor that requires hours of coding and rating. Here, we describe a method to distribute these tasks across a large group through online crowdsourcing. Using Amazon's Mechanical Turk, crowdsourced workers (microworkers completed four groups of tasks to evaluate the question, "Do nutrition-obesity studies with conclusions concordant with popular opinion receive more attention in the scientific community than do those that are discordant?" 1 Microworkers who passed a qualification test (19% passed evaluated abstracts to determine if they were about human studies investigating nutrition and obesity. Agreement between the first two raters' conclusions was moderate (κ = 0.586, with consensus being reached in 96% of abstracts. 2 Microworkers iteratively synthesized free-text answers describing the studied foods into one coherent term. Approximately 84% of foods were agreed upon, with only 4 and 8% of ratings failing manual review in different steps. 3 Microworkers were asked to rate the perceived obesogenicity of the synthesized food terms. Over 99% of responses were complete and usable, and opinions of the microworkers qualitatively matched the authors' expert expectations (e.g., sugar-sweetened beverages were thought to cause obesity and fruits and vegetables were thought to prevent obesity. 4 Microworkers extracted citation counts for each paper through Google Scholar. Microworkers reached consensus or unanimous agreement for all successful searches. To answer the example question, data were aggregated and analyzed, and showed no significant association between popular opinion and attention the paper received as measured by Scimago Journal Rank and citation counts. Direct microworker costs totaled \$221.75, (estimated cost at minimum wage: \$312.61. We discuss important points to consider to ensure good quality control and appropriate pay for microworkers. With good

10. Using Crowdsourcing to Evaluate Published Scientific Literature: Methods and Example

Science.gov (United States)

Brown, Andrew W.; Allison, David B.

2014-01-01

Systematically evaluating scientific literature is a time consuming endeavor that requires hours of coding and rating. Here, we describe a method to distribute these tasks across a large group through online crowdsourcing. Using Amazon's Mechanical Turk, crowdsourced workers (microworkers) completed four groups of tasks to evaluate the question, “Do nutrition-obesity studies with conclusions concordant with popular opinion receive more attention in the scientific community than do those that are discordant?” 1) Microworkers who passed a qualification test (19% passed) evaluated abstracts to determine if they were about human studies investigating nutrition and obesity. Agreement between the first two raters' conclusions was moderate (κ = 0.586), with consensus being reached in 96% of abstracts. 2) Microworkers iteratively synthesized free-text answers describing the studied foods into one coherent term. Approximately 84% of foods were agreed upon, with only 4 and 8% of ratings failing manual review in different steps. 3) Microworkers were asked to rate the perceived obesogenicity of the synthesized food terms. Over 99% of responses were complete and usable, and opinions of the microworkers qualitatively matched the authors' expert expectations (e.g., sugar-sweetened beverages were thought to cause obesity and fruits and vegetables were thought to prevent obesity). 4) Microworkers extracted citation counts for each paper through Google Scholar. Microworkers reached consensus or unanimous agreement for all successful searches. To answer the example question, data were aggregated and analyzed, and showed no significant association between popular opinion and attention the paper received as measured by Scimago Journal Rank and citation counts. Direct microworker costs totaled \$221.75, (estimated cost at minimum wage: \$312.61). We discuss important points to consider to ensure good quality control and appropriate pay for microworkers. With good reliability and

11. Numerical Recipes in C++: The Art of Scientific Computing (2nd edn). Numerical Recipes Example Book (C++) (2nd edn). Numerical Recipes Multi-Language Code CD ROM with LINUX or UNIX Single-Screen License Revised Version

International Nuclear Information System (INIS)

Borcherds, P

2003-01-01

The two Numerical Recipes books are marvellous. The principal book, The Art of Scientific Computing, contains program listings for almost every conceivable requirement, and it also contains a well written discussion of the algorithms and the numerical methods involved. The Example Book provides a complete driving program, with helpful notes, for nearly all the routines in the principal book. The first edition of Numerical Recipes: The Art of Scientific Computing was published in 1986 in two versions, one with programs in Fortran, the other with programs in Pascal. There were subsequent versions with programs in BASIC and in C. The second, enlarged edition was published in 1992, again in two versions, one with programs in Fortran (NR(F)), the other with programs in C (NR(C)). In 1996 the authors produced Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing as a supplement, called Volume 2, with the original (Fortran) version referred to as Volume 1. Numerical Recipes in C++ (NR(C++)) is another version of the 1992 edition. The numerical recipes are also available on a CD ROM: if you want to use any of the recipes, I would strongly advise you to buy the CD ROM. The CD ROM contains the programs in all the languages. When the first edition was published I bought it, and have also bought copies of the other editions as they have appeared. Anyone involved in scientific computing ought to have a copy of at least one version of Numerical Recipes, and there also ought to be copies in every library. If you already have NR(F), should you buy the NR(C++) and, if not, which version should you buy? In the preface to Volume 2 of NR(F), the authors say 'C and C++ programmers have not been far from our minds as we have written this volume, and we think that you will find that time spent in absorbing its principal lessons will be amply repaid in the future as C and C++ eventually develop standard parallel extensions'. In the preface and introduction to NR

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

International Nuclear Information System (INIS)

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

1981-01-01

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

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

International Nuclear Information System (INIS)

Le Coq, G.; Libmann, M.

1978-01-01

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

14. 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

15. Literature survey, numerical examples, and recommended design studies for main-coolant pumps. Final report

International Nuclear Information System (INIS)

Allaire, P.E.; Barrett, L.E.

1982-06-01

This report presents an up-to-date literature survey, examples of calculations of seal forces or other pump properties, and recommendations for future work pertaining to primary coolant pumps and primary recirculating pumps in the nuclear power industry. Five main areas are covered: pump impeller forces, fluid annuli, bearings, seals, and rotor calculations. The main conclusion is that forces in pump impellers is perhaps the least well understood area, seals have had some good design work done on them recently, fluid annuli effects are being discussed in the literature, bearing designs are fairly well known, and rotor calculations have been discussed widely in the literature. It should be noted, however, that usually the literature in a given area is not applied to pumps in nuclear power stations. The most immediate need for a combined theoretical and experimental design capability exists in mechanical face seals

16. EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY

Energy Technology Data Exchange (ETDEWEB)

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

2007-01-11

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

17. Methods of gas hydrate concentration estimation with field examples

Digital Repository Service at National Institute of Oceanography (India)

Kumar, D.; Dash, R.; Dewangan, P.

physics and seismic inversion: examples from the northern deepwater Gulf of Mexico: The Leading Edge, 23, 60-66. Dash R., 2007, Crustal structure and marine gas hydrate studies near Vancouver Island using seismic tomography: PhD thesis, University...-resistivity logs: Examples from Green Canyon, Gulf of Mexico: SEG expanded abstracts, 26, 1579-1583. Singh, S. C., Minshull, T. A., and Spence, G. D., 1993, Velocity structure of a gas hydrate reflector: Science, 260, 204-207. Sloan, E. D. Jr., 1998, Clathrate...

18. Numerical methods for axisymmetric and 3D nonlinear beams

Science.gov (United States)

Pinton, Gianmarco F.; Trahey, Gregg E.

2005-04-01

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

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

CERN Document Server

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

1971-01-01

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

20. Numerical methods for modeling photonic-crystal VCSELs

DEFF Research Database (Denmark)

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

2010-01-01

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

1. Application of the dual reciprocity boundary element method for numerical modelling of solidification process

Directory of Open Access Journals (Sweden)

E. Majchrzak

2008-12-01

Full Text Available The dual reciprocity boundary element method is applied for numerical modelling of solidification process. This variant of the BEM is connected with the transformation of the domain integral to the boundary integrals. In the paper the details of the dual reciprocity boundary element method are presented and the usefulness of this approach to solidification process modelling is demonstrated. In the final part of the paper the examples of computations are shown.

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

OpenAIRE

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

2014-01-01

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

3. Investigating Convergence Patterns for Numerical Methods Using Data Analysis

Science.gov (United States)

Gordon, Sheldon P.

2013-01-01

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

4. A numerical test of the collective coordinate method

International Nuclear Information System (INIS)

Dobrowolski, T.; Tatrocki, P.

2008-01-01

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

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

KAUST Repository

Happola, Juho

2017-09-19

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

6. Application of numerical analysis methods to thermoluminescence dosimetry

International Nuclear Information System (INIS)

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

1989-01-01

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

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

KAUST Repository

Happola, Juho

2017-01-01

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

8. A numerical method for solving singular De`s

Energy Technology Data Exchange (ETDEWEB)

Mahaver, W.T.

1996-12-31

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

9. Resolution of VTI anisotropy with elastic full-waveform inversion: theory and basic numerical examples

Science.gov (United States)

Podgornova, O.; Leaney, S.; Liang, L.

2018-03-01

Extracting medium properties from seismic data faces some limitations due to the finite frequency content of the data and restricted spatial positions of the sources and receivers. Some distributions of the medium properties make low impact on the data (including none). If these properties are used as the inversion parameters, then the inverse problem becomes over-parametrized, leading to ambiguous results. We present an analysis of multiparameter resolution for the linearized inverse problem in the framework of elastic full-waveform inversion. We show that the spatial and multiparameter sensitivities are intertwined and non-sensitive properties are spatial distributions of some non-trivial combinations of the conventional elastic parameters. The analysis accounts for the Hessian information and frequency content of the data; it is semi-analytical (in some scenarios analytical), easy to interpret, and enhances results of the widely used radiation pattern analysis. Single-type scattering is shown to have limited sensitivity, even for full-aperture data. Finite-frequency data lose multiparameter sensitivity at smooth and fine spatial scales. Also, we establish ways to quantify a spatial-multiparameter coupling and demonstrate that the theoretical predictions agree well with the numerical results.

10. A two-dimensional adaptive numerical grids generation method and its realization

International Nuclear Information System (INIS)

Xu Tao; Shui Hongshou

1998-12-01

A two-dimensional adaptive numerical grids generation method and its particular realization is discussed. This method is effective and easy to realize if the control functions are given continuously, and the grids for some regions is showed in this case. For Computational Fluid Dynamics, because the control values of adaptive grids-numerical solution is given in dispersed form, it is needed to interpolate these values to get the continuous control functions. These interpolation techniques are discussed, and some efficient adaptive grids are given. A two-dimensional fluid dynamics example was also given

11. An Effective Numerical Method and Its Utilization to Solution of Fractional Models Used in Bioengineering Applications

Directory of Open Access Journals (Sweden)

Petráš Ivo

2011-01-01

Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.

12. 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

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

International Nuclear Information System (INIS)

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)

14. Numerical methods for Bayesian inference in the face of aging

International Nuclear Information System (INIS)

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

1996-01-01

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

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

International Nuclear Information System (INIS)

Inc, Mustafa

2008-01-01

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

16. Interdisciplinary Study of Numerical Methods and Power Plants Engineering

Directory of Open Access Journals (Sweden)

Ioana OPRIS

2014-08-01

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

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

Directory of Open Access Journals (Sweden)

Henrich Glaser-Opitz

2016-02-01

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

18. Numerical simulation methods for wave propagation through optical waveguides

International Nuclear Information System (INIS)

Sharma, A.

1993-01-01

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

19. APPROBATION OF THE NUMERICAL METHOD OF CALCULATING THE DYNAMIC STRESS-STRAIN STATE OF THE THREE-DIMENSIONAL SYSTEM “FOUNDATION – FACILITY OF THE PRESSURE FRONT HYDRAULIC ENGINEERING STRUCTURE – WATER RESERVOIR” ON THE EXAMPLE OF THE CLUSTER-REGULATOR

Directory of Open Access Journals (Sweden)

Dmitry S. Dmitriev

2018-03-01

Full Text Available In the article, the results of approbation of the developed technique of the refined numerical simula-tion of the dynamic stress-strain state of the three-dimensional system “ground base (earth foundation – reser-voir – construction of the pressure head of the hydraulic system” under seismic influences. A comparison is made between two different ways of modeling the fluid interacting with the structure and the base of the hydroe-lectric power station. The issues of choosing the dimensions of the base unit and taking into account the inertial load from it, as well as the method of determining the initial seismic action, are touched upon.

20. Unified algorithm for partial differential equations and examples of numerical computation

International Nuclear Information System (INIS)

Watanabe, Tsuguhiro

1999-01-01

A new unified algorithm is proposed to solve partial differential equations which describe nonlinear boundary value problems, eigenvalue problems and time developing boundary value problems. The algorithm is composed of implicit difference scheme and multiple shooting scheme and is named as HIDM (Higher order Implicit Difference Method). A new prototype computer programs for 2-dimensional partial differential equations is constructed and tested successfully to several problems. Extension of the computer programs to 3 or more higher order dimension problems will be easy due to the direct product type difference scheme. (author)

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

International Nuclear Information System (INIS)

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

2. Numerical simulation of compressible two-phase flow using a diffuse interface method

International Nuclear Information System (INIS)

2013-01-01

Highlights: ► Compressible two-phase gas–gas and gas–liquid flows simulation are conducted. ► Interface conditions contain shock wave and cavitations. ► A high-resolution diffuse interface method is investigated. ► The numerical results exhibit very good agreement with experimental results. -- Abstract: In this article, a high-resolution diffuse interface method is investigated for simulation of compressible two-phase gas–gas and gas–liquid flows, both in the presence of shock wave and in flows with strong rarefaction waves similar to cavitations. A Godunov method and HLLC Riemann solver is used for discretization of the Kapila five-equation model and a modified Schmidt equation of state (EOS) is used to simulate the cavitation regions. This method is applied successfully to some one- and two-dimensional compressible two-phase flows with interface conditions that contain shock wave and cavitations. The numerical results obtained in this attempt exhibit very good agreement with experimental results, as well as previous numerical results presented by other researchers based on other numerical methods. In particular, the algorithm can capture the complex flow features of transient shocks, such as the material discontinuities and interfacial instabilities, without any oscillation and additional diffusion. Numerical examples show that the results of the method presented here compare well with other sophisticated modeling methods like adaptive mesh refinement (AMR) and local mesh refinement (LMR) for one- and two-dimensional problems

3. 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.

4. High accuracy mantle convection simulation through modern numerical methods

KAUST Repository

Kronbichler, Martin

2012-08-21

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

5. Development of numerical methods for reactive transport; Developpement de methodes numeriques pour le transport reactif

Energy Technology Data Exchange (ETDEWEB)

Bouillard, N

2006-12-15

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

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

International Nuclear Information System (INIS)

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

2003-01-01

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

7. 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...

8. 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...

9. The Economics of Adaptation: Concepts, Methods and Examples

DEFF Research Database (Denmark)

Callaway, John MacIntosh; Naswa, Prakriti; Trærup, Sara Lærke Meltofte

and sectoral level strategies, plans and policies. Furthermore, we see it at the local level, where people are already adapting to the early impacts of climate change that affect livelihoods through, for example, changing rainfall patterns, drought, and frequency and intensity of extreme events. Analyses...... of the costs and benefits of climate change impacts and adaptation measures are important to inform future action. Despite the growth in the volume of research and studies on the economics of climate change adaptation over the past 10 years, there are still important gaps and weaknesses in the existing...... knowledge that limit effective and efficient decision-making and implementation of adaptation measures. Much of the literature to date has focussed on aggregate (national, regional and global) estimates of the economic costs of climate change impacts. There has been much less attention to the economics...

10. Workshop on Numerical Methods for Ordinary Differential Equations

CERN Document Server

Gear, Charles; Russo, Elvira

1989-01-01

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

11. New numerical method for solving the solute transport equation

International Nuclear Information System (INIS)

Ross, B.; Koplik, C.M.

1978-01-01

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

12. 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.

13. A numerical method for complex structural dynamics in nuclear plant facilities

International Nuclear Information System (INIS)

Zeitner, W.

1979-01-01

The solution of dynamic problems is often connected with difficulties in setting up a system of equations of motion because of the constraint conditions of the system. Such constraint conditions may be of geometric nature as for example gaps or slidelines, they may be compatibility conditions or thermodynamic criteria for the energy balance of a system. The numerical method proposed in this paper for the treatment of a dynamic problem with constraint conditions requires only to set up the equations of motion without considering the constraints. This always leads to a relatively simple formulation. The constraint conditions themselves are included in the integration procedure by a numerical application of Gauss' principle. (orig.)

14. Numerical methods and computers used in elastohydrodynamic lubrication

Science.gov (United States)

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

1982-01-01

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

15. Numerical

Directory of Open Access Journals (Sweden)

M. Boumaza

2015-07-01

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

16. Numerical method for the dispersion relation of a hot and inhomogeneous plasma with an electron beam

International Nuclear Information System (INIS)

Devia, A.; Orrego, C.E.; Buitrago, G.

1990-01-01

A numerical method that is based in kinetic theory (Vlasov-Poison equations) was developed in order to calculate the dispersion relation for the interaction between a hot cylindrical and electron beam in any temperature and density. The plasma-beam system is located in a strong magnetic field. Many examples showing the effect of the temperatures and densities on the dispersion relation are given. (Author)

17. 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.

18. 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.

19. 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.

20. Climate Action Gaming Experiment: Methods and Example Results

Directory of Open Access Journals (Sweden)

Clifford Singer

2015-09-01

Full Text Available An exercise has been prepared and executed to simulate international interactions on policies related to greenhouse gases and global albedo management. Simulation participants are each assigned one of six regions that together contain all of the countries in the world. Participants make quinquennial policy decisions on greenhouse gas emissions, recapture of CO2 from the atmosphere, and/or modification of the global albedo. Costs of climate change and of implementing policy decisions impact each region’s gross domestic product. Participants are tasked with maximizing economic benefits to their region while nearly stabilizing atmospheric CO2 concentrations by the end of the simulation in Julian year 2195. Results are shown where regions most adversely affected by effects of greenhouse gas emissions resort to increases in the earth’s albedo to reduce net solar insolation. These actions induce temperate region countries to reduce net greenhouse gas emissions. An example outcome is a trajectory to the year 2195 of atmospheric greenhouse emissions and concentrations, sea level, and global average temperature.

1. Stability of numerical method for semi-linear stochastic pantograph differential equations

Directory of Open Access Journals (Sweden)

Yu Zhang

2016-01-01

Full Text Available Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations. Some suitable conditions for the mean-square stability of an analytical solution are obtained. Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution is stable, then the exponential Euler method applied to the system is mean-square stable for arbitrary step-size h > 0 \$h>0\$ . Numerical examples further illustrate the obtained theoretical results.

2. Numerical analysis of jet breakup behavior using particle method

International Nuclear Information System (INIS)

Shibata, Kazuya; Koshizuka, Seiichi; Oka, Yoshiaki

2002-01-01

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

3. A Method for Snow Reanalysis: The Sierra Nevada (USA) Example

Science.gov (United States)

Girotto, Manuela; Margulis, Steven; Cortes, Gonzalo; Durand, Michael

2017-01-01

This work presents a state-of-the art methodology for constructing snow water equivalent (SWE) reanalysis. The method is comprised of two main components: (1) a coupled land surface model and snow depletion curve model, which is used to generate an ensemble of predictions of SWE and snow cover area for a given set of (uncertain) inputs, and (2) a reanalysis step, which updates estimation variables to be consistent with the satellite observed depletion of the fractional snow cover time series. This method was applied over the Sierra Nevada (USA) based on the assimilation of remotely sensed fractional snow covered area data from the Landsat 5-8 record (1985-2016). The verified dataset (based on a comparison with over 9000 station years of in situ data) exhibited mean and root-mean-square errors less than 3 and 13 cm, respectively, and correlation greater than 0.95 compared with in situ SWE observations. The method (fully Bayesian), resolution (daily, 90-meter), temporal extent (31 years), and accuracy provide a unique dataset for investigating snow processes. This presentation illustrates how the reanalysis dataset was used to provide a basic accounting of the stored snowpack water in the Sierra Nevada over the last 31 years and ultimately improve real-time streamflow predictions.

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

International Nuclear Information System (INIS)

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

2015-01-01

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

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

Science.gov (United States)

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

2018-04-01

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

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

International Nuclear Information System (INIS)

Hirschel, E.H.; Geller, W.

1977-01-01

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

7. Rigid inclusions-Comparison between analytical and numerical methods

International Nuclear Information System (INIS)

Gomez Perez, R.; Melentijevic, S.

2014-01-01

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

8. 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...

9. Adaptive and dynamic meshing methods for numerical simulations

Science.gov (United States)

Acikgoz, Nazmiye

-hoc application of the simulated annealing technique, which improves the likelihood of removing poor elements from the grid. Moreover, a local implementation of the simulated annealing is proposed to reduce the computational cost. Many challenging multi-physics and multi-field problems that are unsteady in nature are characterized by moving boundaries and/or interfaces. When the boundary displacements are large, which typically occurs when implicit time marching procedures are used, degenerate elements are easily formed in the grid such that frequent remeshing is required. To deal with this problem, in the second part of this work, we propose a new r-adaptation methodology. The new technique is valid for both simplicial (e.g., triangular, tet) and non-simplicial (e.g., quadrilateral, hex) deforming grids that undergo large imposed displacements at their boundaries. A two- or three-dimensional grid is deformed using a network of linear springs composed of edge springs and a set of virtual springs. The virtual springs are constructed in such a way as to oppose element collapsing. This is accomplished by confining each vertex to its ball through springs that are attached to the vertex and its projection on the ball entities. The resulting linear problem is solved using a preconditioned conjugate gradient method. The new method is compared with the classical spring analogy technique in two- and three-dimensional examples, highlighting the performance improvements achieved by the new method. Meshes are an important part of numerical simulations. Depending on the geometry and flow conditions, the most suitable mesh for each particular problem is different. Meshes are usually generated by either using a suitable software package or solving a PDE. In both cases, engineering intuition plays a significant role in deciding where clusterings should take place. In addition, for unsteady problems, the gradients vary for each time step, which requires frequent remeshing during simulations

10. Numerical methods for the simulation of continuous sedimentation in ideal clarifier-thickener units

Energy Technology Data Exchange (ETDEWEB)

Buerger, R.; Karlsen, K.H.; Risebro, N.H.; Towers, J.D.

2001-10-01

We consider a model of continuous sedimentation. Under idealizing assumptions, the settling of the solid particles under the influence of gravity can be described by the initial value problem for a nonlinear hyperbolic partial differential equation with a flux function that depends discontinuously on height. The purpose of this contribution is to present and demonstrate two numerical methods for simulating continuous sedimentation: a front tracking method and a finite finite difference method. The basic building blocks in the front tracking method are the solutions of a finite number of certain Riemann problems and a procedure for tracking local collisions of shocks. The solutions of the Riemann problems are recalled herein and the front tracking algorithm is described. As an alternative to the front tracking method, a simple scalar finite difference algorithm is proposed. This method is based on discretizing the spatially varying flux parameters on a mesh that is staggered with respect to that of the conserved variable, resulting in a straightforward generalization of the well-known Engquist-Osher upwind finite difference method. The result is an easily implemented upwind shock capturing method. Numerical examples demonstrate that the front tracking and finite difference methods can be used as efficient and accurate simulation tools for continuous sedimentation. The numerical results for the finite difference method indicate that discontinuities in the local solids concentration are resolved sharply and agree with those produced by the front tracking method. The latter is free of numerical dissipation, which leads to sharply resolved concentration discontinuities, but is more complicated to implement than the former. Available mathematical results for the proposed numerical methods are also briefly reviewed. (author)

11. 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

12. Uniqueness and numerical methods in inverse obstacle scattering

International Nuclear Information System (INIS)

Kress, Rainer

2007-01-01

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

13. Teaching Research Methods and Statistics in eLearning Environments: Pedagogy, Practical Examples, and Possible Futures

Science.gov (United States)

Rock, Adam J.; Coventry, William L.; Morgan, Methuen I.; Loi, Natasha M.

2016-01-01

Generally, academic psychologists are mindful of the fact that, for many students, the study of research methods and statistics is anxiety provoking (Gal et al., 1997). Given the ubiquitous and distributed nature of eLearning systems (Nof et al., 2015), teachers of research methods and statistics need to cultivate an understanding of how to effectively use eLearning tools to inspire psychology students to learn. Consequently, the aim of the present paper is to discuss critically how using eLearning systems might engage psychology students in research methods and statistics. First, we critically appraise definitions of eLearning. Second, we examine numerous important pedagogical principles associated with effectively teaching research methods and statistics using eLearning systems. Subsequently, we provide practical examples of our own eLearning-based class activities designed to engage psychology students to learn statistical concepts such as Factor Analysis and Discriminant Function Analysis. Finally, we discuss general trends in eLearning and possible futures that are pertinent to teachers of research methods and statistics in psychology. PMID:27014147

14. Teaching Research Methods and Statistics in eLearning Environments: Pedagogy, Practical Examples, and Possible Futures.

Science.gov (United States)

Rock, Adam J; Coventry, William L; Morgan, Methuen I; Loi, Natasha M

2016-01-01

Generally, academic psychologists are mindful of the fact that, for many students, the study of research methods and statistics is anxiety provoking (Gal et al., 1997). Given the ubiquitous and distributed nature of eLearning systems (Nof et al., 2015), teachers of research methods and statistics need to cultivate an understanding of how to effectively use eLearning tools to inspire psychology students to learn. Consequently, the aim of the present paper is to discuss critically how using eLearning systems might engage psychology students in research methods and statistics. First, we critically appraise definitions of eLearning. Second, we examine numerous important pedagogical principles associated with effectively teaching research methods and statistics using eLearning systems. Subsequently, we provide practical examples of our own eLearning-based class activities designed to engage psychology students to learn statistical concepts such as Factor Analysis and Discriminant Function Analysis. Finally, we discuss general trends in eLearning and possible futures that are pertinent to teachers of research methods and statistics in psychology.

