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.
Advanced Numerical and Theoretical Methods for Photonic Crystals and Metamaterials
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.
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
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
International Nuclear Information System (INIS)
Longatte, E.; Baj, F.; Hoarau, Y.; Braza, M.; Ruiz, D.; Canteneur, C.
2013-01-01
Highlights: ► Proposal of hybrid computational methods for investigating dynamical system stability. ► Modeling turbulence disequilibrium due to interaction with moving solid boundaries. ► Providing computational procedure for large size system solution approximation through model reduction. -- Abstract: This article proposes a review of recent and current developments in the modeling and advanced numerical methods used to simulate large-size systems involving multi-physics in the field of mechanics. It addresses the complex issue of stability analysis of dynamical systems submitted to external turbulent flows and aims to establish accurate stability maps applicable to heat exchanger design. The purpose is to provide dimensionless stability limit modeling that is suitable for a variety of configurations and is as accurate as possible in spite of the large scale of the systems to be considered. The challenge lies in predicting local effects that may impact global systems. A combination of several strategies that are suited concurrently to multi-physics, multi-scale and large-size system computation is therefore required. Based on empirical concepts, the heuristic models currently used in the framework of standard stability analysis suffer from a lack of predictive capabilities. On the other hand, numerical approaches based on fully-coupled fluid–solid dynamics system computation remain expensive due to the multi-physics patterns of physics and the large number of degrees of freedom involved. In this context, since experimentation cannot be achieved and numerical simulation is unavoidable but prohibitive, a hybrid strategy is proposed in order to take advantage of both numerical local solutions and empirical global solutions
International Nuclear Information System (INIS)
Yoshida, Hiroyuki; Takase, Kazuyuki
2008-01-01
Thermal-hydraulic design of the current boiling water reactor (BWR) is performed with the subchannel analysis codes which incorporated the correlations based on empirical results including actual-size tests. Then, for the Innovative Water Reactor for Flexible Fuel Cycle (FLWR) core, an actual size test of an embodiment of its design is required to confirm or modify such correlations. In this situation, development of a method that enables the thermal-hydraulic design of nuclear reactors without these actual size tests is desired, because these tests take a long time and entail great cost. For this reason, we developed an advanced thermal-hydraulic design method for FLWRs using innovative two-phase flow simulation technology. In this study, a detailed Two-Phase Flow simulation code using advanced Interface Tracking method: TPFIT is developed to calculate the detailed information of the two-phase flow. In this paper, firstly, we tried to verify the TPFIT code by comparing it with the existing 2-channel air-water mixing experimental results. Secondary, the TPFIT code was applied to simulation of steam-water two-phase flow in a model of two subchannels of a current BWRs and FLWRs rod bundle. The fluid mixing was observed at a gap between the subchannels. The existing two-phase flow correlation for fluid mixing is evaluated using detailed numerical simulation data. This data indicates that pressure difference between fluid channels is responsible for the fluid mixing, and thus the effects of the time average pressure difference and fluctuations must be incorporated in the two-phase flow correlation for fluid mixing. When inlet quality ratio of subchannels is relatively large, it is understood that evaluation precision of the existing two-phase flow correlations for fluid mixing are relatively low. (author)
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.
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.
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
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)
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.
Bertarelli, A; Carra, F; Cerutti, F; Dallocchio, A; Mariani, N; Timmins, M; Peroni, L; Scapin, M
2011-01-01
Beam Intercepting Devices are potentially exposed to severe accidental events triggered by direct impacts of energetic particle beams. State-of-the-art numerical methods are required to simulate the behaviour of affected components. A review of the different dynamic response regimes is presented, along with an indication of the most suited tools to treat each of them. The consequences on LHC tungsten collimators of a number of beam abort scenarios were extensively studied, resorting to a novel category of numerical explicit methods, named Hydrocodes. Full shower simulations were performed providing the energy deposition distribution. Structural dynamics and shock wave propagation analyses were carried out with varying beam parameters, identifying important thresholds for collimator operation, ranging from the onset of permanent damage up to catastrophic failure. Since the main limitation of these tools lies in the limited information available on constitutive material models under extreme conditions, a dedica...
Bertarelli, A; Carra, F; Cerutti, F; Dallocchio, A; Mariani, N; Timmins, M; Peroni, L; Scapin, M
2011-01-01
Beam Intercepting Devices are potentially exposed to severe accidental events triggered by direct impacts of energetic particle beams. State-of-the-art numerical methods are required to simulate the behaviour of affected components. A review of the different dynamic response regimes is presented, along with an indication of the most suited tools to treat each of them. The consequences on LHC tungsten collimators of a number of beam abort scenarios were extensively studied, resorting to a novel category of numerical explicit methods, named Hydrocodes. Full shower simulations were performed providing the energy deposition distribution. Structural dynamics and shock wave propagation analyses were carried out with varying beam parameters, identifying important thresholds for collimator operation, ranging from the onset of permanent damage up to catastrophic failure. Since the main limitation of these tools lies in the limited information available on constitutive material models under extreme conditions, a dedica...
Advances in dynamic and mean field games theory, applications, and numerical methods
Viscolani, Bruno
2017-01-01
This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environments Models for climate change negotiations Nash Equilibria for dynamic games involving Volterra integral equations Differential games in healthcare markets Linear-quadratic Gaussian dynamic games Aircraft control in wind shear conditions Advances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinar...