15. Numerical proceessing of radioimmunoassay results using logit-log transformation method

International Nuclear Information System (INIS)

Textoris, R.

1983-01-01

The mathematical model and algorithm are described of the numerical processing of the results of a radioimmunoassay by the logit-log transformation method and by linear regression with weight factors. The limiting value of the curve for zero concentration is optimized with regard to the residual sum by the iterative method by multiple repeats of the linear regression. Typical examples are presented of the approximation of calibration curves. The method proved suitable for all hitherto used RIA sets and is well suited for small computers with internal memory of min. 8 Kbyte. (author)

International Nuclear Information System (INIS)

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

1985-01-01

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

17. Numerical Verification Methods for Spherical \$t\$-Designs

OpenAIRE

Chen, Xiaojun

2009-01-01

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

18. 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

19. Examples of Applications of Vortex Methods to Wind Energy

DEFF Research Database (Denmark)

Branlard, Emmanuel Simon Pierre

2017-01-01

The current chapter presents wind-energy simulations obtained with the vortex code OmniVor (described in Chap. 44 ) and compared to BEM, CFD and measurements. The chapter begins by comparing rotor loads obtained with vortex methods, BEM and actuator-line simulations of wind turbines under uniform...... and yawed inflows. The second section compares wakes and flow fields obtained by actuator-disk simulations and a free-wake vortex code that uses vortex segments and vortex particles. The third section compares different implementations of viscous diffusion models and investigate their effects...

20. Numerical simulation methods for electron and ion optics

International Nuclear Information System (INIS)

Munro, Eric

2011-01-01

This paper summarizes currently used techniques for simulation and computer-aided design in electron and ion beam optics. Topics covered include: field computation, methods for computing optical properties (including Paraxial Rays and Aberration Integrals, Differential Algebra and Direct Ray Tracing), simulation of Coulomb interactions, space charge effects in electron and ion sources, tolerancing, wave optical simulations and optimization. Simulation examples are presented for multipole aberration correctors, Wien filter monochromators, imaging energy filters, magnetic prisms, general curved axis systems and electron mirrors.

1. 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.

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

Science.gov (United States)

Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

2015-08-01

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

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

International Nuclear Information System (INIS)

Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

2015-01-01

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

4. On the methods and examples of aircraft impact analysis

International Nuclear Information System (INIS)

Arros, J.

2012-01-01

Conclusions: Aircraft impact analysis can be performed today within feasible run times using PCs and available advanced commercial finite element software tools. Adequate element and material model technologies exist. Explicit time integration enables analysis of very large deformation Missile/Target impacts. Meshless/particle based methods may be beneficial for large deformation concrete “punching shear” analysis – potentially solves the “element erosion” problem associated with FE, but are not generally implemented yet in major commercial software. Verification of the complicated modeling technologies continues to be a challenge. Not much work has been done yet on ACI shock loading – redundant and physically separated safety trains key to success. Analysis approach and detail should be “balanced” - commensurate with the significant uncertainties - do not “over-do” details of some parts of the model (e.g., the plane) and the analysis

5. Liability for oil spill damages: issues, methods, and examples

International Nuclear Information System (INIS)

Grigalunas, T.A.; Opaluch, J.J.; Diamantides, J.; Mazzotta, M.

1998-01-01

Liability is an important incentive-based instrument for preventing oil spills and provides a sustainable approach for restoring coastal resources injured by spills. However, the use of liability for environmental damages raises many challenges, including quantification of money measures of damages. In this article, case studies are used to illustrate the issues, methods, and challenges associated with assessing a range of damages, from those that can be measured relatively easily using market information to more 'esoteric', and much more difficult, cases involving non-market-valued losses. Also discussed are issues raised by the new national and international regulatory focus on restoration and by the simplified, compensatory formula used by some states. (author)

6. Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies

Energy Technology Data Exchange (ETDEWEB)

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

2014-09-01

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

7. Numerical experiment on finite element method for matching data

International Nuclear Information System (INIS)

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

1993-03-01

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

8. 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)

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

Science.gov (United States)

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

2015-05-01

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

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

International Nuclear Information System (INIS)

Lee, Jooyoung; Kosterlitz, J.M.

1991-11-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Lucas, D.S.

2004-10-03

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

12. Method and data analysis example of fatigue tests

International Nuclear Information System (INIS)

Nogami, Shuhei

2015-01-01

In the design and operation of a nuclear fusion reactor, it is important to accurately assess the fatigue life. Fatigue life is evaluated by preparing a database on the relationship between the added stress / strain amplitude and the number of cycles to failure based on the fatigue tests on standard specimens, and by comparing this relationship with the generated stress / strain of the actual constructions. This paper mainly chooses low-cycle fatigue as an object, and explains standard test methods, fatigue limit, life prediction formula and the like. Using reduced-activation ferrite steel F82H as a material, strain controlled low-cycle fatigue test was performed under room temperature atmosphere. From these results, the relationship between strain and the number of cycles to failure was analyzed. It was found that the relationship is asymptotic to the formula of Coffin-Manson Law under high-strain (low-cycle condition), and asymptotic to the formula of Basquin Law under low-strain (high-cycle condition). For F82H to be used for the blanket of a nuclear fusion prototype reactor, the arrangement of fatigue life data up to about 700°C and the establishment of optimal fatigue design curves are urgent tasks. As for fusion reactor structural materials, the evaluation of neutron irradiation effect on fatigue damage behavior and life is indispensable. For this purpose, it is necessary to establish standardized testing techniques when applied to small specimens. (A.O.)

13. Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods

International Nuclear Information System (INIS)

Ernst, Frederick J

2007-01-01

metric tensor components. The first two chapters of this book are devoted to some basic ideas: in the introductory chapter 1 the authors discuss the concept of integrability, comparing the integrability of the vacuum Ernst equation with the integrability of nonlinear equations of Korteweg-de Vries (KdV) type, while in chapter 2 they describe various circumstances in which the vacuum Ernst equation has been determined to be relevant, not only in connection with gravitation but also, for example, in the construction of solutions of the self-dual Yang-Mills equations. It is also in this chapter that one of several equivalent linear systems for the Ernst equation is described. The next two chapters are devoted to Dmitry Korotkin's concept of algebro-geometric solutions of a linear system: in chapter 3 the structure of such solutions of the vacuum Ernst equation, which involve Riemann theta functions of hyperelliptic algebraic curves of any genus, is contrasted with the periodic structure of such solutions of the KdV equation. How such solutions can be obtained, for example, by solving a matrix Riemann-Hilbert problem and how the metric tensor of the associated spacetime can be evaluated is described in detail. In chapter 4 the asymptotic behaviour and the similarity structure of the general algebro-geometric solutions of the Ernst equation are described, and the relationship of such solutions to the perhaps more familiar multi-soliton solutions is discussed. The next three chapters are based upon the authors' own published research: in chapter 5 it is shown that a problem involving counter-rotating infinitely thin disks of matter can be solved in terms of genus two Riemann theta functions, while in chapter 6 the authors describe numerical methods that facilitate the construction of such solutions, and in chapter 7 three-dimensional graphs are displayed that depict all metrical fields of the associated spacetime. Finally, in chapter 8, the difficulties associated with

14. BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

Science.gov (United States)

Katsaounis, T. D.

2005-02-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using

15. 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.

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

Directory of Open Access Journals (Sweden)

R. Grzymkowski

2011-07-01

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

17. 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.)

18. 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

19. 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.

20. 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)

1. Introducing Geoscience Students to Numerical Modeling of Volcanic Hazards: The example of Tephra2 on VHub.org

Directory of Open Access Journals (Sweden)

Leah M. Courtland

2012-07-01

Full Text Available The Tephra2 numerical model for tephra fallout from explosive volcanic eruptions is specifically designed to enable students to probe ideas in model literacy, including code validation and verification, the role of simplifying assumptions, and the concepts of uncertainty and forecasting. This numerical model is implemented on the VHub.org website, a venture in cyberinfrastructure that brings together volcanological models and educational materials. The VHub.org resource provides students with the ability to explore and execute sophisticated numerical models like Tephra2. We present a strategy for using this model to introduce university students to key concepts in the use and evaluation of Tephra2 for probabilistic forecasting of volcanic hazards. Through this critical examination students are encouraged to develop a deeper understanding of the applicability and limitations of hazard models. Although the model and applications are intended for use in both introductory and advanced geoscience courses, they could easily be adapted to work in other disciplines, such as astronomy, physics, computational methods, data analysis, or computer science.

2. Development of numerical methods for reactive transport; Developpement de methodes numeriques pour le transport reactif

Energy Technology Data Exchange (ETDEWEB)

Bouillard, N

2006-12-15

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

3. 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)

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

International Nuclear Information System (INIS)

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

2007-01-01

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

5. Numerical Simulation of Plasma Antenna with FDTD Method

International Nuclear Information System (INIS)

Chao, Liang; Yue-Min, Xu; Zhi-Jiang, Wang

2008-01-01

We adopt cylindrical-coordinate FDTD algorithm to simulate and analyse a 0.4-m-long column configuration plasma antenna. FDTD method is useful for solving electromagnetic problems, especially when wave characteristics and plasma properties are self-consistently related to each other. Focus on the frequency from 75 MHz to 400 MHz, the input impedance and radiation efficiency of plasma antennas are computed. Numerical results show that, different from copper antenna, the characteristics of plasma antenna vary simultaneously with plasma frequency and collision frequency. The property can be used to construct dynamically reconBgurable antenna. The investigation is meaningful and instructional for the optimization of plasma antenna design

6. Numerical simulation of plasma antenna with FDTD method

International Nuclear Information System (INIS)

Liang Chao; Xu Yuemin; Wang Zhijiang

2008-01-01

We adopt cylindrical-coordinate FDTD algorithm to simulate and analyse a 0.4-m-long column configuration plasma antenna. FDTD method is useful for solving electromagnetic problems, especially when wave characteristics and plasma properties are self-consistently related to each other. Focus on the frequency from 75 MHz to 400 MHz, the input impedance and radiation efficiency of plasma antennas are computed. Numerical results show that, different from copper antenna, the characteristics of plasma antenna vary simultaneously with plasma frequency and collision frequency. The property can be used to construct dynamically reconfigurable antenna. The investigation is meaningful and instructional for the optimization of plasma antenna design. (authors)

7. Uncertainties related to numerical methods for neutron spectra unfolding

International Nuclear Information System (INIS)

Glodic, S.; Ninkovic, M.; Adarougi, N.A.

1987-10-01

One of the often used techniques for neutron detection in radiation protection utilities is the Bonner multisphere spectrometer. Besides its advantages and universal applicability for evaluating integral parameters of neutron fields in health physics practices, the outstanding problems of the method are data analysis and the accuracy of the results. This paper briefly discusses some numerical problems related to neutron spectra unfolding, such as uncertainty of the response matrix as a source of error, and the possibility of real time data reduction using spectrometers. (author)

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

Directory of Open Access Journals (Sweden)

Ali BEAZIT

2010-06-01

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

9. 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

10. Bayesian Methods for the Physical Sciences. Learning from Examples in Astronomy and Physics.

Science.gov (United States)

Andreon, Stefano; Weaver, Brian

2015-05-01

Chapter 1: This chapter presents some basic steps for performing a good statistical analysis, all summarized in about one page. Chapter 2: This short chapter introduces the basics of probability theory inan intuitive fashion using simple examples. It also illustrates, again with examples, how to propagate errors and the difference between marginal and profile likelihoods. Chapter 3: This chapter introduces the computational tools and methods that we use for sampling from the posterior distribution. Since all numerical computations, and Bayesian ones are no exception, may end in errors, we also provide a few tips to check that the numerical computation is sampling from the posterior distribution. Chapter 4: Many of the concepts of building, running, and summarizing the resultsof a Bayesian analysis are described with this step-by-step guide using a basic (Gaussian) model. The chapter also introduces examples using Poisson and Binomial likelihoods, and how to combine repeated independent measurements. Chapter 5: All statistical analyses make assumptions, and Bayesian analyses are no exception. This chapter emphasizes that results depend on data and priors (assumptions). We illustrate this concept with examples where the prior plays greatly different roles, from major to negligible. We also provide some advice on how to look for information useful for sculpting the prior. Chapter 6: In this chapter we consider examples for which we want to estimate more than a single parameter. These common problems include estimating location and spread. We also consider examples that require the modeling of two populations (one we are interested in and a nuisance population) or averaging incompatible measurements. We also introduce quite complex examples dealing with upper limits and with a larger-than-expected scatter. Chapter 7: Rarely is a sample randomly selected from the population we wish to study. Often, samples are affected by selection effects, e.g., easier

11. Between Certainty and Uncertainty Statistics and Probability in Five Units with Notes on Historical Origins and Illustrative Numerical Examples

CERN Document Server

Laudański, Ludomir M

2013-01-01

„Between Certainty & Uncertainty” is a one-of–a-kind short course on statistics for students, engineers  and researchers.  It is a fascinating introduction to statistics and probability with notes on historical origins and 80 illustrative numerical examples organized in the five units:   ·         Chapter 1  Descriptive Statistics:  Compressing small samples, basic averages - mean and variance, their main properties including God’s proof; linear transformations and z-scored statistics .   ·         Chapter 2 Grouped data: Udny Yule’s concept of qualitative and quantitative variables. Grouping these two kinds of data. Graphical tools. Combinatorial rules and qualitative variables.  Designing frequency histogram. Direct and coded evaluation of quantitative data. Significance of percentiles.   ·         Chapter 3 Regression and correlation: Geometrical distance and equivalent distances in two orthogonal directions  as a prerequisite to the concept of two regressi...

12. Research development and teaching of numerical methods at the Atomic Centre of Bariloche, Argentina

International Nuclear Information System (INIS)

Pissanetzky, S.; Sarmiento, G.S.

1981-01-01

The areas of study of numerical methods, particularly the finite element method, are listed. These include numerical simulation of the thermo-mechanical behaviour of nuclear fuel elements and of the heat transfer in the industrial processing of sheaths for nuclear fuel cladding. Computer programs to support these studies are listed. Two examples of applications of these programs are given. The first is the modelling of high-vacuum annealing furnaces, particularly those used to manufacture zircaloy tubes for reactor sheaths. The second is the modelling of localized thermochemical problems in nuclear fuel elements and other nuclear reactor components. Details of where to obtain further information of work covered in this summary are given. (U.K.)

13. 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.

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

Energy Technology Data Exchange (ETDEWEB)

D. S. Lucas

2004-10-01

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

15. Numerical evaluation of methods for computing tomographic projections

International Nuclear Information System (INIS)

Zhuang, W.; Gopal, S.S.; Hebert, T.J.

1994-01-01

Methods for computing forward/back projections of 2-D images can be viewed as numerical integration techniques. The accuracy of any ray-driven projection method can be improved by increasing the number of ray-paths that are traced per projection bin. The accuracy of pixel-driven projection methods can be increased by dividing each pixel into a number of smaller sub-pixels and projecting each sub-pixel. The authors compared four competing methods of computing forward/back projections: bilinear interpolation, ray-tracing, pixel-driven projection based upon sub-pixels, and pixel-driven projection based upon circular, rather than square, pixels. This latter method is equivalent to a fast, bi-nonlinear interpolation. These methods and the choice of the number of ray-paths per projection bin or the number of sub-pixels per pixel present a trade-off between computational speed and accuracy. To solve the problem of assessing backprojection accuracy, the analytical inverse Fourier transform of the ramp filtered forward projection of the Shepp and Logan head phantom is derived

16. A first course in ordinary differential equations analytical and numerical methods

CERN Document Server

Hermann, Martin

2014-01-01

This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed t...

17. Quantitative numerical method for analysing slip traces observed by AFM

International Nuclear Information System (INIS)

Veselý, J; Cieslar, M; Coupeau, C; Bonneville, J

2013-01-01

Atomic force microscopy (AFM) is used more and more routinely to study, at the nanometre scale, the slip traces produced on the surface of deformed crystalline materials. Taking full advantage of the quantitative height data of the slip traces, which can be extracted from these observations, requires however an adequate and robust processing of the images. In this paper an original method is presented, which allows the fitting of AFM scan-lines with a specific parameterized step function without any averaging treatment of the original data. This yields a quantitative and full description of the changes in step shape along the slip trace. The strength of the proposed method is established on several typical examples met in plasticity by analysing nano-scale structures formed on the sample surface by emerging dislocations. (paper)

18. The solitary wave solution of coupled Klein-Gordon-Zakharov equations via two different numerical methods

Science.gov (United States)

2013-09-01

In this research, we propose two different methods to solve the coupled Klein-Gordon-Zakharov (KGZ) equations: the Differential Quadrature (DQ) and Globally Radial Basis Functions (GRBFs) methods. In the DQ method, the derivative value of a function with respect to a point is directly approximated by a linear combination of all functional values in the global domain. The principal work in this method is the determination of weight coefficients. We use two ways for obtaining these coefficients: cosine expansion (CDQ) and radial basis functions (RBFs-DQ), the former is a mesh-based method and the latter categorizes in the set of meshless methods. Unlike the DQ method, the GRBF method directly substitutes the expression of the function approximation by RBFs into the partial differential equation. The main problem in the GRBFs method is ill-conditioning of the interpolation matrix. Avoiding this problem, we study the bases introduced in Pazouki and Schaback (2011) [44]. Some examples are presented to compare the accuracy and easy implementation of the proposed methods. In numerical examples, we concentrate on Inverse Multiquadric (IMQ) and second-order Thin Plate Spline (TPS) radial basis functions. The variable shape parameter (exponentially and random) strategies are applied in the IMQ function and the results are compared with the constant shape parameter.

International Nuclear Information System (INIS)

Neuman, S.P.

1983-01-01

Radionuclide transport in the subsurface is often modeled with the aid of the advection-dispersion equation. A review of existing computer methods for the solution of this equation shows that there is need for improvement. To answer this need, a new adaptive numerical method is proposed based on an Eulerian-Lagrangian formulation. The method is based on a decomposition of the concentration field into two parts, one advective and one dispersive, in a rigorous manner that does not leave room for ambiguity. The advective component of steep concentration fronts is tracked forward with the aid of moving particles clustered around each front. Away from such fronts the advection problem is handled by an efficient modified method of characteristics called single-step reverse particle tracking. When a front dissipates with time, its forward tracking stops automatically and the corresponding cloud of particles is eliminated. The dispersion problem is solved by an unconventional Lagrangian finite element formulation on a fixed grid which involves only symmetric and diagonal matrices. Preliminary tests against analytical solutions of ne- and two-dimensional dispersion in a uniform steady state velocity field suggest that the proposed adaptive method can handle the entire range of Peclet numbers from 0 to infinity, with Courant numbers well in excess of 1

20. Single-Phase Full-Wave Rectifier as an Effective Example to Teach Normalization, Conduction Modes, and Circuit Analysis Methods

Directory of Open Access Journals (Sweden)

Predrag Pejovic

2013-12-01

Full Text Available Application of a single phase rectifier as an example in teaching circuit modeling, normalization, operating modes of nonlinear circuits, and circuit analysis methods is proposed.The rectifier supplied from a voltage source by an inductive impedance is analyzed in the discontinuous as well as in the continuous conduction mode. Completely analytical solution for the continuous conduction mode is derived. Appropriate numerical methods are proposed to obtain the circuit waveforms in both of the operating modes, and to compute the performance parameters. Source code of the program that performs such computation is provided.

1. Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

International Nuclear Information System (INIS)

Katsaounis, T D

2005-01-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall

2. Numerical simulations of a family of the coupled viscous Burgers, equation using the lattice Boltzmann method

International Nuclear Information System (INIS)

He, Y B; Tang, X H

2016-01-01

In this paper, in order to extend the lattice Boltzmann method (LBM) to deal with more nonlinear systems, a one-dimensional and five-velocity lattice Boltzmann scheme with an amending function for a family of the coupled viscous Burgers’ equation (CVBE) is proposed. With the Taylor and Chapman–Enskog expansion, a family of the CVBE is recovered correctly from the lattice Boltzmann equation through selecting the equilibrium distribution functions and amending functions properly. The method is applied to some test examples with an analytical solution. The results are compared with those obtained by the finite difference method (FDM); it is shown that the numerical solutions agree well with the analytical solutions and the errors obtained by the present method are smaller than the FDM. Furthermore, some problems without analytical solutions are numerically studied by the present method and the FDM. The results show that the numerical solutions of the LBM are in good agreement with those obtained by the FDM, which can validate the effectiveness and stability of the LBM. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

3. Numerical approximations of nonlinear fractional differential difference equations by using modified He-Laplace method

Directory of Open Access Journals (Sweden)

J. Prakash

2016-03-01

Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.

4. 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.

5. Classical and quantum aspects of topological solitons (using numerical methods)

International Nuclear Information System (INIS)

Weidig, T.

1999-08-01

In Introduction, we review integrable and topological solitons. In Numerical Methods, we describe how to minimise functionals, time-integrate configurations and solve eigenvalue problems. We also present the Simulated Annealing scheme for minimisation in solitonic systems. In Classical Aspects, we analyse the effect of the potential term on the structure of minimal-energy solutions for any topological charge n. The simplest holomorphic baby Skyrme model has no known stable minimal-energy solution for n > 1. The one-vacuum baby Skyrme model possesses non-radially symmetric multi-skyrmions that look like 'skyrmion lattices' formed by skyrmions with n = 2. The two-vacua baby Skyrme model has radially symmetric multi-skyrmions. We implement Simulated Annealing and it works well for higher order terms. We find that the spatial part of the six-derivative term is zero. In Quantum Aspects, we find the first order quantum mass correction for the φ 4 kink using the semi-classical expansion. We derive a trace formula which gives the mass correction by using the eigenmodes and values of the soliton and vacuum perturbations. We show that the zero mode is the most important contribution. We compute the mass correction of φ 4 kink and Sine-Gordon numerically by solving the eigenvalue equations and substituting into the trace formula. (author)

6. Comparison between numeric and approximate analytic solutions for the prediction of soil metal uptake by roots. Example of cadmium.

Science.gov (United States)

Schneider, André; Lin, Zhongbing; Sterckeman, Thibault; Nguyen, Christophe

2018-04-01

The dissociation of metal complexes in the soil solution can increase the availability of metals for root uptake. When it is accounted for in models of bioavailability of soil metals, the number of partial differential equations (PDEs) increases and the computation time to numerically solve these equations may be problematic when a large number of simulations are required, for example for sensitivity analyses or when considering root architecture. This work presents analytical solutions for the set of PDEs describing the bioavailability of soil metals including the kinetics of complexation for three scenarios where the metal complex in solution was fully inert, fully labile, or partially labile. The analytical solutions are only valid i) at steady-state when the PDEs become ordinary differential equations, the transient phase being not covered, ii) when diffusion is the major mechanism of transport and therefore, when convection is negligible, iii) when there is no between-root competition. The formulation of the analytical solutions is for cylindrical geometry but the solutions rely on the spread of the depletion profile around the root, which was modelled assuming a planar geometry. The analytical solutions were evaluated by comparison with the corresponding PDEs for cadmium in the case of the French agricultural soils. Provided that convection was much lower than diffusion (Péclet's number<0.02), the cumulative uptakes calculated from the analytic solutions were in very good agreement with those calculated from the PDEs, even in the case of a partially labile complex. The analytic solutions can be used instead of the PDEs to predict root uptake of metals. The analytic solutions were also used to build an indicator of the contribution of a complex to the uptake of the metal by roots, which can be helpful to predict the effect of soluble organic matter on the bioavailability of soil metals. Copyright © 2017 Elsevier B.V. All rights reserved.

7. Mathematical analysis and numerical methods for science and technology

CERN Document Server

Dautray, Robert

These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which ...

8. Numerical methods for Eulerian and Lagrangian conservation laws

CERN Document Server

Després, Bruno

2017-01-01

This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.

9. Numerical methods for two-phase flow with contact lines

Energy Technology Data Exchange (ETDEWEB)

Walker, Clauido

2012-07-01

This thesis focuses on numerical methods for two-phase flows, and especially flows with a moving contact line. Moving contact lines occur where the interface between two fluids is in contact with a solid wall. At the location where both fluids and the wall meet, the common continuum descriptions for fluids are not longer valid, since the dynamics around such a contact line are governed by interactions at the molecular level. Therefore the standard numerical continuum models have to be adjusted to handle moving contact lines. In the main part of the thesis a method to manipulate the position and the velocity of a contact line in a two-phase solver, is described. The Navier-Stokes equations are discretized using an explicit finite difference method on a staggered grid. The position of the interface is tracked with the level set method and the discontinuities at the interface are treated in a sharp manner with the ghost fluid method. The contact line is tracked explicitly and its dynamics can be described by an arbitrary function. The key part of the procedure is to enforce a coupling between the contact line and the Navier-Stokes equations as well as the level set method. Results for different contact line models are presented and it is demonstrated that they are in agreement with analytical solutions or results reported in the literature.The presented Navier-Stokes solver is applied as a part in a multiscale method to simulate capillary driven flows. A relation between the contact angle and the contact line velocity is computed by a phase field model resolving the micro scale dynamics in the region around the contact line. The relation of the microscale model is then used to prescribe the dynamics of the contact line in the macro scale solver. This approach allows to exploit the scale separation between the contact line dynamics and the bulk flow. Therefore coarser meshes can be applied for the macro scale flow solver compared to global phase field simulations

10. Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods

KAUST Repository

2017-09-10

In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).

11. Stability analysis of single-phase thermosyphon loops by finite difference numerical methods

International Nuclear Information System (INIS)

Ambrosini, W.