Oetjen, Jan; Engel, Max; Prasad Pudasaini, Shiva; Schüttrumpf, Holger; Brückner, Helmut
2017-04-01
Coasts around the world are affected by high-energy wave events like storm surges or tsunamis depending on their regional climatological and geological settings. By focusing on tsunami impacts, we combine the abilities and experiences of different scientific fields aiming at improved insights of near- and onshore tsunami hydrodynamics. We investigate the transport of coarse clasts - so called boulders - due to tsunami impacts by a multi-methodology approach of numerical modelling, laboratory experiments, and sedimentary field records. Coupled numerical hydrodynamic and boulder transport models (BTM) are widely applied for analysing the impact characteristics of the transport by tsunami, such as wave height and flow velocity. Numerical models able to simulate past tsunami events and the corresponding boulder transport patterns with high accuracy and acceptable computational effort can be utilized as powerful forecasting models predicting the impact of a coast approaching tsunami. We have conducted small-scale physical experiments in the tilting flume with real shaped boulder models. Utilizing the structure from motion technique (Westoby et al., 2012) we reconstructed real boulders from a field study on the Island of Bonaire (Lesser Antilles, Caribbean Sea, Engel & May, 2012). The obtained three-dimensional boulder meshes are utilized for creating downscaled replica of the real boulder for physical experiments. The results of the irregular shaped boulder are compared to experiments with regular shaped boulder models to achieve a better insight about the shape related influence on transport patterns. The numerical model is based on the general two-phase mass flow model by Pudasaini (2012) enhanced for boulder transport simulations. The boulder is implemented using the immersed boundary technique (Peskin, 2002) and the direct forcing approach. In this method Cartesian grids (fluid and particle phase) and Lagrangian meshes (boulder) are combined. By applying the
Bayesian analysis of general failure data from an ageing distribution: advances in numerical methods
International Nuclear Information System (INIS)
Procaccia, H.; Villain, B.; Clarotti, C.A.
1996-01-01
EDF and ENEA carried out a joint research program for developing the numerical methods and computer codes needed for Bayesian analysis of component-lives in the case of ageing. Early results of this study were presented at ESREL'94. Since then the following further steps have been gone: input data have been generalized to the case that observed lives are censored both on the right and on the left; allowable life distributions are Weibull and gamma - their parameters are both unknown and can be statistically dependent; allowable priors are histograms relative to different parametrizations of the life distribution of concern; first-and-second-order-moments of the posterior distributions can be computed. In particular the covariance will give some important information about the degree of the statistical dependence between the parameters of interest. An application of the code to the appearance of a stress corrosion cracking in a tube of the PWR Steam Generator system is presented. (authors)
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.)
International Nuclear Information System (INIS)
1993-01-01
The purpose of the meeting was to review proposed contributions from CRP participating organizations to discuss in detail the experimental data on seismic isolators, to review the numerical methods for the analysis of the seismic isolators, and to perform a first comparison of the calculation results. The aim of the CRP was to validate the reliable numerical methods used for both detailed evaluation of dynamic behaviour of isolation devices and isolated nuclear structures of different nuclear power plant types. The full maturity of seismic isolation for nuclear applications was stressed, as well as the excellent behaviour of isolated structures during the recent earthquakes in Japan and the USA. Participants from Italy, USA, Japan, Russian federation, Republic of Korea, United Kingdom, India and European Commission have presented overview papers on the present programs and their status of contribution to the CRP
Energy Technology Data Exchange (ETDEWEB)
NONE
1993-07-01
The purpose of the meeting was to review proposed contributions from CRP participating organizations to discuss in detail the experimental data on seismic isolators, to review the numerical methods for the analysis of the seismic isolators, and to perform a first comparison of the calculation results. The aim of the CRP was to validate the reliable numerical methods used for both detailed evaluation of dynamic behaviour of isolation devices and isolated nuclear structures of different nuclear power plant types. The full maturity of seismic isolation for nuclear applications was stressed, as well as the excellent behaviour of isolated structures during the recent earthquakes in Japan and the USA. Participants from Italy, USA, Japan, Russian federation, Republic of Korea, United Kingdom, India and European Commission have presented overview papers on the present programs and their status of contribution to the CRP.
Atwater, James; Wheeler, Richard, Jr.; Akse, James; Jovanovic, Goran; Reed, Brian
2013-01-01
To support long-duration manned missions in space such as a permanent lunar base, Mars transit, or Mars Surface Mission, improved methods for the treatment of solid wastes, particularly methods that recover valuable resources, are needed. The ability to operate under microgravity and hypogravity conditions is essential to meet this objective. The utilization of magnetic forces to manipulate granular magnetic media has provided the means to treat solid wastes under variable gravity conditions by filtration using a consolidated magnetic media bed followed by thermal processing of the solid wastes in a fluidized bed reactor. Non-uniform magnetic fields will produce a magnetic field gradient in a bed of magnetically susceptible media toward the distributor plate of a fluidized bed reactor. A correctly oriented magnetic field gradient will generate a downward direct force on magnetic media that can substitute for gravitational force in microgravity, or which may augment low levels of gravity, such as on the Moon or Mars. This approach is termed Gradient Magnetically Assisted Fluidization (G-MAFB), in which the magnitude of the force on the fluidized media depends upon the intensity of the magnetic field (H), the intensity of the field gradient (dH/dz), and the magnetic susceptibility of the media. Fluidized beds based on the G-MAFB process can operate in any gravitational environment by tuning the magnetic field appropriately. Magnetic materials and methods have been developed that enable G-MAFB operation under variable gravity conditions.