1998-01-01

In this paper, examples of the application of finite difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is here addressed for its relevance for thermal-hydraulic system code applications, in the aim to point out the effect of truncation error on stability prediction. The methodology adopted for analysing in a systematic way the effect of various finite difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the field of validity of model assumptions. (author). 14 refs., 8 figs

12. Mathematical and numerical methods for partial differential equations applications for engineering sciences

CERN Document Server

2014-01-01

This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material, as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic

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

Energy Technology Data Exchange (ETDEWEB)

Chartier, Timothy P.

2011-03-08

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

14. Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters

KAUST Repository

Kou, Jisheng

2015-07-16

In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton\\'s method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.

15. Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2015-01-01

In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton's method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.

16. Bayesian methods for the physical sciences learning from examples in astronomy and physics

CERN Document Server

Andreon, Stefano

2015-01-01

Statistical literacy is critical for the modern researcher in Physics and Astronomy. This book empowers researchers in these disciplines by providing the tools they will need to analyze their own data. Chapters in this book provide a statistical base from which to approach new problems, including numerical advice and a profusion of examples. The examples are engaging analyses of real-world problems taken from modern astronomical research. The examples are intended to be starting points for readers as they learn to approach their own data and research questions. Acknowledging that scientific progress now hinges on the availability of data and the possibility to improve previous analyses, data and code are distributed throughout the book. The JAGS symbolic language used throughout the book makes it easy to perform Bayesian analysis and is particularly valuable as readers may use it in a myriad of scenarios through slight modifications.

17. 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.

18. 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.

19. Numerical methods for incompressible viscous flows with engineering applications

Science.gov (United States)

Rose, M. E.; Ash, R. L.

1988-01-01

A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

20. Mathematical and Numerical Methods for Non-linear Beam Dynamics

International Nuclear Information System (INIS)

Herr, W

2014-01-01

Non-linear effects in accelerator physics are important for both successful operation of accelerators and during the design stage. Since both of these aspects are closely related, they will be treated together in this overview. Some of the most important aspects are well described by methods established in other areas of physics and mathematics. The treatment will be focused on the problems in accelerators used for particle physics experiments. Although the main emphasis will be on accelerator physics issues, some of the aspects of more general interest will be discussed. In particular, we demonstrate that in recent years a framework has been built to handle the complex problems in a consistent form, technically superior and conceptually simpler than the traditional techniques. The need to understand the stability of particle beams has substantially contributed to the development of new techniques and is an important source of examples which can be verified experimentally. Unfortunately, the documentation of these developments is often poor or even unpublished, in many cases only available as lectures or conference proceedings

1. Numerical Simulation of Tubular Pumping Systems with Different Regulation Methods

Science.gov (United States)

Zhu, Honggeng; Zhang, Rentian; Deng, Dongsheng; Feng, Xusong; Yao, Linbi

2010-06-01

Since the flow in tubular pumping systems is basically along axial direction and passes symmetrically through the impeller, most satisfying the basic hypotheses in the design of impeller and having higher pumping system efficiency in comparison with vertical pumping system, they are being widely applied to low-head pumping engineering. In a pumping station, the fluctuation of water levels in the sump and discharge pool is most common and at most time the pumping system runs under off-design conditions. Hence, the operation of pump has to be flexibly regulated to meet the needs of flow rates, and the selection of regulation method is as important as that of pump to reduce operation cost and achieve economic operation. In this paper, the three dimensional time-averaged Navier-Stokes equations are closed by RNG κ-ɛ turbulent model, and two tubular pumping systems with different regulation methods, equipped with the same pump model but with different designed system structures, are numerically simulated respectively to predict the pumping system performances and analyze the influence of regulation device and help designers make final decision in the selection of design schemes. The computed results indicate that the pumping system with blade-adjusting device needs longer suction box, and the increased hydraulic loss will lower the pumping system efficiency in the order of 1.5%. The pumping system with permanent magnet motor, by means of variable speed regulation, obtains higher system efficiency partly for shorter suction box and partly for different structure design. Nowadays, the varied speed regulation is realized by varied frequency device, the energy consumption of which is about 3˜4% of output power of the motor. Hence, when the efficiency of variable frequency device is considered, the total pumping system efficiency will probably be lower.

2. Numerical Methods for Pricing American Options with Time-Fractional PDE Models

Directory of Open Access Journals (Sweden)

Zhiqiang Zhou

2016-01-01

Full Text Available In this paper we develop a Laplace transform method and a finite difference method for solving American option pricing problem when the change of the option price with time is considered as a fractal transmission system. In this scenario, the option price is governed by a time-fractional partial differential equation (PDE with free boundary. The Laplace transform method is applied to the time-fractional PDE. It then leads to a nonlinear equation for the free boundary (i.e., optimal early exercise boundary function in Laplace space. After numerically finding the solution of the nonlinear equation, the Laplace inversion is used to transform the approximate early exercise boundary into the time space. Finally the approximate price of the American option is obtained. A boundary-searching finite difference method is also proposed to solve the free-boundary time-fractional PDEs for pricing the American options. Numerical examples are carried out to compare the Laplace approach with the finite difference method and it is confirmed that the former approach is much faster than the latter one.

3. High accuracy mantle convection simulation through modern numerical methods

KAUST Repository

Kronbichler, Martin; Heister, Timo; Bangerth, Wolfgang

2012-01-01

Numerical simulation of the processes in the Earth's mantle is a key piece in understanding its dynamics, composition, history and interaction with the lithosphere and the Earth's core. However, doing so presents many practical difficulties related

4. A method of numerically controlled machine part programming

Science.gov (United States)

1970-01-01

Computer program is designed for automatically programmed tools. Preprocessor computes desired tool path and postprocessor computes actual commands causing machine tool to follow specific path. It is used on a Cincinnati ATC-430 numerically controlled machine tool.

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

Energy Technology Data Exchange (ETDEWEB)

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

2005-09-12

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

6. Using Mixed Methods to Analyze Video Data: A Mathematics Teacher Professional Development Example

Science.gov (United States)

DeCuir-Gunby, Jessica T.; Marshall, Patricia L.; McCulloch, Allison W.

2012-01-01

This article uses data from 65 teachers participating in a K-2 mathematics professional development research project as an example of how to analyze video recordings of teachers' classroom lessons using mixed methods. Through their discussion, the authors demonstrate how using a mixed methods approach to classroom video analysis allows researchers…

7. Review of Methods and Approaches for Deriving Numeric ...

Science.gov (United States)

EPA will propose numeric criteria for nitrogen/phosphorus pollution to protect estuaries, coastal areas and South Florida inland flowing waters that have been designated Class I, II and III , as well as downstream protective values (DPVs) to protect estuarine and marine waters. In accordance with the formal determination and pursuant to a subsequent consent decree, these numeric criteria are being developed to translate and implement Florida’s existing narrative nutrient criterion, to protect the designated use that Florida has previously set for these waters, at Rule 62-302.530(47)(b), F.A.C. which provides that “In no case shall nutrient concentrations of a body of water be altered so as to cause an imbalance in natural populations of aquatic flora or fauna.” Under the Clean Water Act and EPA’s implementing regulations, these numeric criteria must be based on sound scientific rationale and reflect the best available scientific knowledge. EPA has previously published a series of peer reviewed technical guidance documents to develop numeric criteria to address nitrogen/phosphorus pollution in different water body types. EPA recognizes that available and reliable data sources for use in numeric criteria development vary across estuarine and coastal waters in Florida and flowing waters in South Florida. In addition, scientifically defensible approaches for numeric criteria development have different requirements that must be taken into consider

8. New method of processing heat treatment experiments with numerical simulation support

Science.gov (United States)

Kik, T.; Moravec, J.; Novakova, I.

2017-08-01

In this work, benefits of combining modern software for numerical simulations of welding processes with laboratory research was described. Proposed new method of processing heat treatment experiments leading to obtaining relevant input data for numerical simulations of heat treatment of large parts was presented. It is now possible, by using experiments on small tested samples, to simulate cooling conditions comparable with cooling of bigger parts. Results from this method of testing makes current boundary conditions during real cooling process more accurate, but also can be used for improvement of software databases and optimization of a computational models. The point is to precise the computation of temperature fields for large scale hardening parts based on new method of temperature dependence determination of the heat transfer coefficient into hardening media for the particular material, defined maximal thickness of processed part and cooling conditions. In the paper we will also present an example of the comparison standard and modified (according to newly suggested methodology) heat transfer coefficient data’s and theirs influence on the simulation results. It shows how even the small changes influence mainly on distribution of temperature, metallurgical phases, hardness and stresses distribution. By this experiment it is also possible to obtain not only input data and data enabling optimization of computational model but at the same time also verification data. The greatest advantage of described method is independence of used cooling media type.

9. Talbot's method for the numerical inversion of Laplace transforms: an implementation for personal computers

International Nuclear Information System (INIS)

Garratt, T.J.

1989-05-01

Safety assessments of radioactive waste disposal require efficient computer models for the important processes. The present paper is based on an efficient computational technique which can be used to solve a wide variety of safety assessment models. It involves the numerical inversion of analytical solutions to the Laplace-transformed differential equations using a method proposed by Talbot. This method has been implemented on a personal computer in a user-friendly manner. The steps required to implement a particular transform and run the program are outlined. Four examples are described which illustrate the flexibility, accuracy and efficiency of the program. The improvements in computational efficiency described in this paper have application to the probabilistic safety assessment codes ESCORT and MASCOT which are currently under development. Also, it is hoped that the present work will form the basis of software for personal computers which could be used to demonstrate safety assessment procedures to a wide audience. (author)

10. Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

2012-01-01

In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

11. A method for the direct generation of comprehensive numerical solar building transfer functions

Energy Technology Data Exchange (ETDEWEB)

Chen, T.Y. [The Hong Kong Polytechnic University (China). Dept. of Building Services Engineering

2003-02-01

This paper describes a method for the direct generation of comprehensive numerical room transfer functions with any derived parameters as output, such as operative temperature or thermal load. Complex conductive, convective and radiant heat transfer processes, or any derived thermal parameters in buildings can be explicitly and precisely described by a generalized thermal network. This allows the s-transfer and z-transfer functions to be directly generated, using semi-symbolic analysis techniques, Cayley's expansion of determinant and Heaviside's expansion theorem. A simple algorithm is developed for finding the roots of the denominator in the inverse transform of the s-transfer functions, which ensures that no single root is missing. The techniques have been applied to generating the transfer functions of a passive solar room with floor heating. The example calculation demonstrates the high efficiency of the computational method. (author)

12. 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.

13. Numerical simulation methods to richtmyer-meshkov instabilities

International Nuclear Information System (INIS)

Zhou Ning; Yu Yan; Tang Weijun

2003-01-01

Front tracking algorithms have generally assumed that the computational medium is divided into piece-wise smooth subdomains bounded by interfaces and that strong wave interactions are solved via Riemann solutions. However, in multi-dimensional cases, the Riemann solution of multiple shock wave interactions are far more complicated and still subject to analytical study. For this reason, it is very desirable to be able to track contact discontinuities only. A new numerical algorithm to couple a tracked contact surface and an untracked strong shock wave are described. The new tracking algorithm reduces the complication of computation, and maintains the sharp resolution of the contact surface. The numerical results are good. (authors)

14. 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

15. 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

16. Applying multi-resolution numerical methods to geodynamics

Science.gov (United States)

Davies, David Rhodri

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

17. Computer programs of information processing of nuclear physical methods as a demonstration material in studying nuclear physics and numerical methods

Science.gov (United States)

Bateev, A. B.; Filippov, V. P.

2017-01-01

The principle possibility of using computer program Univem MS for Mössbauer spectra fitting as a demonstration material at studying such disciplines as atomic and nuclear physics and numerical methods by students is shown in the article. This program is associated with nuclear-physical parameters such as isomer (or chemical) shift of nuclear energy level, interaction of nuclear quadrupole moment with electric field and of magnetic moment with surrounded magnetic field. The basic processing algorithm in such programs is the Least Square Method. The deviation of values of experimental points on spectra from the value of theoretical dependence is defined on concrete examples. This value is characterized in numerical methods as mean square deviation. The shape of theoretical lines in the program is defined by Gaussian and Lorentzian distributions. The visualization of the studied material on atomic and nuclear physics can be improved by similar programs of the Mössbauer spectroscopy, X-ray Fluorescence Analyzer or X-ray diffraction analysis.

18. The Navier-Stokes Equations Theory and Numerical Methods

CERN Document Server

Masuda, Kyûya; Rautmann, Reimund; Solonnikov, Vsevolod

1990-01-01

These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.

19. On Numerical Methods in Non-Newtonian Flows

International Nuclear Information System (INIS)

Fileas, G.

1982-12-01

The constitutive equations for non-Newtonian flows are presented and the various flow models derived from continuum mechanics and molecular theories are considered and evaluated. Detailed account is given of numerical simulation employing differential and integral models of different kinds of non-Newtonian flows using finite-difference and finite-element techniques. Appreciating the fact that no book or concentrated material on Numerical Non-Newtonian Fluid Flow exists at the present, procedures for computer set-ups are described and references are given for finite-difference, finite-element and molecular-theory based programmes for several kinds of flow. Achievements and unreached goals in the field of numerical simulation of non-Newtonian flows are discussed and the lack of numerical work in the fields of suspension flows and heat transfer is pointed out. Finally, FFOCUS is presented as a newly built computer program which can simulate freezing flows on Newtonian fluids through various geometries and is aimed to be further developed to handle non-Newtonian freezing flows and certain types of suspension phenomena involved in corium flow after a hypothetical core melt-down accident in a PWR. (author)

20. Numerical simulation methods of fires in nuclear power plants

International Nuclear Information System (INIS)

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

1992-01-01

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

1. A method of piecewise-smooth numerical branching

Czech Academy of Sciences Publication Activity Database

Ligurský, Tomáš; Renard, Y.

2017-01-01

Roč. 97, č. 7 (2017), s. 815-827 ISSN 1521-4001 R&D Projects: GA MŠk LQ1602 Institutional support: RVO:68145535 Keywords : numerical branching * piecewise smooth * steady-state problem * contact problem * Coulomb friction Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics http://onlinelibrary.wiley.com/doi/10.1002/zamm.201600219/epdf

2. Discrete variational derivative method a structure-preserving numerical method for partial differential equations

CERN Document Server

Furihata, Daisuke

2010-01-01

Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer

3. Sparse grid spectral methods for the numerical solution of partial differential equations with periodic boundary conditions

International Nuclear Information System (INIS)

Kupka, F.

1997-11-01

This thesis deals with the extension of sparse grid techniques to spectral methods for the solution of partial differential equations with periodic boundary conditions. A review on boundary and initial-boundary value problems and a discussion on numerical resolution is used to motivate this research. Spectral methods are introduced by projection techniques, and by three model problems: the stationary and the transient Helmholtz equations, and the linear advection equation. The approximation theory on the hyperbolic cross is reviewed and its close relation to sparse grids is demonstrated. This approach extends to non-periodic problems. Various Sobolev spaces with dominant mixed derivative are introduced to provide error estimates for Fourier approximation and interpolation on the hyperbolic cross and on sparse grids by means of Sobolev norms. The theorems are immediately applicable to the stability and convergence analysis of sparse grid spectral methods. This is explicitly demonstrated for the three model problems. A variant of the von Neumann condition is introduced to simplify the stability analysis of the time-dependent model problems. The discrete Fourier transformation on sparse grids is discussed together with its software implementation. Results on numerical experiments are used to illustrate the performance of the new method with respect to the smoothness properties of each example. The potential of the method in mathematical modelling is estimated and generalizations to other sparse grid methods are suggested. The appendix includes a complete Fortran90 program to solve the linear advection equation by the sparse grid Fourier collocation method and a third-order Runge-Kutta routine for integration in time. (author)

4. The Fundamentals of Economic Dynamics and Policy Analyses : Learning through Numerical Examples. Part Ⅳ. Overlapping Generations Model

OpenAIRE

Futamura, Hiroshi

2015-01-01

An overlapping generations model is an applied dynamic general equilibrium model for which the lifecycle models are employed as main analytical tools. At any point in time, there are overlapping generations consisting of individuals born this year, individuals born last year, individuals born two years ago, and so on. As we saw in the analysis of lifecycle models, each individual makes an optimal consumption-saving plan to maximize lifetime utility over her/his lifecycle. For example, an indi...

5. A CNN-Based Method of Vehicle Detection from Aerial Images Using Hard Example Mining

Directory of Open Access Journals (Sweden)

Yohei Koga

2018-01-01

Full Text Available Recently, deep learning techniques have had a practical role in vehicle detection. While much effort has been spent on applying deep learning to vehicle detection, the effective use of training data has not been thoroughly studied, although it has great potential for improving training results, especially in cases where the training data are sparse. In this paper, we proposed using hard example mining (HEM in the training process of a convolutional neural network (CNN for vehicle detection in aerial images. We applied HEM to stochastic gradient descent (SGD to choose the most informative training data by calculating the loss values in each batch and employing the examples with the largest losses. We picked 100 out of both 500 and 1000 examples for training in one iteration, and we tested different ratios of positive to negative examples in the training data to evaluate how the balance of positive and negative examples would affect the performance. In any case, our method always outperformed the plain SGD. The experimental results for images from New York showed improved performance over a CNN trained in plain SGD where the F1 score of our method was 0.02 higher.

6. Methods of noxious insects control by radiation on example of 'Stegobium paniceum L.'

International Nuclear Information System (INIS)

Krajewski, A.

1997-01-01

The radiation method of disinfestation on example of 'Stegobium paniceum L.' has been described. The different stadia of insect growth have been irradiated. Their radiosensitivity have been estimated on the base of dose-response relationship. Biological radiation effects have been observed as insect procreation limitation. 26 refs, 4 figs, 1 tab

7. Innovative Public Procurement Methods: Examples Of Selected Country And Lessons For Turkey

Directory of Open Access Journals (Sweden)

Elif Ayşe ŞAHİN İPEK

2016-12-01

Full Text Available Innovative public procurement considered as demand-side policies aimed at economic competitiveness, growth and development through the development of private sector innovation supply. In this study it is examined the methods of innovative procurement policy and country examples. It is exerted obstacles and solutions from the results of this examination.

8. Collecting and analyzing qualitative data: Hermeneutic principles, methods and case examples

Science.gov (United States)

Michael E. Patterson; Daniel R. Williams

2002-01-01

Over the past three decades, the use of qualitative research methods has become commonplace in social science as a whole and increasingly represented in tourism and recrearion research. In tourism, for example, Markwell and Basche (1998) recently noted the emergence of a pluralistic perspective on science and the growth of research employing qualitative frameworks....

9. Numerical method of applying shadow theory to all regions of multilayered dielectric gratings in conical mounting.

Science.gov (United States)

Wakabayashi, Hideaki; Asai, Masamitsu; Matsumoto, Keiji; Yamakita, Jiro

2016-11-01

Nakayama's shadow theory first discussed the diffraction by a perfectly conducting grating in a planar mounting. In the theory, a new formulation by use of a scattering factor was proposed. This paper focuses on the middle regions of a multilayered dielectric grating placed in conical mounting. Applying the shadow theory to the matrix eigenvalues method, we compose new transformation and improved propagation matrices of the shadow theory for conical mounting. Using these matrices and scattering factors, being the basic quantity of diffraction amplitudes, we formulate a new description of three-dimensional scattering fields which is available even for cases where the eigenvalues are degenerate in any region. Some numerical examples are given for cases where the eigenvalues are degenerate in the middle regions.

10. Penalty methods for the numerical solution of American multi-asset option problems

Science.gov (United States)

Nielsen, Bjørn Fredrik; Skavhaug, Ola; Tveito, Aslak

2008-12-01

We derive and analyze a penalty method for solving American multi-asset option problems. A small, non-linear penalty term is added to the Black-Scholes equation. This approach gives a fixed solution domain, removing the free and moving boundary imposed by the early exercise feature of the contract. Explicit, implicit and semi-implicit finite difference schemes are derived, and in the case of independent assets, we prove that the approximate option prices satisfy some basic properties of the American option problem. Several numerical experiments are carried out in order to investigate the performance of the schemes. We give examples indicating that our results are sharp. Finally, the experiments indicate that in the case of correlated underlying assets, the same properties are valid as in the independent case.

11. Implementing a flipped classroom approach in a university numerical methods mathematics course

Science.gov (United States)

Johnston, Barbara M.

2017-05-01

This paper describes and analyses the implementation of a 'flipped classroom' approach, in an undergraduate mathematics course on numerical methods. The approach replaced all the lecture contents by instructor-made videos and was implemented in the consecutive years 2014 and 2015. The sequential case study presented here begins with an examination of the attitudes of the 2014 cohort to the approach in general as well as analysing their use of the videos. Based on these responses, the instructor makes a number of changes (for example, the use of 'cloze' summary notes and the introduction of an extra, optional tutorial class) before repeating the 'flipped classroom' approach the following year. The attitudes to the approach and the video usage of the 2015 cohort are then compared with the 2014 cohort and further changes that could be implemented for the next cohort are suggested.

12. Some variance reduction methods for numerical stochastic homogenization.

Science.gov (United States)

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

2016-04-28

We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here. © 2016 The Author(s).

13. Numerical simulation of the flow field in pump intakes by means of Lattice Boltzmann methods

International Nuclear Information System (INIS)

Schneider, A; Conrad, D; Böhle, M

2013-01-01

Lattice Boltzmann Methods are nowadays popular schemes for solving fluid flow problems of engineering interest. This popularity is due to the advantages of these schemes: For example, the meshing of the fluid domain can be performed fully automatically which results in great simplicity in handling complex geometries. In this paper a numerical scheme for the flow simulation in pump intakes based on a Lattice Boltzmann large eddy approach is presented. The ability of this scheme to capture the flow phenomena of the intake flow at different operating conditions is analysed. For the operational reliability and efficiency of pumps and pump systems, the incoming flow conditions are crucial. Since the efficiency and reliability requirements of pumps are rising and must be guaranteed, the flow conditions in pump intakes have to be evaluated during plant planning. Recent trends show that pump intakes are built more and more compact, which makes the flow in the intake even more complex. Numerical methods are a promising technique for conduction flow analysis in pump intakes, because they can be realised rapidly and cheaply

14. Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method

Energy Technology Data Exchange (ETDEWEB)

Yang, Xiaofeng, E-mail: xfyang@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Zhao, Jia, E-mail: zhao62@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 (United States); Wang, Qi, E-mail: qwang@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Beijing Computational Science Research Center, Beijing (China); School of Materials Science and Engineering, Nankai University, Tianjin (China)

2017-03-15

The Molecular Beam Epitaxial model is derived from the variation of a free energy, that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear logarithmic potential in terms of the gradient of a height function. One challenge in solving the MBE model numerically is how to develop proper temporal discretization for the nonlinear terms in order to preserve energy stability at the time-discrete level. In this paper, we resolve this issue by developing a first and second order time-stepping scheme based on the “Invariant Energy Quadratization” (IEQ) method. The novelty is that all nonlinear terms are treated semi-explicitly, and the resulted semi-discrete equations form a linear system at each time step. Moreover, the linear operator is symmetric positive definite and thus can be solved efficiently. We then prove that all proposed schemes are unconditionally energy stable. The semi-discrete schemes are further discretized in space using finite difference methods and implemented on GPUs for high-performance computing. Various 2D and 3D numerical examples are presented to demonstrate stability and accuracy of the proposed schemes.

15. Numerical Exposure Assessment Method for Low Frequency Range and Application to Wireless Power Transfer.

Directory of Open Access Journals (Sweden)

SangWook Park

Full Text Available In this paper, a numerical exposure assessment method is presented for a quasi-static analysis by the use of finite-difference time-domain (FDTD algorithm. The proposed method is composed of scattered field FDTD method and quasi-static approximation for analyzing of the low frequency band electromagnetic problems. The proposed method provides an effective tool to compute induced electric fields in an anatomically realistic human voxel model exposed to an arbitrary non-uniform field source in the low frequency ranges. The method is verified, and excellent agreement with theoretical solutions is found for a dielectric sphere model exposed to a magnetic dipole source. The assessment method serves a practical example of the electric fields, current densities, and specific absorption rates induced in a human head and body in close proximity to a 150-kHz wireless power transfer system for cell phone charging. The results are compared to the limits recommended by the International Commission on Non-Ionizing Radiation Protection (ICNIRP and the IEEE standard guidelines.

16. Numerical Exposure Assessment Method for Low Frequency Range and Application to Wireless Power Transfer

Science.gov (United States)

Kim, Minhyuk

2016-01-01

In this paper, a numerical exposure assessment method is presented for a quasi-static analysis by the use of finite-difference time-domain (FDTD) algorithm. The proposed method is composed of scattered field FDTD method and quasi-static approximation for analyzing of the low frequency band electromagnetic problems. The proposed method provides an effective tool to compute induced electric fields in an anatomically realistic human voxel model exposed to an arbitrary non-uniform field source in the low frequency ranges. The method is verified, and excellent agreement with theoretical solutions is found for a dielectric sphere model exposed to a magnetic dipole source. The assessment method serves a practical example of the electric fields, current densities, and specific absorption rates induced in a human head and body in close proximity to a 150-kHz wireless power transfer system for cell phone charging. The results are compared to the limits recommended by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and the IEEE standard guidelines. PMID:27898688

17. Numerical Exposure Assessment Method for Low Frequency Range and Application to Wireless Power Transfer.

Science.gov (United States)

Park, SangWook; Kim, Minhyuk

2016-01-01

In this paper, a numerical exposure assessment method is presented for a quasi-static analysis by the use of finite-difference time-domain (FDTD) algorithm. The proposed method is composed of scattered field FDTD method and quasi-static approximation for analyzing of the low frequency band electromagnetic problems. The proposed method provides an effective tool to compute induced electric fields in an anatomically realistic human voxel model exposed to an arbitrary non-uniform field source in the low frequency ranges. The method is verified, and excellent agreement with theoretical solutions is found for a dielectric sphere model exposed to a magnetic dipole source. The assessment method serves a practical example of the electric fields, current densities, and specific absorption rates induced in a human head and body in close proximity to a 150-kHz wireless power transfer system for cell phone charging. The results are compared to the limits recommended by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and the IEEE standard guidelines.

18. Parameter estimation method that directly compares gravitational wave observations to numerical relativity

Science.gov (United States)

Lange, J.; O'Shaughnessy, R.; Boyle, M.; Calderón Bustillo, J.; Campanelli, M.; Chu, T.; Clark, J. A.; Demos, N.; Fong, H.; Healy, J.; Hemberger, D. A.; Hinder, I.; Jani, K.; Khamesra, B.; Kidder, L. E.; Kumar, P.; Laguna, P.; Lousto, C. O.; Lovelace, G.; Ossokine, S.; Pfeiffer, H.; Scheel, M. A.; Shoemaker, D. M.; Szilagyi, B.; Teukolsky, S.; Zlochower, Y.

2017-11-01

We present and assess a Bayesian method to interpret gravitational wave signals from binary black holes. Our method directly compares gravitational wave data to numerical relativity (NR) simulations. In this study, we present a detailed investigation of the systematic and statistical parameter estimation errors of this method. This procedure bypasses approximations used in semianalytical models for compact binary coalescence. In this work, we use the full posterior parameter distribution for only generic nonprecessing binaries, drawing inferences away from the set of NR simulations used, via interpolation of a single scalar quantity (the marginalized log likelihood, ln L ) evaluated by comparing data to nonprecessing binary black hole simulations. We also compare the data to generic simulations, and discuss the effectiveness of this procedure for generic sources. We specifically assess the impact of higher order modes, repeating our interpretation with both l ≤2 as well as l ≤3 harmonic modes. Using the l ≤3 higher modes, we gain more information from the signal and can better constrain the parameters of the gravitational wave signal. We assess and quantify several sources of systematic error that our procedure could introduce, including simulation resolution and duration; most are negligible. We show through examples that our method can recover the parameters for equal mass, zero spin, GW150914-like, and unequal mass, precessing spin sources. Our study of this new parameter estimation method demonstrates that we can quantify and understand the systematic and statistical error. This method allows us to use higher order modes from numerical relativity simulations to better constrain the black hole binary parameters.

19. A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

Directory of Open Access Journals (Sweden)

Murat Osmanoglu

2013-01-01

Full Text Available We have considered linear partial differential algebraic equations (LPDAEs of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.

20. Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables

Directory of Open Access Journals (Sweden)

Sandvik Leiv

2011-04-01

Full Text Available Abstract Background The number of events per individual is a widely reported variable in medical research papers. Such variables are the most common representation of the general variable type called discrete numerical. There is currently no consensus on how to compare and present such variables, and recommendations are lacking. The objective of this paper is to present recommendations for analysis and presentation of results for discrete numerical variables. Methods Two simulation studies were used to investigate the performance of hypothesis tests and confidence interval methods for variables with outcomes {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}, and {0, 1, 2, 3, 4, 5}, using the difference between the means as an effect measure. Results The Welch U test (the T test with adjustment for unequal variances and its associated confidence interval performed well for almost all situations considered. The Brunner-Munzel test also performed well, except for small sample sizes (10 in each group. The ordinary T test, the Wilcoxon-Mann-Whitney test, the percentile bootstrap interval, and the bootstrap-t interval did not perform satisfactorily. Conclusions The difference between the means is an appropriate effect measure for comparing two independent discrete numerical variables that has both lower and upper bounds. To analyze this problem, we encourage more frequent use of parametric hypothesis tests and confidence intervals.

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

Science.gov (United States)

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

2013-02-01

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

2. Applying Process Improvement Methods to Clinical and Translational Research: Conceptual Framework and Case Examples.

Science.gov (United States)

Daudelin, Denise H; Selker, Harry P; Leslie, Laurel K

2015-12-01

There is growing appreciation that process improvement holds promise for improving quality and efficiency across the translational research continuum but frameworks for such programs are not often described. The purpose of this paper is to present a framework and case examples of a Research Process Improvement Program implemented at Tufts CTSI. To promote research process improvement, we developed online training seminars, workshops, and in-person consultation models to describe core process improvement principles and methods, demonstrate the use of improvement tools, and illustrate the application of these methods in case examples. We implemented these methods, as well as relational coordination theory, with junior researchers, pilot funding awardees, our CTRC, and CTSI resource and service providers. The program focuses on capacity building to address common process problems and quality gaps that threaten the efficient, timely and successful completion of clinical and translational studies. © 2015 The Authors. Clinical and Translational Science published by Wiley Periodicals, Inc.

3. On the potential of computational methods and numerical simulation in ice mechanics

International Nuclear Information System (INIS)

Bergan, Paal G; Cammaert, Gus; Skeie, Geir; Tharigopula, Venkatapathi

2010-01-01

This paper deals with the challenge of developing better methods and tools for analysing interaction between sea ice and structures and, in particular, to be able to calculate ice loads on these structures. Ice loads have traditionally been estimated using empirical data and 'engineering judgment'. However, it is believed that computational mechanics and advanced computer simulations of ice-structure interaction can play an important role in developing safer and more efficient structures, especially for irregular structural configurations. The paper explains the complexity of ice as a material in computational mechanics terms. Some key words here are large displacements and deformations, multi-body contact mechanics, instabilities, multi-phase materials, inelasticity, time dependency and creep, thermal effects, fracture and crushing, and multi-scale effects. The paper points towards the use of advanced methods like ALE formulations, mesh-less methods, particle methods, XFEM, and multi-domain formulations in order to deal with these challenges. Some examples involving numerical simulation of interaction and loads between level sea ice and offshore structures are presented. It is concluded that computational mechanics may prove to become a very useful tool for analysing structures in ice; however, much research is still needed to achieve satisfactory reliability and versatility of these methods.

4. Theory of difference equations numerical methods and applications

CERN Document Server

Lakshmikantham, Vangipuram

1988-01-01

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

5. SELECT NUMERICAL METHODS FOR MODELING THE DYNAMICS SYSTEMS

Directory of Open Access Journals (Sweden)

Tetiana D. Panchenko

2016-07-01

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

6. A asymptotic numerical method for the steady-state convection diffusion equation

International Nuclear Information System (INIS)

Wu Qiguang

1988-01-01

In this paper, A asymptotic numerical method for the steady-state Convection diffusion equation is proposed, which need not take very fine mesh size in the neighbourhood of the boundary layer. Numerical computation for model problem show that we can obtain the numerical solution in the boundary layer with moderate step size

7. A rapid numerical method for solving Serre-Green-Naghdi equations describing long free surface gravity waves

Science.gov (United States)

Favrie, N.; Gavrilyuk, S.

2017-07-01

A new numerical method for solving the Serre-Green-Naghdi (SGN) equations describing dispersive waves on shallow water is proposed. From the mathematical point of view, the SGN equations are the Euler-Lagrange equations for a ‘master’ lagrangian submitted to a differential constraint which is the mass conservation law. One major numerical challenge in solving the SGN equations is the resolution of an elliptic problem at each time instant. This is the most time-consuming part of the numerical method. The idea is to replace the ‘master’ lagrangian by a one-parameter family of ‘augmented’ lagrangians, depending on a greater number of variables, for which the corresponding Euler-Lagrange equations are hyperbolic. In such an approach, the ‘master’ lagrangian is recovered by the augmented lagrangian in some limit (for example, when the corresponding parameter is large). The choice of such a family of augmented lagrangians is proposed and discussed. The corresponding hyperbolic system is numerically solved by a Godunov type method. Numerical solutions are compared with exact solutions to the SGN equations. It appears that the computational time in solving the hyperbolic system is much lower than in the case where the elliptic operator is inverted. The new method is applied, in particular, to the study of ‘Favre waves’ representing non-stationary undular bores produced after reflection of the fluid flow with a free surface at an immobile wall.

8. 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)

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

Energy Technology Data Exchange (ETDEWEB)

DeLillo, T.K. [Wichita State Univ., KS (United States); Pfaltzgraff, J.A. [Univ. of North Carolina, Chapel Hill, NC (United States)

1996-12-31

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

10. An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

KAUST Repository

2017-01-01

Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

11. An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

KAUST Repository

2017-03-22

Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

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

International Nuclear Information System (INIS)

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

2006-01-01

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

13. Numerical comparison of improved methods of testing in contingency tables with small frequencies

Energy Technology Data Exchange (ETDEWEB)

Sugiura, Nariaki; Otake, Masanori

1968-11-14

The significance levels of various tests for a general c x k contingency table are usually given by large sample theory. But they are not accurate for the one having small frequencies. In this paper, a numerical evaluation was made to determine how good the approximation of significance level is for various improved tests that have been developed by Nass, Yoshimura, Gart, etc. for c x k contingency table with small frequencies in some of cells. For this purpose we compared the significance levels of the various approximate methods (i) with those of one-sided tail defined in terms of exact probabilities for given marginals in 2 x 2 table; (ii) with those of exact probabilities accumulated in the order of magnitude of Chi/sup 2/ statistic or likelihood ratio (=LR) statistic in 2 x 3 table mentioned by Yates. In 2 x 2 table it is well known that Yates' correction gives satisfactory result for small cell frequencies and the other methods that we have not referred here, can be considered if we devote our attention only to 2 x 2 or 2 x k table. But we are mainly interested in comparing the methods that are applicable to a general c x k table. It appears that such a comparison for the various improved methods in the same example has not been made explicitly, even though these tests are frequently used in biological and medical research. 9 references, 6 figures, 6 tables.

14. Three numerical methods for the computation of the electrostatic energy

International Nuclear Information System (INIS)

Poenaru, D.N.; Galeriu, D.

1975-01-01

The FORTRAN programs for computation of the electrostatic energy of a body with axial symmetry by Lawrence, Hill-Wheeler and Beringer methods are presented in detail. The accuracy, time of computation and the required memory of these methods are tested at various deformations for two simple parametrisations: two overlapping identical spheres and a spheroid. On this basis the field of application of each method is recomended

15. Maximum-likelihood method for numerical inversion of Mellin transform

International Nuclear Information System (INIS)

Iqbal, M.

1997-01-01

A method is described for inverting the Mellin transform which uses an expansion in Laguerre polynomials and converts the Mellin transform to Laplace transform, then the maximum-likelihood regularization method is used to recover the original function of the Mellin transform. The performance of the method is illustrated by the inversion of the test functions available in the literature (J. Inst. Math. Appl., 20 (1977) 73; Math. Comput., 53 (1989) 589). Effectiveness of the method is shown by results obtained through demonstration by means of tables and diagrams

16. Approaches to qualitative research in mathematics education examples of methodology and methods

CERN Document Server

Bikner-Ahsbahs, Angelika; Presmeg, Norma

2014-01-01

This volume documents a range of qualitative research approaches emerged within mathematics education over the last three decades, whilst at the same time revealing their underlying methodologies. Continuing the discussion as begun in the two 2003 ZDM issues dedicated to qualitative empirical methods, this book presents astate of the art overview on qualitative research in mathematics education and beyond. The structure of the book allows the reader to use it as an actual guide for the selection of an appropriate methodology, on a basis of both theoretical depth and practical implications. The methods and examples illustrate how different methodologies come to life when applied to a specific question in a specific context. Many of the methodologies described are also applicable outside mathematics education, but the examples provided are chosen so as to situate the approach in a mathematical context.

17. Method for selection of optimal road safety composite index with examples from DEA and TOPSIS method.

Science.gov (United States)

Rosić, Miroslav; Pešić, Dalibor; Kukić, Dragoslav; Antić, Boris; Božović, Milan

2017-01-01

18. Wind power plants and the landscape: Analysis of conflict and methods of solution - practical examples

International Nuclear Information System (INIS)

Brux, H.

1993-01-01

The conflict between wind power plants and the appearance of the landscape is explained. Legal regulations forcing one to take it into account are pointed out. After an introduction into the theoretical basis, methods of solution for the operation of aesthetic landscape judgments are introduced by examples from planning practice. Finally, the frequently unused possibilities of site optimisation with the aid of applied biology and landscape planning are pointed out. (orig.) [de

19. Numerical methods of higher order of accuracy for incompressible flows

Czech Academy of Sciences Publication Activity Database

Kozel, K.; Louda, Petr; Příhoda, Jaromír

2010-01-01

Roč. 80, č. 8 (2010), s. 1734-1745 ISSN 0378-4754 Institutional research plan: CEZ:AV0Z20760514 Keywords : higher order methods * upwind methods * backward-facing step Subject RIV: BK - Fluid Dynamics Impact factor: 0.812, year: 2010

20. Numerical Methods for Plate Forming by Line Heating

DEFF Research Database (Denmark)

Clausen, Henrik Bisgaard

2000-01-01

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

1. Multi-example feature-constrained back-projection method for image super-resolution

Institute of Scientific and Technical Information of China (English)

Junlei Zhang; Dianguang Gai; Xin Zhang; Xuemei Li

2017-01-01

Example-based super-resolution algorithms,which predict unknown high-resolution image information using a relationship model learnt from known high- and low-resolution image pairs, have attracted considerable interest in the field of image processing. In this paper, we propose a multi-example feature-constrained back-projection method for image super-resolution. Firstly, we take advantage of a feature-constrained polynomial interpolation method to enlarge the low-resolution image. Next, we consider low-frequency images of different resolutions to provide an example pair. Then, we use adaptive k NN search to find similar patches in the low-resolution image for every image patch in the high-resolution low-frequency image, leading to a regression model between similar patches to be learnt. The learnt model is applied to the low-resolution high-frequency image to produce high-resolution high-frequency information. An iterative back-projection algorithm is used as the final step to determine the final high-resolution image.Experimental results demonstrate that our method improves the visual quality of the high-resolution image.

2. A Lie-admissible method of integration of Fokker-Planck equations with non-linear coefficients (exact and numerical solutions)

International Nuclear Information System (INIS)

Fronteau, J.; Combis, P.

1984-08-01

A Lagrangian method is introduced for the integration of non-linear Fokker-Planck equations. Examples of exact solutions obtained in this way are given, and also the explicit scheme used for the computation of numerical solutions. The method is, in addition, shown to be of a Lie-admissible type

3. Stable numerical method in computation of stellar evolution

International Nuclear Information System (INIS)

Sugimoto, Daiichiro; Eriguchi, Yoshiharu; Nomoto, Ken-ichi.

1982-01-01

To compute the stellar structure and evolution in different stages, such as (1) red-giant stars in which the density and density gradient change over quite wide ranges, (2) rapid evolution with neutrino loss or unstable nuclear flashes, (3) hydrodynamical stages of star formation or supernova explosion, (4) transition phases from quasi-static to dynamical evolutions, (5) mass-accreting or losing stars in binary-star systems, and (6) evolution of stellar core whose mass is increasing by shell burning or decreasing by penetration of convective envelope into the core, we face ''multi-timescale problems'' which can neither be treated by simple-minded explicit scheme nor implicit one. This problem has been resolved by three prescriptions; one by introducing the hybrid scheme suitable for the multi-timescale problems of quasi-static evolution with heat transport, another by introducing also the hybrid scheme suitable for the multi-timescale problems of hydrodynamic evolution, and the other by introducing the Eulerian or, in other words, the mass fraction coordinate for evolution with changing mass. When all of them are combined in a single computer code, we can compute numerically stably any phase of stellar evolution including transition phases, as far as the star is spherically symmetric. (author)

4. Numerical method for solving integral equations of neutron transport. II

International Nuclear Information System (INIS)

Loyalka, S.K.; Tsai, R.W.

1975-01-01

In a recent paper it was pointed out that the weakly singular integral equations of neutron transport can be quite conveniently solved by a method based on subtraction of singularity. This previous paper was devoted entirely to the consideration of simple one-dimensional isotropic-scattering and one-group problems. The present paper constitutes interesting extensions of the previous work in that in addition to a typical two-group anisotropic-scattering albedo problem in the slab geometry, the method is also applied to an isotropic-scattering problem in the x-y geometry. These results are compared with discrete S/sub N/ (ANISN or TWOTRAN-II) results, and for the problems considered here, the proposed method is found to be quite effective. Thus, the method appears to hold considerable potential for future applications. (auth)

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

Energy Technology Data Exchange (ETDEWEB)

Baglama, J.; Farrell, P.A.; Reichel, L.; Ruttan, A. [Kent State Univ., OH (United States); Calvetti, D. [Stevens Inst. of Technology, Hoboken, NJ (United States)

1996-12-31

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

6. Numerical methods in image processing for applications in jewellery industry

OpenAIRE

Petrla, Martin

2016-01-01

Presented thesis deals with a problem from the field of image processing for application in multiple scanning of jewelery stones. The aim is to develop a method for preprocessing and subsequent mathematical registration of images in order to increase the effectivity and reliability of the output quality control. For these purposes the thesis summerizes mathematical definition of digital image as well as theoretical base of image registration. It proposes a method adjusting every single image ...

7. An efficient soil water balance model based on hybrid numerical and statistical methods

Science.gov (United States)

Mao, Wei; Yang, Jinzhong; Zhu, Yan; Ye, Ming; Liu, Zhao; Wu, Jingwei

2018-04-01

Most soil water balance models only consider downward soil water movement driven by gravitational potential, and thus cannot simulate upward soil water movement driven by evapotranspiration especially in agricultural areas. In addition, the models cannot be used for simulating soil water movement in heterogeneous soils, and usually require many empirical parameters. To resolve these problems, this study derives a new one-dimensional water balance model for simulating both downward and upward soil water movement in heterogeneous unsaturated zones. The new model is based on a hybrid of numerical and statistical methods, and only requires four physical parameters. The model uses three governing equations to consider three terms that impact soil water movement, including the advective term driven by gravitational potential, the source/sink term driven by external forces (e.g., evapotranspiration), and the diffusive term driven by matric potential. The three governing equations are solved separately by using the hybrid numerical and statistical methods (e.g., linear regression method) that consider soil heterogeneity. The four soil hydraulic parameters required by the new models are as follows: saturated hydraulic conductivity, saturated water content, field capacity, and residual water content. The strength and weakness of the new model are evaluated by using two published studies, three hypothetical examples and a real-world application. The evaluation is performed by comparing the simulation results of the new model with corresponding results presented in the published studies, obtained using HYDRUS-1D and observation data. The evaluation indicates that the new model is accurate and efficient for simulating upward soil water flow in heterogeneous soils with complex boundary conditions. The new model is used for evaluating different drainage functions, and the square drainage function and the power drainage function are recommended. Computational efficiency of the new

8. Generalized Heisenberg algebra and algebraic method: The example of an infinite square-well potential

International Nuclear Information System (INIS)

Curado, E.M.F.; Hassouni, Y.; Rego-Monteiro, M.A.; Rodrigues, Ligia M.C.S.

2008-01-01

We discuss the role of generalized Heisenberg algebras (GHA) in obtaining an algebraic method to describe physical systems. The method consists in finding the GHA associated to a physical system and the relations between its generators and the physical observables. We choose as an example the infinite square-well potential for which we discuss the representations of the corresponding GHA. We suggest a way of constructing a physical realization of the generators of some GHA and apply it to the square-well potential. An expression for the position operator x in terms of the generators of the algebra is given and we compute its matrix elements

9. Pedagogies in Action: A Community Resource Linking Teaching Methods to Examples of their Use

Science.gov (United States)

Manduca, C. A.; Fox, S. P.; Iverson, E. A.; Kirk, K.; Ormand, C. J.

2009-12-01

10. A Numerical Matrix-Based method in Harmonic Studies in Wind Power Plants

DEFF Research Database (Denmark)

2016-01-01

In the low frequency range, there are some couplings between the positive- and negative-sequence small-signal impedances of the power converter due to the nonlinear and low bandwidth control loops such as the synchronization loop. In this paper, a new numerical method which also considers...... these couplings will be presented. The numerical data are advantageous to the parametric differential equations, because analysing the high order and complex transfer functions is very difficult, and finally one uses the numerical evaluation methods. This paper proposes a numerical matrix-based method, which...

11. Teaching Research Methods and Statistics in eLearning Environments:Pedagogy, Practical Examples and Possible Futures

Directory of Open Access Journals (Sweden)

2016-03-01

Full Text Available Generally, academic psychologists are mindful of the fact that, for many students, the study of research methods and statistics is anxiety provoking (Gal, Ginsburg, & Schau, 1997. Given the ubiquitous and distributed nature of eLearning systems (Nof, Ceroni, Jeong, & Moghaddam, 2015, teachers of research methods and statistics need to cultivate an understanding of how to effectively use eLearning tools to inspire psychology students to learn. Consequently, the aim of the present paper is to discuss critically how using eLearning systems might engage psychology students in research methods and statistics. First, we critically appraise definitions of eLearning. Second, we examine numerous important pedagogical principles associated with effectively teaching research methods and statistics using eLearning systems. Subsequently, we provide practical examples of our own eLearning-based class activities designed to engage psychology students to learn statistical concepts such as Factor Analysis and Discriminant Function Analysis. Finally, we discuss general trends in eLearning and possible futures that are pertinent to teachers of research methods and statistics in psychology.

12. Proceeding of 1998-workshop on MHD computations. Study on numerical methods related to plasma confinement

International Nuclear Information System (INIS)

Kako, T.; Watanabe, T.

1999-04-01

This is the proceeding of 'Study on Numerical Methods Related to Plasma Confinement' held in National Institute for Fusion Science. In this workshop, theoretical and numerical analyses of possible plasma equilibria with their stability properties are presented. These are also various talks on mathematical as well as numerical analyses related to the computational methods for fluid dynamics and plasma physics. The 14 papers are indexed individually. (J.P.N.)

13. Proceeding of 1998-workshop on MHD computations. Study on numerical methods related to plasma confinement

Energy Technology Data Exchange (ETDEWEB)

Kako, T.; Watanabe, T. [eds.

1999-04-01

This is the proceeding of 'Study on Numerical Methods Related to Plasma Confinement' held in National Institute for Fusion Science. In this workshop, theoretical and numerical analyses of possible plasma equilibria with their stability properties are presented. These are also various talks on mathematical as well as numerical analyses related to the computational methods for fluid dynamics and plasma physics. The 14 papers are indexed individually. (J.P.N.)

14. Numerical functional integration method for studying the properties of the physical vacuum

International Nuclear Information System (INIS)

Lobanov, Yu.Yu.

1998-01-01

The new approach to investigate the physical vacuum in quantum theories including its nonperturbative topological structure is discussed. This approach is based on the representation of the matrix element of the evolution operator in Euclidean metrics in a form of the functional integral with a certain measure in the corresponding space and on the use of approximation formulas which we constructed for this kind of integral. No preliminary discretization of space and time is required, as well as no simplifying assumptions like semiclassical approximation, collective excitations, introduction of ''short-time'' propagators, etc. are necessary in this approach. The method allows to use the more preferable deterministic algorithms instead of the traditional stochastic technique. It has been proven that our approach has important advantages over the other known methods, including the higher efficiency of computations. Examples of application of the method to the numerical study of some potential nuclear models and to the computation of the topological susceptibility and the θ-vacua energy are presented. (author)

15. Numerical methods and applications in many fermion systems

Energy Technology Data Exchange (ETDEWEB)

Luitz, David J.

2013-02-07

This thesis presents results covering several topics in correlated many fermion systems. A Monte Carlo technique (CT-INT) that has been implemented, used and extended by the author is discussed in great detail in chapter 3. The following chapter discusses how CT-INT can be used to calculate the two particle Green's function and explains how exact frequency summations can be obtained. A benchmark against exact diagonalization is presented. The link to the dynamical cluster approximation is made in the end of chapter 4, where these techniques are of immense importance. In chapter 5 an extensive CT-INT study of a strongly correlated Josephson junction is shown. In particular, the signature of the first order quantum phase transition between a Kondo and a local moment regime in the Josephson current is discussed. The connection to an experimental system is made with great care by developing a parameter extraction strategy. As a final result, we show that it is possible to reproduce experimental data from a numerically exact CT-INT model-calculation. The last topic is a study of graphene edge magnetism. We introduce a general effective model for the edge states, incorporating a complicated interaction Hamiltonian and perform an exact diagonalization study for different parameter regimes. This yields a strong argument for the importance of forbidden umklapp processes and of the strongly momentum dependent interaction vertex for the formation of edge magnetism. Additional fragments concerning the use of a Legendre polynomial basis for the representation of the two particle Green's function, the analytic continuation of the self energy for the Anderson Kane Mele Model as well as the generation of test data with a given covariance matrix are documented in the appendix. A final appendix provides some very important matrix identities that are used for the discussion of technical details of CT-INT.

16. Numerical methods and applications in many fermion systems

International Nuclear Information System (INIS)

Luitz, David J.