Numerical methods using Matlab
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
Zhang, Weizhong; Yoshida, Hiroyuki; Ose, Yasuo; Ohnuki, Akira; Akimoto, Hajime; Hotta, Akitoshi; Fujimura, Ken
In relation to the design of an innovative FLexible-fuel-cycle Water Reactor (FLWR), investigation of thermal-hydraulic performance in tight-lattice rod bundles of the FLWR is being carried out at Japan Atomic Energy Agency (JAEA). The FLWR core adopts a tight triangular lattice arrangement with about 1 mm gap clearance between adjacent fuel rods. In view of importance of accurate prediction of cross flow between subchannels in the evaluation of the boiling transition (BT) in the FLWR core, this study presents a statistical evaluation of numerical simulation results obtained by a detailed two-phase flow simulation code, TPFIT, which employs an advanced interface tracking method. In order to clarify mechanisms of cross flow in such tight lattice rod bundles, the TPFIT is applied to simulate water-steam two-phase flow in two modeled subchannels. Attention is focused on instantaneous fluctuation characteristics of cross flow. With the calculation of correlation coefficients between differential pressure and gas/liquid mixing coefficients, time scales of cross flow are evaluated, and effects of mixing section length, flow pattern and gap spacing on correlation coefficients are investigated. Differences in mechanism between gas and liquid cross flows are pointed out.
Essential numerical computer methods
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 ...
Energy Technology Data Exchange (ETDEWEB)
Kollias, Pavlos [McGill Univ., Montreal, QC (Canada
2016-09-06
This the final report for the DE-SC0007096 - Advancing Clouds Lifecycle Representation in Numerical Models Using Innovative Analysis Methods that Bridge ARM Observations and Models Over a Breadth of Scales - PI: Pavlos Kollias. The final report outline the main findings of the research conducted using the aforementioned award in the area of cloud research from the cloud scale (10-100 m) to the mesoscale (20-50 km).
NATO Advanced Study Institute on Advanced Physical Oceanographic Numerical Modelling
1986-01-01
This book is a direct result of the NATO Advanced Study Institute held in Banyuls-sur-mer, France, June 1985. The Institute had the same title as this book. It was held at Laboratoire Arago. Eighty lecturers and students from almost all NATO countries attended. The purpose was to review the state of the art of physical oceanographic numerical modelling including the parameterization of physical processes. This book represents a cross-section of the lectures presented at the ASI. It covers elementary mathematical aspects through large scale practical aspects of ocean circulation calculations. It does not encompass every facet of the science of oceanographic modelling. We have, however, captured most of the essence of mesoscale and large-scale ocean modelling for blue water and shallow seas. There have been considerable advances in modelling coastal circulation which are not included. The methods section does not include important material on phase and group velocity errors, selection of grid structures, advanc...
Advanced differential quadrature methods
Zong, Zhi
2009-01-01
Modern Tools to Perform Numerical DifferentiationThe original direct differential quadrature (DQ) method has been known to fail for problems with strong nonlinearity and material discontinuity as well as for problems involving singularity, irregularity, and multiple scales. But now researchers in applied mathematics, computational mechanics, and engineering have developed a range of innovative DQ-based methods to overcome these shortcomings. Advanced Differential Quadrature Methods explores new DQ methods and uses these methods to solve problems beyond the capabilities of the direct DQ method.After a basic introduction to the direct DQ method, the book presents a number of DQ methods, including complex DQ, triangular DQ, multi-scale DQ, variable order DQ, multi-domain DQ, and localized DQ. It also provides a mathematical compendium that summarizes Gauss elimination, the Runge-Kutta method, complex analysis, and more. The final chapter contains three codes written in the FORTRAN language, enabling readers to q...
Numerical methods in matrix computations
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.
Recent advances in numerical modeling of detonations
Energy Technology Data Exchange (ETDEWEB)
Mader, C.L.
1986-12-01
Three lectures were presented on recent advances in numerical modeling detonations entitled (1) Jet Initiation and Penetration of Explosives; (2) Explosive Desensitization by Preshocking; (3) Inert Metal-Loaded Explosives.
Strongly correlated systems numerical methods
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...
Directory of Open Access Journals (Sweden)
F. Álvarez-Velarde
2012-01-01
Full Text Available A fast numerical method for the calculation in a zero-dimensional approach of the equilibrium isotopic composition of an iteratively used transmutation system in an advanced fuel cycle, based on the Banach fixed point theorem, is described in this paper. The method divides the fuel cycle in successive stages: fuel fabrication, storage, irradiation inside the transmutation system, cooling, reprocessing, and incorporation of the external material into the new fresh fuel. The change of the fuel isotopic composition, represented by an isotope vector, is described in a matrix formulation. The resulting matrix equations are solved using direct methods with arbitrary precision arithmetic. The method has been successfully applied to a double-strata fuel cycle with light water reactors and accelerator-driven subcritical systems. After comparison to the results of the EVOLCODE 2.0 burn-up code, the observed differences are about a few percents in the mass estimations of the main actinides.
Introduction to precise numerical methods
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.
Numerical methods in multibody dynamics
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...
Operator theory and numerical methods
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.
Numerical methods and analysis of multiscale problems
Madureira, Alexandre L
2017-01-01
This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.
Numerical methods for metamaterial design
2013-01-01
This book describes a relatively new approach for the design of electromagnetic metamaterials. Numerical optimization routines are combined with electromagnetic simulations to tailor the broadband optical properties of a metamaterial to have predetermined responses at predetermined wavelengths. After a review of both the major efforts within the field of metamaterials and the field of mathematical optimization, chapters covering both gradient-based and derivative-free design methods are considered. Selected topics including surrogate-base optimization, adaptive mesh search, and genetic algorithms are shown to be effective, gradient-free optimization strategies. Additionally, new techniques for representing dielectric distributions in two dimensions, including level sets, are demonstrated as effective methods for gradient-based optimization. Each chapter begins with a rigorous review of the optimization strategy used, and is followed by numerous examples that combine the strategy with either electromag...
Numerical methods for image registration
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
Intelligent numerical methods applications to fractional calculus
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.
Partial differential equations with numerical methods
Larsson, Stig
2003-01-01
The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.
A student's guide to numerical methods
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...
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
International Nuclear Information System (INIS)
Uchibori, Akihiro; Ohshima, Hiroyuki; Watanabe, Akira
2010-01-01
SERAPHIM is a computer program for the simulation of the compressible multiphase flow involving the sodium-water chemical reaction under a tube failure accident in a steam generator of sodium cooled fast reactors. In this study, the numerical analysis of the highly underexpanded air jets into the air or into the water was performed as a part of validation of the SERAPHIM program. The multi-fluid model, the second-order TVD scheme and the HSMAC method considering a compressibility were used in this analysis. Combining these numerical methods makes it possible to calculate the multiphase flow including supersonic gaseous jets. In the case of the air jet into the air, the calculated pressure, the shape of the jet and the location of a Mach disk agreed with the existing experimental results. The effect of the difference scheme and the mesh resolution on the prediction accuracy was clarified through these analyses. The behavior of the air jet into the water was also reproduced successfully by the proposed numerical method. (author)
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.
International Nuclear Information System (INIS)
Beauwens, B.; Arkuszewski, J.; Boryszewicz, M.
1981-01-01
Results obtained in the field of linear iterative methods within the Coordinated Research Program on Transport Theory and Advanced Reactor Calculations are summarized. The general convergence theory of linear iterative methods is essentially based on the properties of nonnegative operators on ordered normed spaces. The following aspects of this theory have been improved: new comparison theorems for regular splittings, generalization of the notions of M- and H-matrices, new interpretations of classical convergence theorems for positive-definite operators. The estimation of asymptotic convergence rates was developed with two purposes: the analysis of model problems and the optimization of relaxation parameters. In the framework of factorization iterative methods, model problem analysis is needed to investigate whether the increased computational complexity of higher-order methods does not offset their increased asymptotic convergence rates, as well as to appreciate the effect of standard relaxation techniques (polynomial relaxation). On the other hand, the optimal use of factorization iterative methods requires the development of adequate relaxation techniques and their optimization. The relative performances of a few possibilities have been explored for model problems. Presently, the best results have been obtained with optimal diagonal-Chebyshev relaxation
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
Advanced Combustion Numerics and Modeling - FY18 First Quarter Report
Energy Technology Data Exchange (ETDEWEB)
Whitesides, R. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Killingsworth, N. J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); McNenly, M. J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Petitpas, G. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2018-01-05
This project is focused on early stage research and development of numerical methods and models to improve advanced engine combustion concepts and systems. The current focus is on development of new mathematics and algorithms to reduce the time to solution for advanced combustion engine design using detailed fuel chemistry. The research is prioritized towards the most time-consuming workflow bottlenecks (computer and human) and accuracy gaps that slow ACS program members. Zero-RK, the fast and accurate chemical kinetics solver software developed in this project, is central to the research efforts and continues to be developed to address the current and emerging needs of the engine designers, engine modelers and fuel mechanism developers.
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.)
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)
Advanced Numerical Model for Irradiated Concrete
Energy Technology Data Exchange (ETDEWEB)
Giorla, Alain B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2015-03-01
In this report, we establish a numerical model for concrete exposed to irradiation to address these three critical points. The model accounts for creep in the cement paste and its coupling with damage, temperature and relative humidity. The shift in failure mode with the loading rate is also properly represented. The numerical model for creep has been validated and calibrated against different experiments in the literature [Wittmann, 1970, Le Roy, 1995]. Results from a simplified model are shown to showcase the ability of numerical homogenization to simulate irradiation effects in concrete. In future works, the complete model will be applied to the analysis of the irradiation experiments of Elleuch et al. [1972] and Kelly et al. [1969]. This requires a careful examination of the experimental environmental conditions as in both cases certain critical information are missing, including the relative humidity history. A sensitivity analysis will be conducted to provide lower and upper bounds of the concrete expansion under irradiation, and check if the scatter in the simulated results matches the one found in experiments. The numerical and experimental results will be compared in terms of expansion and loss of mechanical stiffness and strength. Both effects should be captured accordingly by the model to validate it. Once the model has been validated on these two experiments, it can be applied to simulate concrete from nuclear power plants. To do so, the materials used in these concrete must be as well characterized as possible. The main parameters required are the mechanical properties of each constituent in the concrete (aggregates, cement paste), namely the elastic modulus, the creep properties, the tensile and compressive strength, the thermal expansion coefficient, and the drying shrinkage. These can be either measured experimentally, estimated from the initial composition in the case of cement paste, or back-calculated from mechanical tests on concrete. If some
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
Numerical computer methods part D
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.
Numerical methods in software and analysis
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
An introduction to numerical methods and analysis
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
Isogeometric methods for numerical simulation
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.
Numerical computer methods part E
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.