2013-01-01

This thesis presents results covering several topics in correlated many fermion systems. A Monte Carlo technique (CT-INT) that has been implemented, used and extended by the author is discussed in great detail in chapter 3. The following chapter discusses how CT-INT can be used to calculate the two particle Green's function and explains how exact frequency summations can be obtained. A benchmark against exact diagonalization is presented. The link to the dynamical cluster approximation is made in the end of chapter 4, where these techniques are of immense importance. In chapter 5 an extensive CT-INT study of a strongly correlated Josephson junction is shown. In particular, the signature of the first order quantum phase transition between a Kondo and a local moment regime in the Josephson current is discussed. The connection to an experimental system is made with great care by developing a parameter extraction strategy. As a final result, we show that it is possible to reproduce experimental data from a numerically exact CT-INT model-calculation. The last topic is a study of graphene edge magnetism. We introduce a general effective model for the edge states, incorporating a complicated interaction Hamiltonian and perform an exact diagonalization study for different parameter regimes. This yields a strong argument for the importance of forbidden umklapp processes and of the strongly momentum dependent interaction vertex for the formation of edge magnetism. Additional fragments concerning the use of a Legendre polynomial basis for the representation of the two particle Green's function, the analytic continuation of the self energy for the Anderson Kane Mele Model as well as the generation of test data with a given covariance matrix are documented in the appendix. A final appendix provides some very important matrix identities that are used for the discussion of technical details of CT-INT.

17. 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.)

18. Assessment of Soil Liquefaction Potential Based on Numerical Method

DEFF Research Database (Denmark)

2012-01-01

Paying special attention to geotechnical hazards such as liquefaction in huge civil projects like urban railways especially in susceptible regions to liquefaction is of great importance. A number of approaches to evaluate the potential for initiation of liquefaction, such as Seed and Idriss...... simplified method have been developed over the years. Although simplified methods are available in calculating the liquefaction potential of a soil deposit and shear stresses induced at any point in the ground due to earthquake loading, these methods cannot be applied to all earthquakes with the same...... accuracy, also they lack the potential to predict the pore pressure developed in the soil. Therefore, it is necessary to carry out a ground response analysis to obtain pore pressures and shear stresses in the soil due to earthquake loading. Using soil historical, geological and compositional criteria...

19. Control rod computer code IAMCOS: general theory and numerical methods

International Nuclear Information System (INIS)

West, G.

1982-11-01

IAMCOS is a computer code for the description of mechanical and thermal behavior of cylindrical control rods for fast breeders. This code version was applied, tested and modified from 1979 to 1981. In this report are described the basic model (02 version), theoretical definitions and computation methods [fr

20. Hybrid Particle-Continuum Numerical Methods for Aerospace Applications

Science.gov (United States)

2011-01-01

Many applications of MEMS/NEMS devices, which include micro- turbines [3, 4], micro-sensors for chemical con- centrations or gas ow properties [5, 6, 7...Oran, E. S., and Kaplan , C. R., The Coupled Multiscale Multiphysics Method (CM3) for Rareed Gas Flows, AIAA 2010-823, 2010. [63] Holman, T. D

1. Fast Numerical Methods for Stochastic Partial Differential Equations

Science.gov (United States)

2016-04-15

Particle Swarm Optimization (PSO) method. Inspired by the social behavior of the bird flocking or fish schooling, the particle swarm optimization (PSO...Weerasinghe, Hongmei Chi and Yanzhao Cao, Particle Swarm Optimization Simulation via Optimal Halton Sequences, accepted by Procedia Computer Science (2016...Optimization Simulation via Optimal Halton Sequences, accepted by Procedia Computer Science (2016). 2. Haiyan Tian, Hongmei Chi and Yanzhao Cao

2. Deformation of two-phase aggregates using standard numerical methods

Science.gov (United States)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

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

Energy Technology Data Exchange (ETDEWEB)

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

1997-04-01

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

4. 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....

5. Numerical Solution of the Blasius Viscous Flow Problem by Quartic B-Spline Method

Directory of Open Access Journals (Sweden)

Hossein Aminikhah

2016-01-01

Full Text Available A numerical method is proposed to study the laminar boundary layer about a flat plate in a uniform stream of fluid. The presented method is based on the quartic B-spline approximations with minimizing the error L2-norm. Theoretical considerations are discussed. The computed results are compared with some numerical results to show the efficiency of the proposed approach.

6. A numerical method for a model of two-phase flow in a coupled free flow and porous media system

KAUST Repository

Chen, Jie; Sun, Shuyu; Wang, Xiaoping

2014-01-01

In this article, we study two-phase fluid flow in coupled free flow and porous media regions. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the porous medium region. We propose a Robin-Robin domain decomposition method for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Numerical examples are presented to illustrate the effectiveness of this method. © 2014 Elsevier Inc.

7. A numerical method for a model of two-phase flow in a coupled free flow and porous media system

KAUST Repository

Chen, Jie

2014-07-01

In this article, we study two-phase fluid flow in coupled free flow and porous media regions. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the porous medium region. We propose a Robin-Robin domain decomposition method for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Numerical examples are presented to illustrate the effectiveness of this method. © 2014 Elsevier Inc.

8. Practical data correlation of flashpoints of binary mixtures by a reciprocal function: The concept and numerical examples

Directory of Open Access Journals (Sweden)

Hristova Mariana

2011-01-01

Full Text Available Simple data correlation of flashpoint data of binary mixture has been developed on a basic of rational reciprocal function. The new approximation requires has only two coefficients and needs the flashpoint temperature of the pure flammable component to be known. The approximation has been tested by literature data concerning aqueous-alcohol solution and compared to calculations performed by several thermodynamic models predicting flashpoint temperatures. The suggested approximation provides accuracy comparable and to some extent better than that of the thermodynamic methods.

9. Numerical Methods for Plate Forming by Line Heating

DEFF Research Database (Denmark)

Clausen, Henrik Bisgaard

2000-01-01

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

10. An alternative method for determination of oscillator strengths: The example of Sc II

International Nuclear Information System (INIS)

Ruczkowski, J.; Elantkowska, M.; Dembczyński, J.

2014-01-01

We describe our method for determining oscillator strengths and hyperfine structure splittings that is an alternative to the commonly used, purely theoretical calculations, or to the semi-empirical approach combined with theoretically calculated transition integrals. We have developed our own computer programs that allow us to determine all attributes of the structure of complex atoms starting from the measured frequencies emitted by the atoms. As an example, we present the results of the calculation of the structure, electric dipole transitions, and hyperfine splittings of Sc II. The angular coefficients of the transition matrix in pure SL coupling were found from straightforward Racah algebra. The transition matrix was transformed into the actual intermediate coupling by the fine structure eigenvectors obtained from the semi-empirical approach. The transition integrals were treated as free parameters in the least squares fit to experimental gf values. For most transitions, the experimental and the calculated gf-values are consistent with the accuracy claimed in the NIST compilation. - Highlights: • The method of simultaneous determination of all the attributes of atomic structure. • The semi-empirical method of parameterization of oscillator strengths. • Illustration of the method application for the example of Sc II data

11. Efficient Numerical Methods for Nonequilibrium Re-Entry Flows

Science.gov (United States)

2014-01-14

right-hand side is the only quadratic operation). The number of sub- iterations , kmax, used in this update needs to be chosen for optimal convergence and...Upper Symmetric Gauss - Seidel Method for the Euler and Navier-Stokes Equations,”, AIAA Journal, Vol. 26, No. 9, pp. 1025-1026, Sept. 1988. 11Edwards, J.R...Candler, “The Solution of the Navier-Stokes Equations Using Gauss - Seidel Line Relaxation,” Computers and Fluids, Vol. 17, No. 1, pp. 135-150, 1989

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

DEFF Research Database (Denmark)

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

2014-01-01

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

13. Numerical simulation for cracks detection using the finite elements method

Directory of Open Access Journals (Sweden)

S Bennoud

2016-09-01

Full Text Available The means of detection must ensure controls either during initial construction, or at the time of exploitation of all parts. The Non destructive testing (NDT gathers the most widespread methods for detecting defects of a part or review the integrity of a structure. In the areas of advanced industry (aeronautics, aerospace, nuclear …, assessing the damage of materials is a key point to control durability and reliability of parts and materials in service. In this context, it is necessary to quantify the damage and identify the different mechanisms responsible for the progress of this damage. It is therefore essential to characterize materials and identify the most sensitive indicators attached to damage to prevent their destruction and use them optimally. In this work, simulation by finite elements method is realized with aim to calculate the electromagnetic energy of interaction: probe and piece (with/without defect. From calculated energy, we deduce the real and imaginary components of the impedance which enables to determine the characteristic parameters of a crack in various metallic parts.

14. Numerical method for IR background and clutter simulation

Science.gov (United States)

Quaranta, Carlo; Daniele, Gina; Balzarotti, Giorgio

1997-06-01

The paper describes a fast and accurate algorithm of IR background noise and clutter generation for application in scene simulations. The process is based on the hypothesis that background might be modeled as a statistical process where amplitude of signal obeys to the Gaussian distribution rule and zones of the same scene meet a correlation function with exponential form. The algorithm allows to provide an accurate mathematical approximation of the model and also an excellent fidelity with reality, that appears from a comparison with images from IR sensors. The proposed method shows advantages with respect to methods based on the filtering of white noise in time or frequency domain as it requires a limited number of computation and, furthermore, it is more accurate than the quasi random processes. The background generation starts from a reticule of few points and by means of growing rules the process is extended to the whole scene of required dimension and resolution. The statistical property of the model are properly maintained in the simulation process. The paper gives specific attention to the mathematical aspects of the algorithm and provides a number of simulations and comparisons with real scenes.

15. The Numerical Simulation of the Crack Elastoplastic Extension Based on the Extended Finite Element Method

Directory of Open Access Journals (Sweden)

Xia Xiaozhou

2013-01-01

Full Text Available In the frame of the extended finite element method, the exponent disconnected function is introduced to reflect the discontinuous characteristic of crack and the crack tip enrichment function which is made of triangular basis function, and the linear polar radius function is adopted to describe the displacement field distribution of elastoplastic crack tip. Where, the linear polar radius function form is chosen to decrease the singularity characteristic induced by the plastic yield zone of crack tip, and the triangle basis function form is adopted to describe the displacement distribution character with the polar angle of crack tip. Based on the displacement model containing the above enrichment displacement function, the increment iterative form of elastoplastic extended finite element method is deduced by virtual work principle. For nonuniform hardening material such as concrete, in order to avoid the nonsymmetry characteristic of stiffness matrix induced by the non-associate flowing of plastic strain, the plastic flowing rule containing cross item based on the least energy dissipation principle is adopted. Finally, some numerical examples show that the elastoplastic X-FEM constructed in this paper is of validity.

16. Methods tuned on the physical problem. A way to improve numerical codes

International Nuclear Information System (INIS)

Ixaru, L.Gr.

2010-01-01

We consider the problem on how the numerical methods tuned on the physical problem can contribute to the enhancement of the performance of the codes. We illustrate this on two simple cases: solution of time independent one-dimensional Schroedinger equation, and the computation of integrals with oscillatory integrands. In both cases the tuned versions bring a massive gain in accuracy at negligible extra cost. We presented two simple problems where successive levels of tuning enhance significantly the accuracy at negligible extra cost. These problems should be seen as representing only some illustrations on how the codes can be improved but we must also mention that in many cases tuned versions still have to be developed. Just for a suggestion, quadrature formulae which involve the integrand and a number of successive derivatives of this exist, but no formula is available when some of these derivatives are missing, for example when we dispose of y and y'' but not of y'. A direct application will be on the case when the integrand involves the solution of the Schrodinger equation by the method of Numerov. (author)

17. Numerical Simulation of Antennas with Improved Integral Equation Method

International Nuclear Information System (INIS)

Ma Ji; Fang Guang-You; Lu Wei

2015-01-01

Simulating antennas around a conducting object is a challenge task in computational electromagnetism, which is concerned with the behaviour of electromagnetic fields. To analyze this model efficiently, an improved integral equation-fast Fourier transform (IE-FFT) algorithm is presented in this paper. The proposed scheme employs two Cartesian grids with different size and location to enclose the antenna and the other object, respectively. On the one hand, IE-FFT technique is used to store matrix in a sparse form and accelerate the matrix-vector multiplication for each sub-domain independently. On the other hand, the mutual interaction between sub-domains is taken as the additional exciting voltage in each matrix equation. By updating integral equations several times, the whole electromagnetic system can achieve a stable status. Finally, the validity of the presented method is verified through the analysis of typical antennas in the presence of a conducting object. (paper)

18. 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...

19. A Systematic Method For Tracer Test Analysis: An Example Using Beowawe Tracer Data

Energy Technology Data Exchange (ETDEWEB)

G. Michael Shook

2005-01-01

Quantitative analysis of tracer data using moment analysis requires a strict adherence to a set of rules which include data normalization, correction for thermal decay, deconvolution, extrapolation, and integration. If done correctly, the method yields specific information on swept pore volume, flow geometry and fluid velocity, and an understanding of the nature of reservoir boundaries. All calculations required for the interpretation can be done in a spreadsheet. The steps required for moment analysis are reviewed in this paper. Data taken from the literature is used in an example calculation.

20. Numerical methods of estimating the dispersion of radionuclides in atmosphere

International Nuclear Information System (INIS)

Vladu, Mihaela; Ghitulescu, Alina; Popescu, Gheorghe; Piciorea, Iuliana

2007-01-01

Full text: The paper presents the method of dispersion calculation, witch can be applied for the DLE calculation. This is necessary to ensure a secure performance of the Experimental Pilot Plant for Tritium and Deuterium Separation (using the technology for detritiation based upon isotope catalytic exchange between tritiated heavy water and deuterium followed by cryogenic distillation of the hydrogen isotopes). For the calculation of the dispersion of radioactivity effluents in the atmosphere, at a given distance between source and receiver, the Gaussian mathematical model was used. This model is currently applied for estimating the long-term results of dispersion in case of continuous or intermittent emissions as basic information for long-term radioprotection measures for areas of the order of kilometres from the source. We have considered intermittent or continuous emissions of intensity lower than 1% per day relative to the annual emission. It is supposed that the radioactive material released into environment presents a gaussian dispersion both in horizontal and vertical plan. The local dispersion parameters could be determined directly with turbulence measurements or indirectly by determination of atmospheric stability. Weather parameters for characterizing the atmospheric dispersion include: - direction of wind relative to the source; - the speed of the wind at the height of emission; - parameters of dispersion to different distances, depending on the atmospheric turbulence which characterizes the mixing of radioactive materials in the atmosphere; - atmospheric stability range; - the height of mixture stratum; - the type and intensity of precipitations. The choice of the most adequate version of Gaussian model depends on the relation among the height where effluent emission is in progress, H (m), and the height at which the buildings influence the air motion, HB (m). There were defined three zones of distinct dispersion. This zones can have variable lengths

1. The Numerical Wind Atlas - the KAMM/WAsP Method

Energy Technology Data Exchange (ETDEWEB)

Frank, H P; Rathmann, O; Mortensen, N G; Landberg, L

2001-06-01

The method of combining the Karlsruhe Atmospheric Mesoscale Model, KAMM, with the Wind Atlas Analysis and Application Program, WAsP, to make local predictions of the wind resource is presented. It combines the advantages of meso-scale modeling - overview over a big region and use of global data bases - with the local prediction capacity of the small-scale model WAsP. Results are presented for Denmark, Ireland, Northern Portugal and Galicia, and the Faroe Islands. Wind atlas files were calculated from wind data simulated with the meso-scale model using model grids with a resolution of 2.5, 5, and 10 km. Using these wind atlas files in WAsP the local prediction of the mean wind does not depend on the grid resolution of the meso-scale model. The local predictions combining KAMM and WAsP are much better than simple interpolation of the wind simulated by KAMM. In addition an investigation was made on the dependence of wind atlas data on the size of WAsP-maps. It is recommended that a topographic map around a site should extend 10 km out from it. If there is a major roughness change like a coast line further away in a frequent wind direction this should be included at even greater distances, perhaps up to 20 km away.

2. Continuum-Kinetic Models and Numerical Methods for Multiphase Applications

Science.gov (United States)

Nault, Isaac Michael

This thesis presents a continuum-kinetic approach for modeling general problems in multiphase solid mechanics. In this context, a continuum model refers to any model, typically on the macro-scale, in which continuous state variables are used to capture the most important physics: conservation of mass, momentum, and energy. A kinetic model refers to any model, typically on the meso-scale, which captures the statistical motion and evolution of microscopic entitites. Multiphase phenomena usually involve non-negligible micro or meso-scopic effects at the interfaces between phases. The approach developed in the thesis attempts to combine the computational performance benefits of a continuum model with the physical accuracy of a kinetic model when applied to a multiphase problem. The approach is applied to modeling a single particle impact in Cold Spray, an engineering process that intimately involves the interaction of crystal grains with high-magnitude elastic waves. Such a situation could be classified a multiphase application due to the discrete nature of grains on the spatial scale of the problem. For this application, a hyper elasto-plastic model is solved by a finite volume method with approximate Riemann solver. The results of this model are compared for two types of plastic closure: a phenomenological macro-scale constitutive law, and a physics-based meso-scale Crystal Plasticity model.

3. Study on pipe deflection by using numerical method

Science.gov (United States)

Husaini; Zaki Mubarak, Amir; Agustiar, Rizki

2018-05-01

Piping systems are widely used in a refinery or oil and gas industry. The piping system must be properly designed to avoid failure or leakage. Pipe stress analysis is conducted to analyze the loads and critical stress occurred, so that the failure of the pipe can be avoided. In this research, it is analyzed the deflection of a pipe by using Finite Element Method. The pipe is made of A358 / 304SS SCH10S Stainless Steel. It is 16 inches in size with the distance between supports is 10 meters. The fluid flown is Liquid Natural Gas (LNG) with the range of temperature of -120 ° C to -170 ° C, and a density of 461.1 kg / m 3. The flow of LNG causes deflection of the pipe. The pipe deflection must be within the permissible tolerable range. The objective is to analyze the deflection occurred in the piping system. Based on the calculation and simulation, the deflection is 4.4983 mm, which is below the maximum limit of deflection allowed, which is 20.3 mm.

4. Numerical soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method

International Nuclear Information System (INIS)

Kaya, Dogan; El-Sayed, Salah M.

2003-01-01

In this Letter we present an Adomian's decomposition method (shortly ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions

5. The development of efficient numerical time-domain modeling methods for geophysical wave propagation

Science.gov (United States)

Zhu, Lieyuan

This Ph.D. dissertation focuses on the numerical simulation of geophysical wave propagation in the time domain including elastic waves in solid media, the acoustic waves in fluid media, and the electromagnetic waves in dielectric media. This thesis shows that a linear system model can describe accurately the physical processes of those geophysical waves' propagation and can be used as a sound basis for modeling geophysical wave propagation phenomena. The generalized stability condition for numerical modeling of wave propagation is therefore discussed in the context of linear system theory. The efficiency of a series of different numerical algorithms in the time-domain for modeling geophysical wave propagation are discussed and compared. These algorithms include the finite-difference time-domain method, pseudospectral time domain method, alternating directional implicit (ADI) finite-difference time domain method. The advantages and disadvantages of these numerical methods are discussed and the specific stability condition for each modeling scheme is carefully derived in the context of the linear system theory. Based on the review and discussion of these existing approaches, the split step, ADI pseudospectral time domain (SS-ADI-PSTD) method is developed and tested for several cases. Moreover, the state-of-the-art stretched-coordinate perfect matched layer (SCPML) has also been implemented in SS-ADI-PSTD algorithm as the absorbing boundary condition for truncating the computational domain and absorbing the artificial reflection from the domain boundaries. After algorithmic development, a few case studies serve as the real-world examples to verify the capacities of the numerical algorithms and understand the capabilities and limitations of geophysical methods for detection of subsurface contamination. The first case is a study using ground penetrating radar (GPR) amplitude variation with offset (AVO) for subsurface non-aqueous-liquid (NAPL) contamination. The

6. A numerical method for multigroup slab-geometry discrete ordinates problems with no spatial truncation error

International Nuclear Information System (INIS)

Barros, R.C. de; Larsen, E.W.

1991-01-01

A generalization of the one-group Spectral Green's Function (SGF) method is developed for multigroup, slab-geometry discrete ordinates (S N ) problems. The multigroup SGF method is free from spatial truncation errors; it generated numerical values for the cell-edge and cell-average angular fluxes that agree with the analytic solution of the multigroup S N equations. Numerical results are given to illustrate the method's accuracy

7. On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

Directory of Open Access Journals (Sweden)

H. Montazeri

2012-01-01

Full Text Available We consider a system of nonlinear equations F(x=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

8. Studying the properties of Variational Data Assimilation Methods by Applying a Set of Test-Examples

DEFF Research Database (Denmark)

Thomsen, Per Grove; Zlatev, Zahari

2007-01-01

and backward computations are carried out by using the model under consideration and its adjoint equations (both the model and its adjoint are defined by systems of differential equations). The major difficulty is caused by the huge increase of the computational load (normally by a factor more than 100...... assimilation method (numerical algorithms for solving differential equations, splitting procedures and optimization algorithms) have been studied by using these tests. The presentation will include results from testing carried out in the study.......he variational data assimilation methods can successfully be used in different fields of science and engineering. An attempt to utilize available sets of observations in the efforts to improve (i) the models used to study different phenomena (ii) the model results is systematically carried out when...

9. Teaching numerical methods with IPython notebooks and inquiry-based learning

KAUST Repository

Ketcheson, David I.

2014-01-01

A course in numerical methods should teach both the mathematical theory of numerical analysis and the craft of implementing numerical algorithms. The IPython notebook provides a single medium in which mathematics, explanations, executable code, and visualizations can be combined, and with which the student can interact in order to learn both the theory and the craft of numerical methods. The use of notebooks also lends itself naturally to inquiry-based learning methods. I discuss the motivation and practice of teaching a course based on the use of IPython notebooks and inquiry-based learning, including some specific practical aspects. The discussion is based on my experience teaching a Masters-level course in numerical analysis at King Abdullah University of Science and Technology (KAUST), but is intended to be useful for those who teach at other levels or in industry.

10. Efficient numerical methods for fluid- and electrodynamics on massively parallel systems

Energy Technology Data Exchange (ETDEWEB)

Zudrop, Jens

2016-07-01

In the last decade, computer technology has evolved rapidly. Modern high performance computing systems offer a tremendous amount of computing power in the range of a few peta floating point operations per second. In contrast, numerical software development is much slower and most existing simulation codes cannot exploit the full computing power of these systems. Partially, this is due to the numerical methods themselves and partially it is related to bottlenecks within the parallelization concept and its data structures. The goal of the thesis is the development of numerical algorithms and corresponding data structures to remedy both kinds of parallelization bottlenecks. The approach is based on a co-design of the numerical schemes (including numerical analysis) and their realizations in algorithms and software. Various kinds of applications, from multicomponent flows (Lattice Boltzmann Method) to electrodynamics (Discontinuous Galerkin Method) to embedded geometries (Octree), are considered and efficiency of the developed approaches is demonstrated for large scale simulations.

11. Review of bayesian statistical analysis methods for cytogenetic radiation biodosimetry, with a practical example

International Nuclear Information System (INIS)

Ainsbury, Elizabeth A.; Lloyd, David C.; Rothkamm, Kai; Vinnikov, Volodymyr A.; Maznyk, Nataliya A.; Puig, Pedro; Higueras, Manuel

2014-01-01

Classical methods of assessing the uncertainty associated with radiation doses estimated using cytogenetic techniques are now extremely well defined. However, several authors have suggested that a Bayesian approach to uncertainty estimation may be more suitable for cytogenetic data, which are inherently stochastic in nature. The Bayesian analysis framework focuses on identification of probability distributions (for yield of aberrations or estimated dose), which also means that uncertainty is an intrinsic part of the analysis, rather than an 'afterthought'. In this paper Bayesian, as well as some more advanced classical, data analysis methods for radiation cytogenetics are reviewed that have been proposed in the literature. A practical overview of Bayesian cytogenetic dose estimation is also presented, with worked examples from the literature. (authors)

12. Appraisal of numerical methods in predicting the aerodynamics of forward-swept wings

CSIR Research Space (South Africa)

Lombardi, G

1998-07-01

Full Text Available The capabilities of different numerical methods in evaluating the aerodynamic characteristics of a forward-swept wing in subsonic and transonic now are analyzed. The numerical results, obtained by means of potential, Euler, and Navier-Stokes solvers...

13. 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

14. Numerical methods to solve the two-dimensional heat conduction equation

International Nuclear Information System (INIS)

Santos, R.S. dos.

1981-09-01

A class of numerical methods, called 'Hopscotch Algorithms', was used to solve the heat conduction equation in cylindrical geometry. Using a time dependent heat source, the temperature versus time behaviour of cylindric rod was analysed. Numerical simulation was used to study the stability and the convergence of each different method. Another test had the temperature specified on the outer surface as boundary condition. The various Hopscotch methods analysed exhibit differing degrees of accuracy, few of them being so accurate as the ADE method, but requiring more computational operations than the later, were observed. Finally, compared with the so called ODD-EVEN method, two other Hopscotch methods, are more time consuming. (Author) [pt

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

Science.gov (United States)

Rosenbaum, J. S.

1976-01-01

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

16. Stress evolution in elastic-plastic electrodes during electrochemical processes: A numerical method and its applications

Science.gov (United States)

Wen, Jici; Wei, Yujie; Cheng, Yang-Tse

2018-07-01

Monitoring in real time the stress state in high capacity electrodes during charge-discharge processes is pivotal to the performance assessment and structural optimization of advanced batteries. The wafer curvature measurement technique broadly employed in thin-film industry, together with stress analysis using the Stoney equation, has been successfully adopted to measure in situ the stress in thin film electrodes. How large plastic deformation or interfacial delamination during electrochemical cycles in such electrodes affects the applicability of Stoney equation remains unclear. Here we develop a robust electrochemical-mechanical coupled numerical procedure to investigate the influence of large plastic deformation and interfacial failure on the measured stress in thin film electrodes. We identify how the constitutive behavior of electrode materials and film-substrate interfacial properties affect the measured stress-capacity curves of electrodes, and hence establish the relationship of electrode material parameters with the characteristics of stress-capacity curves. Using Li-ions batteries as examples, we show that plastic deformation and interfacial delamination account for the asymmetric stress-capacity loops seen in in situ stress measurements. The methods used here, along with the finite-element code in the supplementary material, may be used to model the electrode behavior as a function of the state of charge.