Excel spreadsheet in teaching numerical methods
Djamila, Harimi
2017-09-01
One of the important objectives in teaching numerical methods for undergraduates’ students is to bring into the comprehension of numerical methods algorithms. Although, manual calculation is important in understanding the procedure, it is time consuming and prone to error. This is specifically the case when considering the iteration procedure used in many numerical methods. Currently, many commercial programs are useful in teaching numerical methods such as Matlab, Maple, and Mathematica. These are usually not user-friendly by the uninitiated. Excel spreadsheet offers an initial level of programming, which it can be used either in or off campus. The students will not be distracted with writing codes. It must be emphasized that general commercial software is required to be introduced later to more elaborated questions. This article aims to report on a teaching numerical methods strategy for undergraduates engineering programs. It is directed to students, lecturers and researchers in engineering field.
Numerical simulation of abutment pressure redistribution during face advance
Klishin, S. V.; Lavrikov, S. V.; Revuzhenko, A. F.
2017-12-01
The paper presents numerical simulation data on the abutment pressure redistribution in rock mass during face advance, including isolines of maximum shear stress and pressure epures. The stress state of rock in the vicinity of a breakage heading is calculated by the finite element method using a 2D nonlinear model of a structurally heterogeneous medium with regard to plasticity and internal self-balancing stress. The thus calculated stress field is used as input data for 3D discrete element modeling of the process. The study shows that the abutment pressure increases as the roof span extends and that the distance between the face breast and the peak point of this pressure depends on the elastoplastic properties and internal self-balancing stress of a rock medium.
Advanced experimental and numerical techniques for cavitation erosion prediction
Chahine, Georges; Franc, Jean-Pierre; Karimi, Ayat
2014-01-01
This book provides a comprehensive treatment of the cavitation erosion phenomenon and state-of-the-art research in the field. It is divided into two parts. Part 1 consists of seven chapters, offering a wide range of computational and experimental approaches to cavitation erosion. It includes a general introduction to cavitation and cavitation erosion, a detailed description of facilities and measurement techniques commonly used in cavitation erosion studies, an extensive presentation of various stages of cavitation damage (including incubation and mass loss), and insights into the contribution of computational methods to the analysis of both fluid and material behavior. The proposed approach is based on a detailed description of impact loads generated by collapsing cavitation bubbles and a physical analysis of the material response to these loads. Part 2 is devoted to a selection of nine papers presented at the International Workshop on Advanced Experimental and Numerical Techniques for Cavitation Erosion (Gr...
Numerical Methods for Partial Differential Equations
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.
International Nuclear Information System (INIS)
Seignole, V.
2005-01-01
This report presents the work of thesis realized under the direction of Jean-Michel Ghidaglia (thesis director, ENS-Cachan) and of Anela Kumbaro (tutor, CEA) within the framework of the modeling of two-phase flows with OAP code. The report consists of two parts of unequal size: the first part concentrates on aspects related exclusively to two-phase flows, while the second one is devoted to the study of a numerical problem inherent to the resolution of two-phase flow systems, but whose action has a broader framework. (author)
Advances in Biosensing Methods
Directory of Open Access Journals (Sweden)
Reema Taneja
2007-02-01
Full Text Available A fractal analysis is presented for the binding and dissociation (if applicable kinetics of analyte-receptor reactions occurring on biosensor surfaces. The applications of the biosensors have appeared in the recent literature. The examples provided together provide the reader with a perspective of the advances in biosensors that are being used to detect analytes of interest. This should also stimulate interest in applying biosensors to other areas of application. The fractal analysis limits the evaluation of the rate constants for binding and dissociation (if applicable for the analyte-receptor reactions occurring in biosensor surfaces. The fractal dimension provides a quantitative measure of the degree of heterogeneity on the biosensor surface. Predictive relations are presented that relate the binding co-efficient with the degree of heterogeneity or the fractal dimension on the biosensor surface
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
Numerical analysis in electromagnetics the TLM method
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
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
Energy Technology Data Exchange (ETDEWEB)
Klein, R I; Stone, J M
2007-11-20
We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.
Numerical methods and modelling for engineering
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...
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
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.)
Advanced Dynamics Analytical and Numerical Calculations with MATLAB
Marghitu, Dan B
2012-01-01
Advanced Dynamics: Analytical and Numerical Calculations with MATLAB provides a thorough, rigorous presentation of kinematics and dynamics while using MATLAB as an integrated tool to solve problems. Topics presented are explained thoroughly and directly, allowing fundamental principles to emerge through applications from areas such as multibody systems, robotics, spacecraft and design of complex mechanical devices. This book differs from others in that it uses symbolic MATLAB for both theory and applications. Special attention is given to solutions that are solved analytically and numerically using MATLAB. The illustrations and figures generated with MATLAB reinforce visual learning while an abundance of examples offer additional support. This book also: Provides solutions analytically and numerically using MATLAB Illustrations and graphs generated with MATLAB reinforce visual learning for students as they study Covers modern technical advancements in areas like multibody systems, robotics, spacecraft and des...
European Conference on Numerical Mathematics and Advanced Applications
Manguoğlu, Murat; Tezer-Sezgin, Münevver; Göktepe, Serdar; Uğur, Ömür
2016-01-01
The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), held every 2 years, provides a forum for discussing recent advances in and aspects of numerical mathematics and scientific and industrial applications. The previous ENUMATH meetings took place in Paris (1995), Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011) and Lausanne (2013). This book presents a selection of invited and contributed lectures from the ENUMATH 2015 conference, which was organised by the Institute of Applied Mathematics (IAM), Middle East Technical University, Ankara, Turkey, from September 14 to 18, 2015. It offers an overview of central recent developments in numerical analysis, computational mathematics, and applications in the form of contributions by leading experts in the field.