17. A numerical test method of California bearing ratio on graded crushed rocks using particle flow modeling

Directory of Open Access Journals (Sweden)

Yingjun Jiang

2015-04-01

Full Text Available In order to better understand the mechanical properties of graded crushed rocks (GCRs and to optimize the relevant design, a numerical test method based on the particle flow modeling technique PFC2D is developed for the California bearing ratio (CBR test on GCRs. The effects of different testing conditions and micro-mechanical parameters used in the model on the CBR numerical results have been systematically studied. The reliability of the numerical technique is verified. The numerical results suggest that the influences of the loading rate and Poisson's ratio on the CBR numerical test results are not significant. As such, a loading rate of 1.0–3.0 mm/min, a piston diameter of 5 cm, a specimen height of 15 cm and a specimen diameter of 15 cm are adopted for the CBR numerical test. The numerical results reveal that the CBR values increase with the friction coefficient at the contact and shear modulus of the rocks, while the influence of Poisson's ratio on the CBR values is insignificant. The close agreement between the CBR numerical results and experimental results suggests that the numerical simulation of the CBR values is promising to help assess the mechanical properties of GCRs and to optimize the grading design. Besides, the numerical study can provide useful insights on the mesoscopic mechanism.

18. 3rd International Conference on Numerical Analysis and Optimization : Theory, Methods, Applications and Technology Transfer

CERN Document Server

Grandinetti, Lucio; Purnama, Anton

2015-01-01

Presenting the latest findings in the field of numerical analysis and optimization, this volume balances pure research with practical applications of the subject. Accompanied by detailed tables, figures, and examinations of useful software tools, this volume will equip the reader to perform detailed and layered analysis of complex datasets. Many real-world complex problems can be formulated as optimization tasks. Such problems can be characterized as large scale, unconstrained, constrained, non-convex, non-differentiable, and discontinuous, and therefore require adequate computational methods, algorithms, and software tools. These same tools are often employed by researchers working in current IT hot topics such as big data, optimization and other complex numerical algorithms on the cloud, devising special techniques for supercomputing systems. The list of topics covered include, but are not limited to: numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, opt...

19. Numerical and statistical based damage analysis by the example of kiln elements; Numerisch und statistisch gestuetzte Schadensanalyse am Beispiel von Brennofenelementen

Energy Technology Data Exchange (ETDEWEB)

Reinert, U. [DEKRA-ETS Europaeische Gesellschaft fuer Technische Sicherheit mbH, Saarbruecken (Germany); Klaer, P. [Saar-Hartmetall und Werkzeuge GmbH, Voelklingen (Germany)

1999-02-01

The nonoxidic ceramics (for example SiC), used as a supporting structure in kilns, are subject to instantaneous damage, which as a rule is accompanied by high costs. Of interest in this context is the question whether a satisfactory statement can be made about the increase of damage frequency as a function of the firing temperature, the firing time, the geometry of the component, the material properties and the loading. Knowledge of these correlations provides the user with the possibility of minimizing the costs of damage by means of suitable selection of material and timely replacement of the components. The procedure presented in the following is based on the combination of numerical studies with statistically evaluated experiments. (orig.)

20. Mathematical and numerical methods for Vlasov-Maxwell equations: the contributions of data mining

International Nuclear Information System (INIS)

2014-01-01

There exist a lot of formulations that can model plasma physics or particle accelerators problems as the Vlasov- Maxwell equations. This paper deals with the applications of data mining techniques in the evaluation of numerical solutions of Vlasov-Maxwell models. This is part of the topic of characterizing the model and approximation errors via learning techniques. We give two examples of application. The first one aims at comparing two Vlasov-Maxwell approximate models. In the second one, a scheme based on data mining techniques is proposed to characterize the errors between a P1 and a P2 finite element Particle-In-Cell approach. Beyond these examples, this original approach should operate in all cases where intricate numerical simulations like for the Vlasov-Maxwell equations take a central part. (authors)

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

Energy Technology Data Exchange (ETDEWEB)

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

1997-07-01

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

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

International Nuclear Information System (INIS)

Toumi, I.; Caruge, D.

1997-01-01

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

3. Numerical methods and parallel algorithms for fast transient strongly coupled fluid-structure dynamics

International Nuclear Information System (INIS)

Faucher, V.

2014-01-01

This HDR is dedicated to the research in the framework of fast transient dynamics for industrial fluid-structure systems carried in the Laboratory of Dynamic Studies from CEA, implementing new numerical methods for the modelling of complex systems and the parallel solution of large coupled problems on supercomputers. One key issue for the proposed approaches is the limitation to its minimum of the number of non-physical parameters, to cope with constraints arising from the area of usage of the concepts: safety for both nuclear applications (CEA, EDF) and aeronautics (ONERA), protection of the citizen (EC/JRC) in particular. Kinematic constraints strongly coupling structures (namely through unilateral contact) or fluid and structures (with both conformant or non-conformant meshes depending on the geometrical situation) are handled through exact methods including Lagrange Multipliers, with consequences on the solution strategy to be dealt with. This latter aspect makes EPX, the simulation code where the methods are integrated, a singular tool in the community of fast transient dynamics software. The document mainly relies on a description of the modelling needs for industrial fast transient scenarios, for nuclear applications in particular, and the proposed solutions built in the framework of the collaboration between CEA, EDF (via the LaMSID laboratory) and the LaMCoS laboratory from INSA Lyon. The main considered examples are the tearing of the fluid-filled tank after impact, the Code Disruptive Accident for a Generation IV reactor or the ruin of reinforced concrete structures under impact. Innovative models and parallel algorithms are thus proposed, allowing to carry out with robustness and performance the corresponding simulations on supercomputers made of interconnected multi-core nodes, with a strict preservation of the quality of the physical solution. This was particularly the main point of the ANR RePDyn project (2010-2013), with CEA as the pilot. (author

4. A practical implicit finite-difference method: examples from seismic modelling

International Nuclear Information System (INIS)

Liu, Yang; Sen, Mrinal K

2009-01-01

We derive explicit and new implicit finite-difference formulae for derivatives of arbitrary order with any order of accuracy by the plane wave theory where the finite-difference coefficients are obtained from the Taylor series expansion. The implicit finite-difference formulae are derived from fractional expansion of derivatives which form tridiagonal matrix equations. Our results demonstrate that the accuracy of a (2N + 2)th-order implicit formula is nearly equivalent to that of a (6N + 2)th-order explicit formula for the first-order derivative, and (2N + 2)th-order implicit formula is nearly equivalent to (4N + 2)th-order explicit formula for the second-order derivative. In general, an implicit method is computationally more expensive than an explicit method, due to the requirement of solving large matrix equations. However, the new implicit method only involves solving tridiagonal matrix equations, which is fairly inexpensive. Furthermore, taking advantage of the fact that many repeated calculations of derivatives are performed by the same difference formula, several parts can be precomputed resulting in a fast algorithm. We further demonstrate that a (2N + 2)th-order implicit formulation requires nearly the same memory and computation as a (2N + 4)th-order explicit formulation but attains the accuracy achieved by a (6N + 2)th-order explicit formulation for the first-order derivative and that of a (4N + 2)th-order explicit method for the second-order derivative when additional cost of visiting arrays is not considered. This means that a high-order explicit method may be replaced by an implicit method of the same order resulting in a much improved performance. Our analysis of efficiency and numerical modelling results for acoustic and elastic wave propagation validates the effectiveness and practicality of the implicit finite-difference method

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

International Nuclear Information System (INIS)

Raymond, P.; Toumi, I.

1992-01-01

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

6. 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

7. 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.)

8. What can a numerical landscape evolution model tell us about the evolution of a real landscape? Two examples of modeling a real landscape without recreating it

Science.gov (United States)

Gasparini, N. M.; Whipple, K. X.; Willenbring, J.; Crosby, B. T.; Brocard, G. Y.

2013-12-01

Numerical landscape evolution models (LEMs) offer us the unique opportunity to watch a landscape evolve under any set of environmental forcings that we can quantify. The possibilities for using LEMs are infinite, but complications arise when trying to model a real landscape. Specifically, numerical models cannot recreate every aspect of a real landscape because exact initial conditions are unknown, there will always be gaps in the known tectonic and climatic history, and the geomorphic transport laws that govern redistribution of mass due to surface processes will always be a simplified representation of the actual process. Yet, even with these constraints, numerical models remain the only tool that offers us the potential to explore a limitless range of evolutionary scenarios, allowing us to, at the very least, identify possible drivers responsible for the morphology of the current landscape, and just as importantly, rule out others. Here we highlight two examples in which we use a numerical model to explore the signature of different forcings on landscape morphology and erosion patterns. In the first landscape, the Northern Bolivian Andes, the relative imprint of rock uplift and precipitation patterns on landscape morphology is widely contested. We use the CHILD LEM to systematically vary climate and tectonics and quantify their fingerprints on channel profiles across a steep mountain front. We find that rock uplift and precipitation patterns in this landscape and others can be teased out by examining channel profiles of variably sized catchments that drain different parts of the topography. In the second landscape, the South Fork Eel River (SFER), northern California, USA, the tectonic history is relatively well known; a wave of rock uplift swept through the watershed from headwaters to outlet, perturbing the landscape and sending a wave of bedrock incision upstream. Nine millennial-scale erosion rates from along the mainstem of the river illustrate a pattern of

9. A novel numerical method for the analysis of electron transport in the presence of pointlike magnetic scatterers

International Nuclear Information System (INIS)

Miyagawa, Yuu; Ueta, Tsuyoshi

2008-01-01

The boundary element method (BEM) is so extended as to treat two-dimensional (2D) electron systems in the presence of pointlike islands of magnetic moment. In the present paper, the pointlike magnetic scatterer is modeled by a cylindrical barrier. The radius of the cylindrical barrier is assumed to be so small, keeping the volume definite, that the pointlike magnetic scatterer is approximated by a Dirac δ function. Then, we make an approximation on the BEM formulation, wherefore we derive a novel numerical method for electron transport in the presence of pointlike magnetic scatterers. In a numerical implementation of the method extended here, the numerical errors of probability conservation are less than 1% for any cases and the computational costs, that is, the required memory amount and CPU time, are much reduced. As examples, the proposed method is applied to transport problems through a quantum wire with four pointlike magnetic scatterers. It is clearly shown that magnetic scatterers, even pointlike magnetic moments, lead to spin flip-flop, localization and resonance

10. Geothermal-Related Thermo-Elastic Fracture Analysis by Numerical Manifold Method

OpenAIRE

Jun He; Quansheng Liu; Zhijun Wu; Yalong Jiang

2018-01-01

One significant factor influencing geothermal energy exploitation is the variation of the mechanical properties of rock in high temperature environments. Since rock is typically a heterogeneous granular material, thermal fracturing frequently occurs in the rock when the ambient temperature changes, which can greatly influence the geothermal energy exploitation. A numerical method based on the numerical manifold method (NMM) is developed in this study to simulate the thermo-elastic fracturing ...

11. A Finite Difference, Semi-implicit, Equation-of-State Efficient Algorithm for the Compositional Flow Modeling in the Subsurface: Numerical Examples

KAUST Repository

Saavedra, Sebastian

2012-07-01

The mathematical model that has been recognized to have the more accurate approximation to the physical laws govern subsurface hydrocarbon flow in reservoirs is the Compositional Model. The features of this model are adequate to describe not only the performance of a multiphase system but also to represent the transport of chemical species in a porous medium. Its importance relies not only on its current relevance to simulate petroleum extraction processes, such as, Primary, Secondary, and Enhanced Oil Recovery Process (EOR) processes but also, in the recent years, carbon dioxide (CO2) sequestration. The purpose of this study is to investigate the subsurface compositional flow under isothermal conditions for several oil well cases. While simultaneously addressing computational implementation finesses to contribute to the efficiency of the algorithm. This study provides the theoretical framework and computational implementation subtleties of an IMplicit Pressure Explicit Composition (IMPEC)-Volume-balance (VB), two-phase, equation-of-state, approach to model isothermal compositional flow based on the finite difference scheme. The developed model neglects capillary effects and diffusion. From the phase equilibrium premise, the model accounts for volumetric performances of the phases, compressibility of the phases, and composition-dependent viscosities. The Equation of State (EoS) employed to approximate the hydrocarbons behaviour is the Peng Robinson Equation of State (PR-EOS). Various numerical examples were simulated. The numerical results captured the complex physics involved, i.e., compositional, gravitational, phase-splitting, viscosity and relative permeability effects. Regarding the numerical scheme, a phase-volumetric-flux estimation eases the calculation of phase velocities by naturally fitting to phase-upstream-upwinding. And contributes to a faster computation and an efficient programming development.

12. Use of helicity methods in evaluating loop integrals: a QCD example

International Nuclear Information System (INIS)

Koerner, J.G.; Sieben, P.

1991-01-01

We discuss the use of helicity methods in evaluating loop diagrams by analyzing a specific example: the one-loop concentration to e + e - → qanti qg in massless QCD. By using covariant helicity representations for the spinor and vector wave functins we obtain the helicity amplitudes directly from the Feynman loop diagrams by covariant contraction. The necessary loop integrations are considerably simplified since one encounters only scalar loop integrals after contraction. We discuss crossing relations that allow one to obtain the corresponding one-loop helicity amplitudes for the crossed processes as e.g. qanti q → (W, Z, γ * ) + g including the real photon cases. As we treat the spin degrees of freedom in four dimensions and only continue momenta to n dimensions (dimensional reduction scheme) we explicate how our results are related to the usual dimensional regularization results. (orig.)

13. Proceeding of 1999-workshop on MHD computations 'study on numerical methods related to plasma confinement'

International Nuclear Information System (INIS)

Kako, T.; Watanabe, T.

2000-06-01

This is the proceeding of 'study on numerical methods related to plasma confinement' held in National Institute for Fusion Science. In this workshop, theoretical and numerical analyses of possible plasma equilibria with their stability properties are presented. There are also various lectures on mathematical as well as numerical analyses related to the computational methods for fluid dynamics and plasma physics. Separate abstracts were presented for 13 of the papers in this report. The remaining 6 were considered outside the subject scope of INIS. (J.P.N.)

14. Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

Energy Technology Data Exchange (ETDEWEB)

Inc, Mustafa [Department of Mathematics, Firat University, 23119 Elazig (Turkey)], E-mail: minc@firat.edu.tr; Ugurlu, Yavuz [Department of Mathematics, Firat University, 23119 Elazig (Turkey)

2007-09-17

In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions.

15. Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

International Nuclear Information System (INIS)

Inc, Mustafa; Ugurlu, Yavuz

2007-01-01

In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions

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

KAUST Repository

Wang, Yi

2016-07-21

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

17. Numerická simulace v biomechanice – forenzní příklad Numerical simulation in biomechanics – a forensic example

Directory of Open Access Journals (Sweden)

Norbert Praxl

2006-02-01

áním odpovídají zcela pasivnímu lidskému tělu. The paper presents an example of a forensic application of biomechanical methods including numerical simulation with human body models. By means of a case study of an unwitnessed lethal fall the course of the biomechanical forensic reconstruction is demonstrated. The traces available at the place of finding and the injuries of the victim are the facts that the analysis is based on. The ultimate expected result of the biomechanical analysis is the assignment of all available traces and the explanation of the event. The injuries observed in the described case were partly typical fall injuries, but there were also some injuries that could not be prima vista assigned. The police investigation at the place of finding also brought to light some facts that could not be satisfactorily explained at first. By using numerical simulation, additional information was obtained that enabled us to explain many aspects of the case that could not have been analysed otherwise. Numerical simulation offers objective and quantitative data enabling a far more exact analysis of the studied event – the kinematical as well as dynamical parameters of the human body and its interaction with the surroundings structures can be studied and even the human body’s internal forces can be analysed enabling thus an accurate injury prediction. All the important unknown parameters (initial conditions of the simulated event, i. e. body position, body orientation, initial velocity etc. can be easily varied so that all the possibilities can be taken into account. Another very important asset of this method is its powerful visualisation capability that enhances the understanding of the studied events even for persons without extensive biomechanical knowledge. The major limitation of numerical simulation at the moment is the lack of muscle activity; the models represent only a totally passive human body so far.

18. Levels of reduction in van Manen's phenomenological hermeneutic method: an empirical example.

Science.gov (United States)

Heinonen, Kristiina

2015-05-01

To describe reduction as a method using van Manen's phenomenological hermeneutic research approach. Reduction involves several levels that can be distinguished for their methodological usefulness. Researchers can use reduction in different ways and dimensions for their methodological needs. A study of Finnish multiple-birth families in which open interviews (n=38) were conducted with public health nurses, family care workers and parents of twins. A systematic literature and knowledge review showed there were no articles on multiple-birth families that used van Manen's method. Discussion The phenomena of the 'lifeworlds' of multiple-birth families consist of three core essential themes as told by parents: 'a state of constant vigilance', 'ensuring that they can continue to cope' and 'opportunities to share with other people'. Reduction provides the opportunity to carry out in-depth phenomenological hermeneutic research and understand people's lives. It helps to keep research stages separate but also enables a consolidated view. Social care and healthcare professionals have to hear parents' voices better to comprehensively understand their situation; they need further tools and training to be able to empower parents of twins. This paper adds an empirical example to the discussion of phenomenology, hermeneutic study and reduction as a method. It opens up reduction for researchers to exploit.

19. 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.

20. Development of parallel implementation of adaptive numerical methods with industrial applications in fluid mechanics

International Nuclear Information System (INIS)

Laucoin, E.

2008-10-01

Numerical resolution of partial differential equations can be made reliable and efficient through the use of adaptive numerical methods.We present here the work we have done for the design, the implementation and the validation of such a method within an industrial software platform with applications in thermohydraulics. From the geometric point of view, this method can deal both with mesh refinement and mesh coarsening, while ensuring the quality of the mesh cells. Numerically, we use the mortar elements formalism in order to extend the Finite Volumes-Elements method implemented in the Trio-U platform and to deal with the non-conforming meshes arising from the adaptation procedure. Finally, we present an implementation of this method using concepts from domain decomposition methods for ensuring its efficiency while running in a parallel execution context. (author)

1. Numerical method for solving the inverse problem of quantum scattering theory

International Nuclear Information System (INIS)

Ajrapetyan, R.G.; Puzynin, I.V.; Zhidkov, E.P.

1996-01-01

A new numerical method for solving the problem of the reconstruction of interaction potential by a phase shift given on a set of closed intervals in (l,k)-plane, satisfying certain geometrical 'Staircase Condition', is suggested. The method is based on the Variable Phase Approach and on the modification of the Continuous Analogy of the Newton Method. 22 refs., 1 fig

2. Application of Numerical Optimization Methods to Perform Molecular Docking on Graphics Processing Units

Directory of Open Access Journals (Sweden)

M. A. Farkov

2014-01-01

Full Text Available An analysis of numerical optimization methods for solving a problem of molecular docking has been performed. Some additional requirements for optimization methods according to GPU architecture features were specified. A promising method for implementation on GPU was selected. Its implementation was described and performance and accuracy tests were performed.

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

International Nuclear Information System (INIS)

Henyey, F.S.; Pomphrey, N.

1987-10-01

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

4. Steady-state transport equation resolution by particle methods, and numerical results

International Nuclear Information System (INIS)

Mercier, B.

1985-10-01

A method to solve steady-state transport equation has been given. Principles of the method are given. The method is studied in two different cases; estimations given by the theory are compared to numerical results. Results got in 1-D (spherical geometry) and in 2-D (axisymmetric geometry) are given [fr

5. A virtual component method in numerical computation of cascades for isotope separation

International Nuclear Information System (INIS)

Zeng Shi; Cheng Lu

2014-01-01

The analysis, optimization, design and operation of cascades for isotope separation involve computations of cascades. In analytical analysis of cascades, using virtual components is a very useful analysis method. For complicated cases of cascades, numerical analysis has to be employed. However, bound up to the conventional idea that the concentration of a virtual component should be vanishingly small, virtual component is not yet applied to numerical computations. Here a method of introducing the method of using virtual components to numerical computations is elucidated, and its application to a few types of cascades is explained and tested by means of numerical experiments. The results show that the concentration of a virtual component is not restrained at all by the 'vanishingly small' idea. For the same requirements on cascades, the cascades obtained do not depend on the concentrations of virtual components. (authors)

6. Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method

Science.gov (United States)

Chang, Chih-Hao; Deng, Xiaolong; Theofanous, Theo G.

2013-06-01

We present a conservative and consistent numerical method for solving the Navier-Stokes equations in flow domains that may be separated by any number of material interfaces, at arbitrarily-high density/viscosity ratios and acoustic-impedance mismatches, subjected to strong shock waves and flow speeds that can range from highly supersonic to near-zero Mach numbers. A principal aim is prediction of interfacial instabilities under superposition of multiple potentially-active modes (Rayleigh-Taylor, Kelvin-Helmholtz, Richtmyer-Meshkov) as found for example with shock-driven, immersed fluid bodies (locally oblique shocks)—accordingly we emphasize fidelity supported by physics-based validation, including experiments. Consistency is achieved by satisfying the jump discontinuities at the interface within a conservative 2nd-order scheme that is coupled, in a conservative manner, to the bulk-fluid motions. The jump conditions are embedded into a Riemann problem, solved exactly to provide the pressures and velocities along the interface, which is tracked by a level set function to accuracy of O(Δx5, Δt4). Subgrid representation of the interface is achieved by allowing curvature of its constituent interfacial elements to obtain O(Δx3) accuracy in cut-cell volume, with attendant benefits in calculating cell- geometric features and interface curvature (O(Δx3)). Overall the computation converges at near-theoretical O(Δx2). Spurious-currents are down to machine error and there is no time-step restriction due to surface tension. Our method is built upon a quadtree-like adaptive mesh refinement infrastructure. When necessary, this is supplemented by body-fitted grids to enhance resolution of the gas dynamics, including flow separation, shear layers, slip lines, and critical layers. Comprehensive comparisons with exact solutions for the linearized Rayleigh-Taylor and Kelvin-Helmholtz problems demonstrate excellent performance. Sample simulations of liquid drops subjected to

7. Efficient numerical methods for simulating surface tension of multi-component mixtures with the gradient theory of fluid interfaces

KAUST Repository

Kou, Jisheng

2015-08-01

Surface tension significantly impacts subsurface flow and transport, and it is the main cause of capillary effect, a major immiscible two-phase flow mechanism for systems with a strong wettability preference. In this paper, we consider the numerical simulation of the surface tension of multi-component mixtures with the gradient theory of fluid interfaces. Major numerical challenges include that the system of the Euler-Lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite. We construct a linear transformation to reduce the Euler-Lagrange equations, and naturally introduce a path function, which is proven to be a monotonic function of the spatial coordinate variable. By using the linear transformation and the path function, we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions. Moreover, the computation of the surface tension is also simplified. The proposed methods do not need to solve the differential equation system, and they are easy to be implemented in practical applications. Numerical examples are tested to verify the efficiency of the proposed methods. © 2014 Elsevier B.V.

8. Towards numerical simulations of supersonic liquid jets using ghost fluid method

International Nuclear Information System (INIS)

Majidi, Sahand; Afshari, Asghar

2015-01-01

Highlights: • A ghost fluid method based solver is developed for numerical simulation of compressible multiphase flows. • The performance of the numerical tool is validated via several benchmark problems. • Emergence of supersonic liquid jets in quiescent gaseous environment is simulated using ghost fluid method for the first time. • Bow-shock formation ahead of the liquid jet is clearly observed in the obtained numerical results. • Radiation of mach waves from the phase-interface witnessed experimentally is evidently captured in our numerical simulations. - Abstract: A computational tool based on the ghost fluid method (GFM) is developed to study supersonic liquid jets involving strong shocks and contact discontinuities with high density ratios. The solver utilizes constrained reinitialization method and is capable of switching between the exact and approximate Riemann solvers to increase the robustness. The numerical methodology is validated through several benchmark test problems; these include one-dimensional multiphase shock tube problem, shock–bubble interaction, air cavity collapse in water, and underwater-explosion. A comparison between our results and numerical and experimental observations indicate that the developed solver performs well investigating these problems. The code is then used to simulate the emergence of a supersonic liquid jet into a quiescent gaseous medium, which is the very first time to be studied by a ghost fluid method. The results of simulations are in good agreement with the experimental investigations. Also some of the famous flow characteristics, like the propagation of pressure-waves from the liquid jet interface and dependence of the Mach cone structure on the inlet Mach number, are reproduced numerically. The numerical simulations conducted here suggest that the ghost fluid method is an affordable and reliable scheme to study complicated interfacial evolutions in complex multiphase systems such as supersonic liquid

9. A numerical method for two-dimensional anisotropic transport problem in cylindrical geometry

International Nuclear Information System (INIS)

Du Mingsheng; Feng Tiekai; Fu Lianxiang; Cao Changshu; Liu Yulan

1988-01-01

The authors deal with the triangular mesh-discontinuous finite element method for solving the time-dependent anisotropic neutron transport problem in two-dimensional cylindrical geometry. A prior estimate of the numerical solution is given. Stability is proved. The authors have computed a two dimensional anisotropic neutron transport problem and a Tungsten-Carbide critical assembly problem by using the numerical method. In comparision with DSN method and the experimental results obtained by others both at home and abroad, the method is satisfactory

10. 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)

11. Numerical Investigations on Several Stabilized Finite Element Methods for the Stokes Eigenvalue Problem

Directory of Open Access Journals (Sweden)

Pengzhan Huang

2011-01-01

Full Text Available Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.