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.)
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...
Hybrid numerical calculation method for bend waveguides
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...
Lagrangian numerical methods for ocean biogeochemical simulations
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.
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
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.
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
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.
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
Conservative numerical methods for solitary wave interactions
Energy Technology Data Exchange (ETDEWEB)
Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)
2003-07-18
The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.
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.
Numerical methods for scientists and engineers
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.
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.
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.)
Advances in Integrated Vehicle Thermal Management and Numerical Simulation
Directory of Open Access Journals (Sweden)
Yan Wang
2017-10-01
Full Text Available With the increasing demands for vehicle dynamic performance, economy, safety and comfort, and with ever stricter laws concerning energy conservation and emissions, vehicle power systems are becoming much more complex. To pursue high efficiency and light weight in automobile design, the power system and its vehicle integrated thermal management (VITM system have attracted widespread attention as the major components of modern vehicle technology. Regarding the internal combustion engine vehicle (ICEV, its integrated thermal management (ITM mainly contains internal combustion engine (ICE cooling, turbo-charged cooling, exhaust gas recirculation (EGR cooling, lubrication cooling and air conditioning (AC or heat pump (HP. As for electric vehicles (EVs, the ITM mainly includes battery cooling/preheating, electric machines (EM cooling and AC or HP. With the rational effective and comprehensive control over the mentioned dynamic devices and thermal components, the modern VITM can realize collaborative optimization of multiple thermodynamic processes from the aspect of system integration. Furthermore, the computer-aided calculation and numerical simulation have been the significant design methods, especially for complex VITM. The 1D programming can correlate multi-thermal components and the 3D simulating can develop structuralized and modularized design. Additionally, co-simulations can virtualize simulation of various thermo-hydraulic behaviors under the vehicle transient operational conditions. This article reviews relevant researching work and current advances in the ever broadening field of modern vehicle thermal management (VTM. Based on the systematic summaries of the design methods and applications of ITM, future tasks and proposals are presented. This article aims to promote innovation of ITM, strengthen the precise control and the performance predictable ability, furthermore, to enhance the level of research and development (R&D.
Numerical methods and optimization a consumer guide
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...
Recent advances in two-phase flow numerics
International Nuclear Information System (INIS)
Mahaffy, J.H.; Macian, R.
1997-01-01
The authors review three topics in the broad field of numerical methods that may be of interest to individuals modeling two-phase flow in nuclear power plants. The first topic is iterative solution of linear equations created during the solution of finite volume equations. The second is numerical tracking of macroscopic liquid interfaces. The final area surveyed is the use of higher spatial difference techniques
Recent advances in two-phase flow numerics
Energy Technology Data Exchange (ETDEWEB)
Mahaffy, J.H.; Macian, R. [Pennsylvania State Univ., University Park, PA (United States)
1997-07-01
The authors review three topics in the broad field of numerical methods that may be of interest to individuals modeling two-phase flow in nuclear power plants. The first topic is iterative solution of linear equations created during the solution of finite volume equations. The second is numerical tracking of macroscopic liquid interfaces. The final area surveyed is the use of higher spatial difference techniques.
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
Numerical Methods for Stochastic Computations A Spectral Method Approach
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
Quantum dynamic imaging theoretical and numerical methods
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...
Advanced modelling and numerical strategies in nuclear thermal-hydraulics
International Nuclear Information System (INIS)
Staedtke, H.
2001-01-01
The first part of the lecture gives a brief review of the current status of nuclear thermal hydraulics as it forms the basis of established system codes like TRAC, RELAP5, CATHARE or ATHLET. Specific emphasis is given to the capabilities and limitations of the underlying physical modelling and numerical solution strategies with regard to the description of complex transient two-phase flow and heat transfer conditions as expected to occur in PWR reactors during off-normal and accident conditions. The second part of the lecture focuses on new challenges and future needs in nuclear thermal-hydraulics which might arise with regard to re-licensing of old plants using bestestimate methodologies or the design and safety analysis of Advanced Light Water Reactors relying largely on passive safety systems. In order to meet these new requirements various advanced modelling and numerical techniques will be discussed including extended wellposed (hyperbolic) two-fluid models, explicit modelling of interfacial area transport or higher order numerical schemes allowing a high resolution of local multi-dimensional flow processes.(author)
Numerical perturbative methods in the quantum theory of physical systems
International Nuclear Information System (INIS)
Adam, G.
1980-01-01
During the last two decades, development of digital electronic computers has led to the deployment of new, distinct methods in theoretical physics. These methods, based on the advances of modern numerical analysis as well as on specific equations describing physical processes, enabled to perform precise calculations of high complexity which have completed and sometimes changed our image of many physical phenomena. Our efforts have concentrated on the development of numerical methods with such intrinsic performances as to allow a successful approach of some Key issues in present theoretical physics on smaller computation systems. The basic principle of such methods is to translate, in numerical analysis language, the theory of perturbations which is suited to numerical rather than to analytical computation. This idea has been illustrated by working out two problems which arise from the time independent Schroedinger equation in the non-relativistic approximation, within both quantum systems with a small number of particles and systems with a large number of particles, respectively. In the first case, we are led to the numerical solution of some quadratic ordinary differential equations (first section of the thesis) and in the second case, to the solution of some secular equations in the Brillouin area (second section). (author)
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.)