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

International Nuclear Information System (INIS)

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

1997-01-01

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

13. New numerical methods for open-loop and feedback solutions to dynamic optimization problems

Science.gov (United States)

is that the resulting control law has an algebraic closed-form structure. The proposed method uses an optimal spatial statistical predictor called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. With universal kriging, an approximation to the optimal feedback map is computed by conceptualizing a set of state-control samples from pre-computed extremals to be a particular realization of a jointly Gaussian spatial process. Feedback policies are computed for a variety of example dynamic optimization problems in order to evaluate the effectiveness of this methodology. This feedback synthesis approach is found to combine good numerical accuracy with low computational overhead, making it a suitable candidate for real-time applications. Particle swarm and universal kriging are combined for a capstone example, a near optimal, near-admissible, full-state feedback control law is computed and tested for the heat-load-limited atmospheric-turn guidance of an aeroassisted transfer vehicle. The performance of this explicit guidance scheme is found to be very promising; initial errors in atmospheric entry due to simulated thruster misfirings are found to be accurately corrected while closely respecting the algebraic state-inequality constraint.

14. Numerical method in reproducing kernel space for an inverse source problem for the fractional diffusion equation

International Nuclear Information System (INIS)

Wang, Wenyan; Han, Bo; Yamamoto, Masahiro

2013-01-01

We propose a new numerical method for reproducing kernel Hilbert space to solve an inverse source problem for a two-dimensional fractional diffusion equation, where we are required to determine an x-dependent function in a source term by data at the final time. The exact solution is represented in the form of a series and the approximation solution is obtained by truncating the series. Furthermore, a technique is proposed to improve some of the existing methods. We prove that the numerical method is convergent under an a priori assumption of the regularity of solutions. The method is simple to implement. Our numerical result shows that our method is effective and that it is robust against noise in L 2 -space in reconstructing a source function. (paper)

15. Experimental Results and Numerical Simulation of the Target RCS using Gaussian Beam Summation Method

Directory of Open Access Journals (Sweden)

Ghanmi Helmi

2018-05-01

Full Text Available This paper presents a numerical and experimental study of Radar Cross Section (RCS of radar targets using Gaussian Beam Summation (GBS method. The purpose GBS method has several advantages over ray method, mainly on the caustic problem. To evaluate the performance of the chosen method, we started the analysis of the RCS using Gaussian Beam Summation (GBS and Gaussian Beam Launching (GBL, the asymptotic models Physical Optic (PO, Geometrical Theory of Diffraction (GTD and the rigorous Method of Moment (MoM. Then, we showed the experimental validation of the numerical results using experimental measurements which have been executed in the anechoic chamber of Lab-STICC at ENSTA Bretagne. The numerical and experimental results of the RCS are studied and given as a function of various parameters: polarization type, target size, Gaussian beams number and Gaussian beams width.

16. Tangent modulus in numerical integration of constitutive relations and its influence on convergence of N-R method

Directory of Open Access Journals (Sweden)

Poruba Z.

2009-06-01

Full Text Available For the numerical solution of elasto-plastic problems with use of Newton-Raphson method in global equilibrium equation it is necessary to determine the tangent modulus in each integration point. To reach the parabolic convergence of Newton-Raphson method it is convenient to use so called algorithmic tangent modulus which is consistent with used integration scheme. For more simple models for example Chaboche combined hardening model it is possible to determine it in analytical way. In case of more robust macroscopic models it is in many cases necessary to use the approximation approach. This possibility is presented in this contribution for radial return method on Chaboche model. An example solved in software Ansys corresponds to line contact problem with assumption of Coulomb's friction. The study shows at the end that the number of iteration of N-R method is higher in case of continuum tangent modulus and many times higher with use of modified N-R method, initial stiffness method.

17. Implementation and assessment of high-resolution numerical methods in TRACE

Energy Technology Data Exchange (ETDEWEB)

Wang, Dean, E-mail: wangda@ornl.gov [Oak Ridge National Laboratory, 1 Bethel Valley RD 6167, Oak Ridge, TN 37831 (United States); Mahaffy, John H.; Staudenmeier, Joseph; Thurston, Carl G. [U.S. Nuclear Regulatory Commission, Washington, DC 20555 (United States)

2013-10-15

Highlights: • Study and implement high-resolution numerical methods for two-phase flow. • They can achieve better numerical accuracy than the 1st-order upwind scheme. • They are of great numerical robustness and efficiency. • Great application for BWR stability analysis and boron injection. -- Abstract: The 1st-order upwind differencing numerical scheme is widely employed to discretize the convective terms of the two-phase flow transport equations in reactor systems analysis codes such as TRACE and RELAP. While very robust and efficient, 1st-order upwinding leads to excessive numerical diffusion. Standard 2nd-order numerical methods (e.g., Lax–Wendroff and Beam–Warming) can effectively reduce numerical diffusion but often produce spurious oscillations for steep gradients. To overcome the difficulties with the standard higher-order schemes, high-resolution schemes such as nonlinear flux limiters have been developed and successfully applied in numerical simulation of fluid-flow problems in recent years. The present work contains a detailed study on the implementation and assessment of six nonlinear flux limiters in TRACE. These flux limiters selected are MUSCL, Van Leer (VL), OSPRE, Van Albada (VA), ENO, and Van Albada 2 (VA2). The assessment is focused on numerical stability, convergence, and accuracy of the flux limiters and their applicability for boiling water reactor (BWR) stability analysis. It is found that VA and MUSCL work best among of the six flux limiters. Both of them not only have better numerical accuracy than the 1st-order upwind scheme but also preserve great robustness and efficiency.

18. Implementation and assessment of high-resolution numerical methods in TRACE

International Nuclear Information System (INIS)

Wang, Dean; Mahaffy, John H.; Staudenmeier, Joseph; Thurston, Carl G.

2013-01-01

Highlights: • Study and implement high-resolution numerical methods for two-phase flow. • They can achieve better numerical accuracy than the 1st-order upwind scheme. • They are of great numerical robustness and efficiency. • Great application for BWR stability analysis and boron injection. -- Abstract: The 1st-order upwind differencing numerical scheme is widely employed to discretize the convective terms of the two-phase flow transport equations in reactor systems analysis codes such as TRACE and RELAP. While very robust and efficient, 1st-order upwinding leads to excessive numerical diffusion. Standard 2nd-order numerical methods (e.g., Lax–Wendroff and Beam–Warming) can effectively reduce numerical diffusion but often produce spurious oscillations for steep gradients. To overcome the difficulties with the standard higher-order schemes, high-resolution schemes such as nonlinear flux limiters have been developed and successfully applied in numerical simulation of fluid-flow problems in recent years. The present work contains a detailed study on the implementation and assessment of six nonlinear flux limiters in TRACE. These flux limiters selected are MUSCL, Van Leer (VL), OSPRE, Van Albada (VA), ENO, and Van Albada 2 (VA2). The assessment is focused on numerical stability, convergence, and accuracy of the flux limiters and their applicability for boiling water reactor (BWR) stability analysis. It is found that VA and MUSCL work best among of the six flux limiters. Both of them not only have better numerical accuracy than the 1st-order upwind scheme but also preserve great robustness and efficiency

19. Theoretical Coalescence: A Method to Develop Qualitative Theory: The Example of Enduring.

Science.gov (United States)

Morse, Janice M

Qualitative research is frequently context bound, lacks generalizability, and is limited in scope. The purpose of this article was to describe a method, theoretical coalescence, that provides a strategy for analyzing complex, high-level concepts and for developing generalizable theory. Theoretical coalescence is a method of theoretical expansion, inductive inquiry, of theory development, that uses data (rather than themes, categories, and published extracts of data) as the primary source for analysis. Here, using the development of the lay concept of enduring as an example, I explore the scientific development of the concept in multiple settings over many projects and link it within the Praxis Theory of Suffering. As comprehension emerges when conducting theoretical coalescence, it is essential that raw data from various different situations be available for reinterpretation/reanalysis and comparison to identify the essential features of the concept. The concept is then reconstructed, with additional inquiry that builds description, and evidence is conducted and conceptualized to create a more expansive concept and theory. By utilizing apparently diverse data sets from different contexts that are linked by certain characteristics, the essential features of the concept emerge. Such inquiry is divergent and less bound by context yet purposeful, logical, and with significant pragmatic implications for practice in nursing and beyond our discipline. Theoretical coalescence is a means by which qualitative inquiry is broadened to make an impact, to accommodate new theoretical shifts and concepts, and to make qualitative research applied and accessible in new ways.

20. The Method of Analysis Derived Coefficients of Database as a New Method of Historical Research (for Example, a Database of Ballistic Parameters of Naval Artillery

Directory of Open Access Journals (Sweden)

Nicholas W. Mitiukov

2015-12-01

Full Text Available In paper there is proposed a new method of historical research, based on analysis of derivatives coefficients of database (for example, the form factor in the database of ballistic data. This method has a much greater protection from subjectivism and direct falsification, compared with the analysis obtained directly from the source of the numerical series, as any intentional or unintentional distortion of the raw data provides a significant contrast ratio derived from the average sample values. Application of this method to the analysis of ballistic data base of naval artillery allowed to find the facts, forcing a new look at some of the events in the history data on the German naval artillery before World War I, probably overpriced for disinformation opponents of the Entente; during the First World War, Spain, apparently held secret talks with the firm Bofors ended purchase of Swedish shells; the first Russian naval rifled guns were created obvious based on the project Blackly, not Krupp as traditionally considered.

1. 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.

2. Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

Energy Technology Data Exchange (ETDEWEB)

Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)

1997-12-31

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)

3. Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

International Nuclear Information System (INIS)

Jo, Jong Chull; Shin, Won Ky

1997-01-01

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available

4. Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

Energy Technology Data Exchange (ETDEWEB)

Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)

1998-12-31

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)

5. Consumers' Kansei Needs Clustering Method for Product Emotional Design Based on Numerical Design Structure Matrix and Genetic Algorithms.

Science.gov (United States)

Yang, Yan-Pu; Chen, Deng-Kai; Gu, Rong; Gu, Yu-Feng; Yu, Sui-Huai

2016-01-01

Consumers' Kansei needs reflect their perception about a product and always consist of a large number of adjectives. Reducing the dimension complexity of these needs to extract primary words not only enables the target product to be explicitly positioned, but also provides a convenient design basis for designers engaging in design work. Accordingly, this study employs a numerical design structure matrix (NDSM) by parameterizing a conventional DSM and integrating genetic algorithms to find optimum Kansei clusters. A four-point scale method is applied to assign link weights of every two Kansei adjectives as values of cells when constructing an NDSM. Genetic algorithms are used to cluster the Kansei NDSM and find optimum clusters. Furthermore, the process of the proposed method is presented. The details of the proposed approach are illustrated using an example of electronic scooter for Kansei needs clustering. The case study reveals that the proposed method is promising for clustering Kansei needs adjectives in product emotional design.

6. A numerical method to estimate AC loss in superconducting coated conductors by finite element modelling

Energy Technology Data Exchange (ETDEWEB)

Hong, Z; Jiang, Q; Pei, R; Campbell, A M; Coombs, T A [Engineering Department, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ (United Kingdom)

2007-04-15

A finite element method code based on the critical state model is proposed to solve the AC loss problem in YBCO coated conductors. This numerical method is based on a set of partial differential equations (PDEs) in which the magnetic field is used as the state variable. The AC loss problems have been investigated both in self-field condition and external field condition. Two numerical approaches have been introduced: the first model is configured on the cross-section plane of the YBCO tape to simulate an infinitely long superconducting tape. The second model represents the plane of the critical current flowing and is able to simulate the YBCO tape with finite length where the end effect is accounted. An AC loss measurement has been done to verify the numerical results and shows a good agreement with the numerical solution.

7. The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling

Energy Technology Data Exchange (ETDEWEB)

Nielsen, Bjoern Fredrik

1997-12-31

The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.

8. The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling

Energy Technology Data Exchange (ETDEWEB)

Nielsen, Bjoern Fredrik

1998-12-31

The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.

9. Numerical comparison of robustness of some reduction methods in rough grids

KAUST Repository

Hou, Jiangyong

2014-04-09

In this article, we present three nonsymmetric mixed hybrid RT 1 2 methods and compare with some recently developed reduction methods which are suitable for the single-phase Darcy flow problem with full anisotropic and highly heterogeneous permeability on general quadrilateral grids. The methods reviewed are multipoint flux approximation (MPFA), multipoint flux mixed finite element method, mixed-finite element with broken RT 1 2 method, MPFA-type mimetic finite difference method, and symmetric mixed-hybrid finite element method. The numerical experiments of these methods on different distorted meshes are compared, as well as their differences in performance of fluxes are discussed. © 2014 Wiley Periodicals, Inc.

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

Energy Technology Data Exchange (ETDEWEB)

Iwashige, Kengo; Ikeda, Takashi [Hitachi, Ltd. (Japan)

1995-09-01

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

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

International Nuclear Information System (INIS)

Kosovichev, A.G.

1984-01-01

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

12. Numerical simulation of bubble deformation in magnetic fluids by finite volume method

International Nuclear Information System (INIS)

Yamasaki, Haruhiko; Yamaguchi, Hiroshi

2017-01-01

Bubble deformation in magnetic fluids under magnetic field is investigated numerically by an interface capturing method. The numerical method consists of a coupled level-set and VOF (Volume of Fluid) method, combined with conservation CIP (Constrained Interpolation Profile) method with the self-correcting procedure. In the present study considering actual physical properties of magnetic fluid, bubble deformation under given uniform magnetic field is analyzed for internal magnetic field passing through a magnetic gaseous and liquid phase interface. The numerical results explain the mechanism of bubble deformation under presence of given magnetic field. - Highlights: • A magnetic field analysis is developed to simulate the bubble dynamics in magnetic fluid with two-phase interface. • The elongation of bubble increased with increasing magnetic flux intensities due to strong magnetic normal force. • Proposed technique explains the bubble dynamics, taking into account of the continuity of the magnetic flux density.

13. New numerical method for iterative or perturbative solution of quantum field theory

International Nuclear Information System (INIS)

Hahn, S.C.; Guralnik, G.S.

1999-01-01

A new computational idea for continuum quantum Field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spin-off of the technology developed for 'exact' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order. (authors)

14. Solutions manual to accompany An introduction to numerical methods and analysis

CERN Document Server

Epperson, James F

2014-01-01

A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, sp

15. Linear and nonlinear properties of numerical methods for the rotating shallow water equations

Science.gov (United States)

Eldred, Chris

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. It is desirable that numerical models posses similar properties, and the prototypical example of such a scheme is the 1981 Arakawa and Lamb (AL81) staggered (C-grid) total energy and potential enstrophy conserving scheme, based on the vector invariant form of the continuous equations. However, this scheme is restricted to a subset of logically square, orthogonal grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos and others) and Discrete Exterior Calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp and others). It is also possible to obtain these properties (along with arguably superior wave dispersion properties) through the use of a collocated (Z-grid) scheme based on the vorticity-divergence form of the continuous equations. Unfortunately, existing examples of these schemes in the literature for general, spherical grids either contain computational modes; or do not conserve total energy and potential enstrophy. This dissertation extends an existing scheme for planar grids to spherical grids, through the use of Nambu brackets (as pioneered by Rick Salmon). To compare these two schemes, the linear modes (balanced states, stationary modes and propagating modes; with and without dissipation) are examined on both uniform planar grids (square, hexagonal) and quasi-uniform spherical grids (geodesic, cubed-sphere). In addition to evaluating the linear modes, the results of the two schemes applied to a set of standard shallow water test cases and a recently developed forced-dissipative turbulence test case from John Thuburn (intended to evaluate the ability the suitability of schemes as the basis for a climate model) on both hexagonal

16. 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

17. A Numerical Algorithm and a Graphical Method to Size a Heat Exchanger

DEFF Research Database (Denmark)

Berning, Torsten

2011-01-01

This paper describes the development of a numerical algorithm and a graphical method that can be employed in order to determine the overall heat transfer coefficient inside heat exchangers. The method is based on an energy balance and utilizes the spreadsheet application software Microsoft ExcelTM...

18. A Numerical Algorithm and a Graphical Method to Size a Heat Exchanger

DEFF Research Database (Denmark)

Berning, Torsten

2011-01-01

This paper describes the development of a numerical algorithm and a graphical method that can be employed in order to determine the overall heat transfer coefficient inside heat exchangers. The method is based on an energy balance and utilizes the spreadsheet application software Microsoft Excel...

19. Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems

International Nuclear Information System (INIS)

Mei Shuli; Du Chengjin; Zhang Senwen

2008-01-01

Homotopy perturbation method (HPM) proposed by Ji-Huan He is very effective and convenient for single-degree-of-freedom systems. In this paper a coupling technique of He's method and precise integration method (PIM) is suggested to solve multi-degree-of-freedom nonlinear dynamic systems. The new technique keeps the merits of the two methods. Some examples are given to illustrate its effectiveness and convenience. Furthermore the obtained solution is of high accuracy

20. Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems

International Nuclear Information System (INIS)

Hykes, J. M.; Ferrer, R. M.

2013-01-01

The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is 98 Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)

1. [Methods in health services research. The example of the evaluation of the German disease management programmes].

Science.gov (United States)

Morfeld, M; Wirtz, M

2006-02-01

According to the established definition of Pfaff, health services research analyses patients' path through the institutions of the health care system. The focus is on development, evaluation and implementation of innovative measures of health care. By increasing its quality health services research strives for an improvement of efficacy and efficiency of the health care system. In order to allow for an appropriate evaluation it is essential to differentiate between structure, process and outcome quality referring to (1) the health care system in its entirety, (2) specific health care units as well as (3) processes of communication in different settings. Health services research comprises a large array of scientific disciplines like public health, medicine, social sciences and social care. For the purpose of managing its tasks adequately a special combination of instruments and methodological procedures is needed. Thus, diverse techniques of evaluation research as well as special requirements for study designs and assessment procedures are of vital importance. The example of the German disease management programmes illustrates the methodical requirements for a scientific evaluation.

2. Vectorization on the star computer of several numerical methods for a fluid flow problem

Science.gov (United States)

Lambiotte, J. J., Jr.; Howser, L. M.

1974-01-01

A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.

3. 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

4. A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations

International Nuclear Information System (INIS)

Saurel, Richard; Franquet, Erwin; Daniel, Eric; Le Metayer, Olivier

2007-01-01

A new projection method is developed for the Euler equations to determine the thermodynamic state in computational cells. It consists in the resolution of a mechanical relaxation problem between the various sub-volumes present in a computational cell. These sub-volumes correspond to the ones traveled by the various waves that produce states with different pressures, velocities, densities and temperatures. Contrarily to Godunov type schemes the relaxed state corresponds to mechanical equilibrium only and remains out of thermal equilibrium. The pressure computation with this relaxation process replaces the use of the conventional equation of state (EOS). A simplified relaxation method is also derived and provides a specific EOS (named the Numerical EOS). The use of the Numerical EOS gives a cure to spurious pressure oscillations that appear at contact discontinuities for fluids governed by real gas EOS. It is then extended to the computation of interface problems separating fluids with different EOS (liquid-gas interface for example) with the Euler equations. The resulting method is very robust, accurate, oscillation free and conservative. For the sake of simplicity and efficiency the method is developed in a Lagrange-projection context and is validated over exact solutions. In a companion paper [F. Petitpas, E. Franquet, R. Saurel, A relaxation-projection method for compressible flows. Part II: computation of interfaces and multiphase mixtures with stiff mechanical relaxation. J. Comput. Phys. (submitted for publication)], the method is extended to the numerical approximation of a non-conservative hyperbolic multiphase flow model for interface computation and shock propagation into mixtures

5. Solar cells elaborated by chemical methods: examples of research and development at CIE-UNAM

International Nuclear Information System (INIS)

Rincon, Marina E.

2008-01-01

Full text: At the Energy Research Center (CIE-UNAM-Mexico), the major areas of renewable energy research are solar thermal energy, photovoltaic energy, geothermal energy, hydrogen energy, materials for renewable energy, and energy planning. Among the efforts to developed solar cells, both physical and chemical methods are in progress at CIE-UNAM. In this contribution we focus on the advancement in efficiency, stability, and cost, of photovoltaic junctions based on chemically deposited films. Examples of early research are a composite thin film electrode comprised of SnO2/Bi2S3 nanocrystallites (5 nm) prepared by sequential deposition of SnO2 and Bi2S3 films onto an optically transparent electrode; the co-deposition of pyrrole and Bi2S3 nanoparticles on chemically deposited bismuth sulfide substrates to explore new approaches to improve light-collection efficiency in polymer photovoltaics; the sensitization of titanium dioxide coatings by chemically deposited cadmium selenide and bismuthe sulfide thin films. Here the good photostability of the coatings was promising for the use of the sensitized films in photocatalytic as well as photovoltaic applications. More recently, chemically deposited cadmium sulfide thin films have been explored in planar hybrid heterojunctions with chemically synthesized poly 3-octylthiophene, as well as all-chemically deposited photovoltaic structures. Examples of the last are: chemically deposited thin films of CdS (80 nm), Sb2S3 (450 nm), and Ag2Se (150 nm) annealed at 300 C and integrated into a p-i-n structure glass/SnO2:F/n-CdS/Sb2S3/p-AgSbSe2/Ag, showing Voc ∼ 550 mV and Jsc ∼ 2.3 mA/cm2 at 1 kW/m2 (tungsten halogen) intensity. Similarly, chemically deposited SnS (450nm) and CuS (80nm) thin films integrated in a photovoltaic structure SnO2:F/CdS/SnS/CuS/Ag, showing Voc>300 mV and Jsc up to 5 mA/cm2 under 850 W/m2 tungsten halogen illumination. These photovoltaic structures have been found to be stable over a period extending over

6. How far away is far enough for extracting numerical waveforms, and how much do they depend on the extraction method?

Energy Technology Data Exchange (ETDEWEB)

Pazos, Enrique [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Dorband, Ernst Nils [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Nagar, Alessandro [Dipartimento di Fisica, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129 Torino (Italy); Palenzuela, Carlos [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Schnetter, Erik [Center for Computation and Technology, 216 Johnston Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Tiglio, Manuel [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States)

2007-06-21

in the extracted waves, compared to the standard method, by between one and three orders of magnitude. In a general scenario, for example a collision of compact objects, there is no precise definition of gravitational radiation at a finite distance, and gravitational wave extraction methods at such distances are thus inherently approximate. The results of this paper bring up the possibility that different choices in the wave extraction procedure at a fixed and finite distance may result in relative differences in the waveforms which are actually larger than the numerical errors in the solution.

7. How far away is far enough for extracting numerical waveforms, and how much do they depend on the extraction method?

International Nuclear Information System (INIS)

Pazos, Enrique; Dorband, Ernst Nils; Nagar, Alessandro; Palenzuela, Carlos; Schnetter, Erik; Tiglio, Manuel

2007-01-01

in the extracted waves, compared to the standard method, by between one and three orders of magnitude. In a general scenario, for example a collision of compact objects, there is no precise definition of gravitational radiation at a finite distance, and gravitational wave extraction methods at such distances are thus inherently approximate. The results of this paper bring up the possibility that different choices in the wave extraction procedure at a fixed and finite distance may result in relative differences in the waveforms which are actually larger than the numerical errors in the solution

8. Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

International Nuclear Information System (INIS)

Johnsen, Eric; Larsson, Johan; Bhagatwala, Ankit V.; Cabot, William H.; Moin, Parviz; Olson, Britton J.; Rawat, Pradeep S.; Shankar, Santhosh K.; Sjoegreen, Bjoern; Yee, H.C.; Zhong Xiaolin; Lele, Sanjiva K.

2010-01-01

Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.

9. Development of a set of benchmark problems to verify numerical methods for solving burnup equations

International Nuclear Information System (INIS)

2017-01-01

Highlights: • Description transmutation chain benchmark problems. • Problems for validating numerical methods for solving burnup equations. • Analytical solutions for the burnup equations. • Numerical solutions for the burnup equations. - Abstract: A comprehensive set of transmutation chain benchmark problems for numerically validating methods for solving burnup equations was created. These benchmark problems were designed to challenge both traditional and modern numerical methods used to solve the complex set of ordinary differential equations used for tracking the change in nuclide concentrations over time due to nuclear phenomena. Given the development of most burnup solvers is done for the purpose of coupling with an established transport solution method, these problems provide a useful resource in testing and validating the burnup equation solver before coupling for use in a lattice or core depletion code. All the relevant parameters for each benchmark problem are described. Results are also provided in the form of reference solutions generated by the Mathematica tool, as well as additional numerical results from MATLAB.

10. 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.

11. Preface of "The Second Symposium on Border Zones Between Experimental and Numerical Application Including Solution Approaches By Extensions of Standard Numerical Methods"

Science.gov (United States)

Ortleb, Sigrun; Seidel, Christian

2017-07-01

In this second symposium at the limits of experimental and numerical methods, recent research is presented on practically relevant problems. Presentations discuss experimental investigation as well as numerical methods with a strong focus on application. In addition, problems are identified which require a hybrid experimental-numerical approach. Topics include fast explicit diffusion applied to a geothermal energy storage tank, noise in experimental measurements of electrical quantities, thermal fluid structure interaction, tensegrity structures, experimental and numerical methods for Chladni figures, optimized construction of hydroelectric power stations, experimental and numerical limits in the investigation of rain-wind induced vibrations as well as the application of exponential integrators in a domain-based IMEX setting.