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
High accuracy mantle convection simulation through modern numerical methods
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.
Mathematica with a Numerical Methods Course
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.
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
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)
Advanced Multilevel Monte Carlo Methods
Jasra, Ajay; Law, Kody; Suciu, Carina
2017-01-01
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the discretization of a associated probability law. The MLMC approach works with a hierarchy of biased approximations which become progressively more accurate and more expensive. Using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider Markov chain Monte Carlo and sequential Monte Carlo methods which have been introduced in the literature and we describe different strategies which facilitate the application of MLMC within these methods.
Advanced Multilevel Monte Carlo Methods
Jasra, Ajay
2017-04-24
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the discretization of a associated probability law. The MLMC approach works with a hierarchy of biased approximations which become progressively more accurate and more expensive. Using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider Markov chain Monte Carlo and sequential Monte Carlo methods which have been introduced in the literature and we describe different strategies which facilitate the application of MLMC within these methods.
Numerical Methods for Free Boundary Problems
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...
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
Nodal methods in numerical reactor calculations
International Nuclear Information System (INIS)
Hennart, J.P.; Valle, E. del
2004-01-01
The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)
Nodal methods in numerical reactor calculations
Energy Technology Data Exchange (ETDEWEB)
Hennart, J P [UNAM, IIMAS, A.P. 20-726, 01000 Mexico D.F. (Mexico); Valle, E del [National Polytechnic Institute, School of Physics and Mathematics, Department of Nuclear Engineering, Mexico, D.F. (Mexico)
2004-07-01
The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)
Advanced methods of fatigue assessment
Radaj, Dieter
2013-01-01
The book in hand presents advanced methods of brittle fracture and fatigue assessment. The Neuber concept of fictitious notch rounding is enhanced with regard to theory and application. The stress intensity factor concept for cracks is extended to pointed and rounded corner notches as well as to locally elastic-plastic material behaviour. The averaged strain energy density within a circular sector volume around the notch tip is shown to be suitable for strength-assessments. Finally, the various implications of cyclic plasticity on fatigue crack growth are explained with emphasis being laid on the DJ-integral approach. This book continues the expositions of the authors’ well known reference work in German language ‘Ermüdungsfestigkeit – Grundlagen für Ingenieure’ (Fatigue strength – fundamentals for engineers).
Advanced construction methods in ACR
International Nuclear Information System (INIS)
Elgohary, M.; Choy, E.; Yu, S.K.W.
2002-01-01
The ACR - Advanced CANDU Reactor, developed by Atomic Energy of Canada Limited (AECL), is designed with constructability considerations as a major requirement during all project phases from the concept design stage to the detail design stage. This necessitated a much more comprehensive approach in including constructability considerations in the design to ensure that the construction duration is met. For the ACR-700, a project schedule of 48 months has been developed for the nth replicated unit with a 36 month construction period duration from First Concrete to Fuel Load. An overall construction strategy that builds on the success of the construction methods that are proven in the construction of the Qinshan CANDU 6 project has been developed for the ACR. The overall construction strategy comprises the 'Open Top' construction technique using a Very Heavy Lift crane, parallel construction activities, with extensive modularization and prefabrication. In addition, significant applications of up to date construction technology will be implemented, e.g. large volume concrete pours, prefabricated rebar, use of climbing forms, composite structures, prefabricated permanent formwork, automatic welding, and utilization of the latest electronic technology tools such as 3D CADDs modelling yields a very high quality, clash free product to allow construction to be completed 'right the first time' and eliminates rework. Integration of 3D CADDs models and scheduling tools such as Primavera has allowed development of actual construction sequences and an iterative approach to schedule verification and improvement. Modularization and prefabrication are major features of the ACR design in order to achieve the project schedule. For the reactor building approximately 80% of the volume will be installed as modules or prefabricated assembles. This ensures critical path activities are achieved. This paper examines the advanced construction methods implemented in the design in order to
Advanced numerical modelling of a fire. Final report
International Nuclear Information System (INIS)
Heikkilae, L.; Keski-Rahkonen, O.
1996-03-01
Experience and probabilistic risk assessments show that fires present a major hazard in a nuclear power plant (NPP). The PALOME project (1988-92) improved the quality of numerical simulation of fires to make it a useful tool for fire safety analysis. Some of the most advanced zone model fire simulation codes were acquired. The performance of the codes was studied through literature and personal interviews in earlier studies and BRI2 code from the Japanese Building Research Institute was selected for further use. In PALOME 2 project this work was continued. Information obtained from large-scale fire tests at the German HDR facility allowed reliable prediction of the rate of heat release and was used for code validation. BRI2 code was validated particularly by participation in the CEC standard problem 'Prediction of effects caused by a cable fire experiment within the HDR-facility'. Participation in the development of a new field model code SOFIE specifically for fire applications as British-Swedish-Finnish cooperation was one of the goals of the project. SOFIE code was implemented at VTT and the first results of validation simulations were obtained. Well instrumented fire tests on electronic cabinets were carried out to determine source terms for simulation of room fires and to estimate fire spread to adjacent cabinets. The particular aim of this study was to measure the rate of heat release from a fire in an electronic cabinet. From the three tests, differing mainly in the amount of the fire load, data was obtained for source terms in numerical modelling of fires in rooms containing electronic cabinets. On the basis of these tests also a simple natural ventilation model was derived. (19 refs.)