12. 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.

13. An analytically based numerical method for computing view factors in real urban environments

Science.gov (United States)

Lee, Doo-Il; Woo, Ju-Wan; Lee, Sang-Hyun

2018-01-01

A view factor is an important morphological parameter used in parameterizing in-canyon radiative energy exchange process as well as in characterizing local climate over urban environments. For realistic representation of the in-canyon radiative processes, a complete set of view factors at the horizontal and vertical surfaces of urban facets is required. Various analytical and numerical methods have been suggested to determine the view factors for urban environments, but most of the methods provide only sky-view factor at the ground level of a specific location or assume simplified morphology of complex urban environments. In this study, a numerical method that can determine the sky-view factors ( ψ ga and ψ wa ) and wall-view factors ( ψ gw and ψ ww ) at the horizontal and vertical surfaces is presented for application to real urban morphology, which are derived from an analytical formulation of the view factor between two blackbody surfaces of arbitrary geometry. The established numerical method is validated against the analytical sky-view factor estimation for ideal street canyon geometries, showing a consolidate confidence in accuracy with errors of less than 0.2 %. Using a three-dimensional building database, the numerical method is also demonstrated to be applicable in determining the sky-view factors at the horizontal (roofs and roads) and vertical (walls) surfaces in real urban environments. The results suggest that the analytically based numerical method can be used for the radiative process parameterization of urban numerical models as well as for the characterization of local urban climate.

14. 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

15. Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

Energy Technology Data Exchange (ETDEWEB)

Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.

2014-10-15

Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.

16. Numerical methods for the simulation of particle generated electromagnetic fields in acclerator physics

International Nuclear Information System (INIS)

Lau, T.

2006-01-01

In this work modifications of the classical Particle-In-Cell method for the solution of the Maxwell-Vlasov equations are investigated with respect to their application in particle accelerator physics. The aim of the work is to find modifications of the method which minimize and under certain conditions even eliminate the numerical dispersion effect along the beam axis in the numerical solution of Maxwell's equations. This is achieved by the development of dedicated time-integration methods for the Finite Integration Technique and two Finite Volume Methods. The methods are theoretically investigated regarding the conservation of a discrete energy and the existence of a discrete continuity equation. Finally, some of the methods are applied to the simulation of a high frequency rf-gun. (orig.)

17. Monotone numerical methods for finite-state mean-field games

KAUST Repository

Gomes, Diogo A.; Saude, Joao

2017-01-01

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

18. Numerical method for solving the three-dimensional time-dependent neutron diffusion equation

International Nuclear Information System (INIS)

Khaled, S.M.; Szatmary, Z.

2005-01-01

A numerical time-implicit method has been developed for solving the coupled three-dimensional time-dependent multi-group neutron diffusion and delayed neutron precursor equations. The numerical stability of the implicit computation scheme and the convergence of the iterative associated processes have been evaluated. The computational scheme requires the solution of large linear systems at each time step. For this purpose, the point over-relaxation Gauss-Seidel method was chosen. A new scheme was introduced instead of the usual source iteration scheme. (author)

19. Solution methods for compartment models of transport through the environment using numerical inversion of Laplace transforms

International Nuclear Information System (INIS)

Garratt, T.J.

1989-05-01

Compartment models for the transport of radionuclides in the biosphere are conventionally solved using a numerical time-stepping procedure. This report examines an alternative method based on the numerical inversion of Laplace transforms, which is potentially more efficient and accurate for some classes of problem. The central problem considered is the most efficient and robust technique for solving the Laplace-transformed rate equations. The conclusion is that Gaussian elimination is the most efficient and robust solution method. A general compartment model has been implemented on a personal computer and used to solve a realistic case including radionuclide decay chains. (author)

20. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

Science.gov (United States)

Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

2013-03-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

1. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

OpenAIRE

Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

2013-01-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and technique...

2. Monotone numerical methods for finite-state mean-field games

KAUST Repository

Gomes, Diogo A.

2017-04-29

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

3. A numerical study of the Regge calculus and smooth lattice methods on a Kasner cosmology

International Nuclear Information System (INIS)

Brewin, Leo

2015-01-01

Two lattice based methods for numerical relativity, the Regge calculus and the smooth lattice relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge calculus is of the order of 110 times slower than the smooth lattice method. (paper)

4. Numerical Simulation of Coupled Nonlinear Schrödinger Equations Using the Generalized Differential Quadrature Method

International Nuclear Information System (INIS)

Mokhtari, R.; Toodar, A. Samadi; Chegini, N. G.

2011-01-01

We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrödinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge—Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out. (general)

5. Numerical methods for strongly correlated many-body systems with bosonic degrees of freedom

International Nuclear Information System (INIS)

Dorfner, Florian Guenter

2017-01-01

Recent experimental advances allow the observation of electronic relaxation processes in solid-state systems in real time. After an initial excitation with an optical pulse, the relaxation depends on the microscopic interactions present in the system. The interaction of electrons with lattice degrees of freedom - the phonons - is ubiquitous in solids and, thus, it represents one of the most important relaxation channels. An analytic description of relaxation dynamics is hard to come by and very few exact solutions exist even for the equilibrium situation. Numerical methods are, in principle, able to solve the problem in both, equilibrium and out-of-equilibrium situations. However, wavefunction-based methods like exact diagonalization or the density matrix renormalization group method scale unfavorably in the number of local basis states. For electron-phonon coupled systems, the situation is especially severe because the local basis dimension can get very large depending on model parameters or in far-from-equilibrium situations. For groundstate problems, two independent strategies exist for density matrix renormalization group methods: the strictly single-site density matrix renormalization group method that scales linearly in the local dimension and the use of a local basis optimization scheme which truncates the local basis to a subset of the eigenstates of the local reduced density matrix with the largest eigenvalues - the optimal mode basis. In this thesis, we combine these two strategies in an improved algorithm which reduces the scaling from linear in the local dimension of the phonon occupation number basis to linear in the dimension of a smaller optimal mode basis. We demonstrate the improved scaling of this method on the example of the Holstein polaron and the half-filled Hubbard-Holstein model. We further describe an algorithm that combines the time-evolving block decimation method with a local basis optimization to lower the scaling with the local

6. Numerical methods for strongly correlated many-body systems with bosonic degrees of freedom

Energy Technology Data Exchange (ETDEWEB)

Dorfner, Florian Guenter

2017-02-23

Recent experimental advances allow the observation of electronic relaxation processes in solid-state systems in real time. After an initial excitation with an optical pulse, the relaxation depends on the microscopic interactions present in the system. The interaction of electrons with lattice degrees of freedom - the phonons - is ubiquitous in solids and, thus, it represents one of the most important relaxation channels. An analytic description of relaxation dynamics is hard to come by and very few exact solutions exist even for the equilibrium situation. Numerical methods are, in principle, able to solve the problem in both, equilibrium and out-of-equilibrium situations. However, wavefunction-based methods like exact diagonalization or the density matrix renormalization group method scale unfavorably in the number of local basis states. For electron-phonon coupled systems, the situation is especially severe because the local basis dimension can get very large depending on model parameters or in far-from-equilibrium situations. For groundstate problems, two independent strategies exist for density matrix renormalization group methods: the strictly single-site density matrix renormalization group method that scales linearly in the local dimension and the use of a local basis optimization scheme which truncates the local basis to a subset of the eigenstates of the local reduced density matrix with the largest eigenvalues - the optimal mode basis. In this thesis, we combine these two strategies in an improved algorithm which reduces the scaling from linear in the local dimension of the phonon occupation number basis to linear in the dimension of a smaller optimal mode basis. We demonstrate the improved scaling of this method on the example of the Holstein polaron and the half-filled Hubbard-Holstein model. We further describe an algorithm that combines the time-evolving block decimation method with a local basis optimization to lower the scaling with the local

7. 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)

8. An Efficient Numerical Method for Computing Synthetic Seismograms for a Layered Half-space with Sources and Receivers at Close or Same Depths

Science.gov (United States)

Zhang, H.-m.; Chen, X.-f.; Chang, S.

- It is difficult to compute synthetic seismograms for a layered half-space with sources and receivers at close to or the same depths using the generalized R/T coefficient method (Kennett, 1983; Luco and Apsel, 1983; Yao and Harkrider, 1983; Chen, 1993), because the wavenumber integration converges very slowly. A semi-analytic method for accelerating the convergence, in which part of the integration is implemented analytically, was adopted by some authors (Apsel and Luco, 1983; Hisada, 1994, 1995). In this study, based on the principle of the Repeated Averaging Method (Dahlquist and Björck, 1974; Chang, 1988), we propose an alternative, efficient, numerical method, the peak-trough averaging method (PTAM), to overcome the difficulty mentioned above. Compared with the semi-analytic method, PTAM is not only much simpler mathematically and easier to implement in practice, but also more efficient. Using numerical examples, we illustrate the validity, accuracy and efficiency of the new method.

9. A different approach to estimate nonlinear regression model using numerical methods

Science.gov (United States)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

10. 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.

11. 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.

12. Implementation of visual programming methods for numerical techniques used in electromagnetic field theory

Directory of Open Access Journals (Sweden)

Metin Varan

2017-08-01

Full Text Available Field theory is one of the two sub-field theories in electrical and electronics engineering that for creates difficulties for undergraduate students. In undergraduate period, field theory has been taught under the theory of electromagnetic fields by which describes using partial differential equations and integral methods. Analytical methods for solution of field problems on the basis of a mathematical model may result the understanding difficulties for undergraduate students due to their mathematical and physical infrastructure. The analytical methods which can be applied in simple model lose their applicability to more complex models. In this case, the numerical methods are used to solve more complex equations. In this study, by preparing some field theory‘s web-based graphical user interface numerical methods of applications it has been aimed to increase learning levels of field theory problems for undergraduate and graduate students while taking in mind their computer programming capabilities.

13. Numerical and experimental validation of a particle Galerkin method for metal grinding simulation

Science.gov (United States)

Wu, C. T.; Bui, Tinh Quoc; Wu, Youcai; Luo, Tzui-Liang; Wang, Morris; Liao, Chien-Chih; Chen, Pei-Yin; Lai, Yu-Sheng

2018-03-01

In this paper, a numerical approach with an experimental validation is introduced for modelling high-speed metal grinding processes in 6061-T6 aluminum alloys. The derivation of the present numerical method starts with an establishment of a stabilized particle Galerkin approximation. A non-residual penalty term from strain smoothing is introduced as a means of stabilizing the particle Galerkin method. Additionally, second-order strain gradients are introduced to the penalized functional for the regularization of damage-induced strain localization problem. To handle the severe deformation in metal grinding simulation, an adaptive anisotropic Lagrangian kernel is employed. Finally, the formulation incorporates a bond-based failure criterion to bypass the prospective spurious damage growth issues in material failure and cutting debris simulation. A three-dimensional metal grinding problem is analyzed and compared with the experimental results to demonstrate the effectiveness and accuracy of the proposed numerical approach.

14. 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.

15. Development of a Generalized Version of the Poisson-Nernst-Planck Equations Using the Hybrid Mixture Theory: Presentation of 2D Numerical Examples

DEFF Research Database (Denmark)

Johannesson, Björn

2010-01-01

A numerical scheme for the transient solution of generalized version of the Poisson-Nernst-Planck equations is presented. The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present problem iteratively. The Poisson......-scale and that it includes the volume fractions of phases in its structure. The background to the Poisson-Nernst-Planck equations can by the HMT approach be described by using the postulates of mass conservation of constituents together with the Gauss’ law used together with consistent constitutive laws. The HMT theory......-Nernst-Planck equations represent a set of diffusion equations for charged species, i.e. dissolved ions. These equations are coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The Nernst-Planck equations describing the diffusion of the ionic species and the Gauss’ law in used are...

16. Application of the Variational Iteration Method to the Initial Value Problems of Q-difference Equations-Some Examples

Directory of Open Access Journals (Sweden)

Yu Xiang Zeng

2013-12-01

Full Text Available The q-difference equations are a class of important models both in q-calculus and applied sciences. The variational iteration method is extended to approximately solve the initial value problems of q-difference equations. A q-analogue of the Lagrange multiplier is presented and three examples are illustrated to show the method's efficiency.

17. Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

Directory of Open Access Journals (Sweden)

2013-01-01

Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.

18. Geothermal-Related Thermo-Elastic Fracture Analysis by Numerical Manifold Method

Directory of Open Access Journals (Sweden)

Jun He

2018-05-01

Full Text Available One significant factor influencing geothermal energy exploitation is the variation of the mechanical properties of rock in high temperature environments. Since rock is typically a heterogeneous granular material, thermal fracturing frequently occurs in the rock when the ambient temperature changes, which can greatly influence the geothermal energy exploitation. A numerical method based on the numerical manifold method (NMM is developed in this study to simulate the thermo-elastic fracturing of rocklike granular materials. The Voronoi tessellation is incorporated into the pre-processor of NMM to represent the grain structure. A contact-based heat transfer model is developed to reflect heat interaction among grains. Based on the model, the transient thermal conduction algorithm for granular materials is established. To simulate the cohesion effects among grains and the fracturing process between grains, a damage-based contact fracture model is developed to improve the contact algorithm of NMM. In the developed numerical method, the heat interaction among grains as well as the heat transfer inside each solid grain are both simulated. Additionally, as damage evolution and fracturing at grain interfaces are also considered, the developed numerical method is applicable to simulate the geothermal-related thermal fracturing process.

19. A novel method of including Landau level mixing in numerical studies of the quantum Hall effect

International Nuclear Information System (INIS)

Wooten, Rachel; Quinn, John; Macek, Joseph

2013-01-01

Landau level mixing should influence the quantum Hall effect for all except the strongest applied magnetic fields. We propose a simple method for examining the effects of Landau level mixing by incorporating multiple Landau levels into the Haldane pseudopotentials through exact numerical diagonalization. Some of the resulting pseudopotentials for the lowest and first excited Landau levels will be presented

20. The Role of Numerical Methods in the Sensitivity Analysis of a ...

African Journals Online (AJOL)

The mathematical modelling of physiochemical interaction in the framework of industrial and environmental physics which relies on an initial value problem is defined by a first order ordinary differential equation. Two numerical methods of studying sensitivity analysis of physiochemical interaction data are developed.

1. 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

2. A purely Lagrangian method for the numerical integration of Fokker-Planck equations

International Nuclear Information System (INIS)

Combis, P.; Fronteau, J.

1986-01-01

A new numerical approach to Fokker-Planck equations is presented, in which the integration grid moves according to the solution of a differential system. The method is purely Lagrangian, the mean effect of the diffusion being inserted into the differential system itself

3. Evaluating Blended and Flipped Instruction in Numerical Methods at Multiple Engineering Schools

Science.gov (United States)

Clark, Renee; Kaw, Autar; Lou, Yingyan; Scott, Andrew; Besterfield-Sacre, Mary

2018-01-01

With the literature calling for comparisons among technology-enhanced or active-learning pedagogies, a blended versus flipped instructional comparison was made for numerical methods coursework using three engineering schools with diverse student demographics. This study contributes to needed comparisons of enhanced instructional approaches in STEM…

4. 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.

5. Implementing a Flipped Classroom Approach in a University Numerical Methods Mathematics Course

Science.gov (United States)

Johnston, Barbara M.

2017-01-01

This paper describes and analyses the implementation of a "flipped classroom" approach, in an undergraduate mathematics course on numerical methods. The approach replaced all the lecture contents by instructor-made videos and was implemented in the consecutive years 2014 and 2015. The sequential case study presented here begins with an…

6. Numerical simulation of pseudoelastic shape memory alloys using the large time increment method

Science.gov (United States)

Gu, Xiaojun; Zhang, Weihong; Zaki, Wael; Moumni, Ziad

2017-04-01

The paper presents a numerical implementation of the large time increment (LATIN) method for the simulation of shape memory alloys (SMAs) in the pseudoelastic range. The method was initially proposed as an alternative to the conventional incremental approach for the integration of nonlinear constitutive models. It is adapted here for the simulation of pseudoelastic SMA behavior using the Zaki-Moumni model and is shown to be especially useful in situations where the phase transformation process presents little or lack of hardening. In these situations, a slight stress variation in a load increment can result in large variations of strain and local state variables, which may lead to difficulties in numerical convergence. In contrast to the conventional incremental method, the LATIN method solve the global equilibrium and local consistency conditions sequentially for the entire loading path. The achieved solution must satisfy the conditions of static and kinematic admissibility and consistency simultaneously after several iterations. 3D numerical implementation is accomplished using an implicit algorithm and is then used for finite element simulation using the software Abaqus. Computational tests demonstrate the ability of this approach to simulate SMAs presenting flat phase transformation plateaus and subjected to complex loading cases, such as the quasi-static behavior of a stent structure. Some numerical results are contrasted to those obtained using step-by-step incremental integration.

7. Comparison of ALE finite element method and adaptive smoothed finite element method for the numerical simulation of friction stir welding

NARCIS (Netherlands)

van der Stelt, A.A.; Bor, Teunis Cornelis; Geijselaers, Hubertus J.M.; Quak, W.; Akkerman, Remko; Huetink, Han; Menary, G

2011-01-01

In this paper, the material flow around the pin during friction stir welding (FSW) is simulated using a 2D plane strain model. A pin rotates without translation in a disc with elasto-viscoplastic material properties and the outer boundary of the disc is clamped. Two numerical methods are used to

8. A numerical dressing method for the nonlinear superposition of solutions of the KdV equation

International Nuclear Information System (INIS)

Trogdon, Thomas; Deconinck, Bernard

2014-01-01

In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg–de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t. (paper)

9. A method for solving the KDV equation and some numerical experiments

International Nuclear Information System (INIS)

Chang Jinjiang.

1993-01-01

In this paper, by means of difference method for discretization of space partial derivatives of KDV equation, an initial value problem in ordinary differential equations of large dimensions is produced. By using this ordinary differential equations the existence and the uniqueness of the solution of the KDV equation and the conservation of scheme are proved. This ordinary differential equation can be solved by using implicit Runge-Kutta methods, so a new method for finding the numerical solution of the KDV equation is presented. Numerical experiments not only describe in detail the procedure of two solitons collision, soliton reflex and soliton produce, but also show that this method is very effective. (author). 7 refs, 3 figs

10. Numerical analysis of the immersed boundary method applied to the flow around a forced oscillating cylinder

International Nuclear Information System (INIS)

Pinto, L C; Silvestrini, J H; Schettini, E B C

2011-01-01

In present paper, Navier-Stokes and Continuity equations for incompressible flow around an oscillating cylinder were numerically solved. Sixth order compact difference schemes were used to solve the spatial derivatives, while the time advance was carried out through second order Adams Bashforth accurate scheme. In order to represent the obstacle in the flow, the Immersed Boundary Method was adopted. In this method a force term is added to the Navier-Stokes equations representing the body. The simulations present results regarding the hydrodynamic coefficients and vortex wakes in agreement to experimental and numerical previous works and the physical lock-in phenomenon was identified. Comparing different methods to impose the IBM, it can be concluded that no alterations regarding the vortex shedding mode were observed. The Immersed Boundary Method techniques used here can represent the surface of an oscillating cylinder in the flow.

11. Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: A numerical comparison

KAUST Repository

Bäck, Joakim

2010-09-17

Much attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty quantification. An open and relevant research topic is the comparison of these two methods. By introducing a suitable generalization of the classical sparse grid SC method, we are able to compare SG and SC on the same underlying multivariate polynomial space in terms of accuracy vs. computational work. The approximation spaces considered here include isotropic and anisotropic versions of Tensor Product (TP), Total Degree (TD), Hyperbolic Cross (HC) and Smolyak (SM) polynomials. Numerical results for linear elliptic SPDEs indicate a slight computational work advantage of isotropic SC over SG, with SC-SM and SG-TD being the best choices of approximation spaces for each method. Finally, numerical results corroborate the optimality of the theoretical estimate of anisotropy ratios introduced by the authors in a previous work for the construction of anisotropic approximation spaces. © 2011 Springer.

12. A fast numerical method for the valuation of American lookback put options

Science.gov (United States)

Song, Haiming; Zhang, Qi; Zhang, Ran

2015-10-01

A fast and efficient numerical method is proposed and analyzed for the valuation of American lookback options. American lookback option pricing problem is essentially a two-dimensional unbounded nonlinear parabolic problem. We reformulate it into a two-dimensional parabolic linear complementary problem (LCP) on an unbounded domain. The numeraire transformation and domain truncation technique are employed to convert the two-dimensional unbounded LCP into a one-dimensional bounded one. Furthermore, the variational inequality (VI) form corresponding to the one-dimensional bounded LCP is obtained skillfully by some discussions. The resulting bounded VI is discretized by a finite element method. Meanwhile, the stability of the semi-discrete solution and the symmetric positive definiteness of the full-discrete matrix are established for the bounded VI. The discretized VI related to options is solved by a projection and contraction method. Numerical experiments are conducted to test the performance of the proposed method.

13. 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)

14. A detailed survey of numerical methods for unconstrained minimization. Pt. 1

International Nuclear Information System (INIS)

Mika, K.; Chaves, T.

1980-01-01

A detailed description of numerical methods for unconstrained minimization is presented. This first part surveys in particular conjugate direction and gradient methods, whereas variable metric methods will be the subject of the second part. Among the results of special interest we quote the following. The conjugate direction methods of Powell, Zangwill and Sutti can be best interpreted if the Smith approach is adopted. The conditions for quadratic termination of Powell's first procedure are analyzed. Numerical results based on nonlinear least squares problems are presented for the following conjugate direction codes: VA04AD from Harwell Subroutine Library and ZXPOW from IMSL, both implementations of Powell's second procedure, DFMND from IBM-SILMATH (Zangwill's method) and Brent's algorithm PRAXIS. VA04AD turns out to be superior in all cases, PRAXIS improves for high-dimensional problems. All codes clearly exhibit superlinear convergence. Akaike's result for the method of steepest descent is derived directly from a set of nonlinear recurrence relations. Numerical results obtained with the highly ill conditioned Hilbert function confirm the theoretical predictions. Several properties of the conjugate gradient method are presented and a new derivation of the equivalence of steepest descent partan and the CG method is given. A comparison of numerical results from the CG codes VA08AD (Fletcher-Reeves), DFMCG (the SSP version of the Fletcher-Reevens algorithm) and VA14AD (Powell's implementation of the Polak-Ribiere formula) reveals that VA14AD is clearly superior in all cases, but that the convergence rate of these codes is only weakly superlinear such that high accuracy solutions require extremely large numbers of function calls. (orig.)

15. Numerical simulation of electromagnetic waves in Schwarzschild space-time by finite difference time domain method and Green function method

Science.gov (United States)

Jia, Shouqing; La, Dongsheng; Ma, Xuelian

2018-04-01

The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.

16. Testing the accuracy and stability of spectral methods in numerical relativity

International Nuclear Information System (INIS)

Boyle, Michael; Lindblom, Lee; Pfeiffer, Harald P.; Scheel, Mark A.; Kidder, Lawrence E.

2007-01-01

The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the Kidder, Scheel, and Teukolsky (KST) representation of the Einstein evolution equations. The basic 'Mexico City tests' widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error or by truncation error in the time integration. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test

17. Improved numerical methods for quantum field theory (Outstanding junior investigator award)

International Nuclear Information System (INIS)

Sokal, A.D.

1992-01-01

We are developing new and more efficient numerical methods for problems in quantum field theory. Our principal goal is to achieve radical reductions in critical slowing-down. We are concentrating at present on three new families of algorithms: multi-grid Monte Carlo, Swendsen-Wang and generalized Wolff-type embedding algorithms. In addition, we are making a high-precision numerical study of the hyperscaling conjecture for the self-avoiding walk, which is closely related to the triviality problem for var-phi 4 quantum field theory

18. Improved numerical methods for quantum field theory (Outstanding junior investigator award)

International Nuclear Information System (INIS)

Sokal, A.D.

1993-01-01

We are developing new and more efficient numerical methods for problems in quantum field theory. Our principal goal is to achieve radical reductions in critical slowing-down. We are concentrating at present on three new families of algorithms: multi-grid Monte Carlo (MGMC), Swendsen-Wang (SW) and generalized Wolff-type embedding algorithms. In addition, we are making a high-precision numerical study of the hyperscaling conjecture for the self-avoiding walk, which is closely related to the triviality problem for var-phi 4 quantum field theory

19. A numeric investigation of co-flowing liquid streams using the Lattice Boltzmann Method

Science.gov (United States)

Somogyi, Andy; Tagg, Randall

2007-11-01

We present a numerical investigation of co-flowing immiscible liquid streams using the Lattice Boltzmann Method (LBM) for multi component, dissimilar viscosity, immiscible fluid flow. When a liquid is injected into another immiscible liquid, the flow will eventually transition from jetting to dripping due to interfacial tension. Our implementation of LBM models the interfacial tension through a variety of techniques. Parallelization is also straightforward for both single and multi component models as only near local interaction is required. We compare the results of our numerical investigation using LBM to several recent physical experiments.

20. Statistical and numerical methods to improve the transient divided bar method

DEFF Research Database (Denmark)

Bording, Thue Sylvester; Nielsen, S.B.; Balling, N.

The divided bar method is a commonly used method to measure thermal conductivity of rock samples in laboratory. We present improvements to this method that allows for simultaneous measurements of both thermal conductivity and thermal diffusivity. The divided bar setup is run in a transient mode...