Advanced approach to numerical forecasting using artificial neural networks
Directory of Open Access Journals (Sweden)
Michael Štencl
2009-01-01
Full Text Available Current global market is driven by many factors, such as the information age, the time and amount of information distributed by many data channels it is practically impossible analyze all kinds of incoming information flows and transform them to data with classical methods. New requirements could be met by using other methods. Once trained on patterns artificial neural networks can be used for forecasting and they are able to work with extremely big data sets in reasonable time. The patterns used for learning process are samples of past data. This paper uses Radial Basis Functions neural network in comparison with Multi Layer Perceptron network with Back-propagation learning algorithm on prediction task. The task works with simplified numerical time series and includes forty observations with prediction for next five observations. The main topic of the article is the identification of the main differences between used neural networks architectures together with numerical forecasting. Detected differences then verify on practical comparative example.
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...
Numerical Forming Simulations and Optimisation in Advanced Materials
International Nuclear Information System (INIS)
Huetink, J.; Boogaard, A. H. van den; Geijselears, H. J. M.; Meinders, T.
2007-01-01
With the introduction of new materials as high strength steels, metastable steels and fibre reinforced composites, the need for advanced physically valid constitutive models arises. In finite deformation problems constitutive relations are commonly formulated in terms the Cauchy stress as a function of the elastic Finger tensor and an objective rate of the Cauchy stress as a function of the rate of deformation tensor. For isotropic materials models this is rather straightforward, but for anisotropic material models, including elastic anisotropy as well as plastic anisotropy, this may lead to confusing formulations. It will be shown that it is more convenient to define the constitutive relations in terms of invariant tensors referred to the deformed metric. Experimental results are presented that show new combinations of strain rate and strain path sensitivity. An adaptive through- thickness integration scheme for plate elements is developed, which improves the accuracy of spring back prediction at minimal costs. A procedure is described to automatically compensate the CAD tool shape numerically to obtain the desired product shape. Forming processes need to be optimized for cost saving and product improvement. Until recently, a trial-and-error process in the factory primarily did this optimization. An optimisation strategy is proposed that assists an engineer to model an optimization problem that suits his needs, including an efficient algorithm for solving the problem
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.
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.
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
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.
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.
Recent advances in radial basis function collocation methods
Chen, Wen; Chen, C S
2014-01-01
This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems. Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world’s ...
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
Numerical methods for coupled fracture problems
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.
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.
Advanced accelerator methods: The cyclotrino
International Nuclear Information System (INIS)
Welch, J.J.; Bertsche, K.J.; Friedman, P.G.; Morris, D.E.; Muller, R.A.
1987-04-01
Several new and unusual, advanced techniques in the small cyclotron are described. The cyclotron is run at low energy, using negative ions and at high harmonics. Electrostatic focusing is used exclusively. The ion source and injection system is in the center, which unfortunately does not provide enough current, but the new system design should solve this problem. An electrostatic extractor that runs at low voltage, under 5 kV, and a microchannel plate detector which is able to discriminate low energy ions from the 14 C are used. The resolution is sufficient for 14 C dating and a higher intensity source should allow dating of a milligram size sample of 30,000 year old material with less than 10% uncertainty
Nonlinear ordinary differential equations analytical approximation and numerical methods
Hermann, Martin
2016-01-01
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...
Numerical Methods for Partial Differential Equations.
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
Numerical methods for stochastic partial differential equations with white noise
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...
Migórski, Stanisław; Sofonea, Mircea
2015-01-01
Highlighting recent advances in variational and hemivariational inequalities with an emphasis on theory, numerical analysis and applications, this volume serves as an indispensable resource to graduate students and researchers interested in the latest results from recognized scholars in this relatively young and rapidly-growing field. Particularly, readers will find that the volume’s results and analysis present valuable insights into the fields of pure and applied mathematics, as well as civil, aeronautical, and mechanical engineering. Researchers and students will find new results on well posedness to stationary and evolutionary inequalities and their rigorous proofs. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities. Finally, the applications presented illustrate the use of these results in the study of miscellaneous mathematical models which describe the contact between deformable bodies and a...
Multi-band effective mass approximations advanced mathematical models and numerical techniques
Koprucki, Thomas
2014-01-01
This book addresses several mathematical models from the most relevant class of kp-Schrödinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects. The goal of numerical simulations using quantum mechanical models in the development of semiconductor nano structures is threefold: First they are needed for a deeper understanding of experimental data and of the operational principle. Secondly, they allow us to predict and optimize in advance the qualitative and quantitative properties of new devices in order to minimize the number of prototypes needed. Semiconductor nano structures are embedded as an active region in semiconductor devices. Thirdly and finally, the results of quantum mechanical simulations of semiconductor nano structures can be used wit...
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.
Numerical Methods for Bayesian Inverse Problems
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.
Numerical Methods for Bayesian Inverse Problems
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.
The proper generalized decomposition for advanced numerical simulations a primer
Chinesta, Francisco; Leygue, Adrien
2014-01-01
Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical mod...
Tensor viscosity method for convection in numerical fluid dynamics
International Nuclear Information System (INIS)
Dukowicz, J.K.; Ramshaw, J.D.
1979-01-01
A new method, called the tensor viscosity method, is described for differencing the convective terms in multidimensional numerical fluid dynamics. The method is the proper generalization to two or three dimensions of interpolated donor cell differencing in one dimension, and is designed to achieve numerical stability with minimal numerical damping. It is a single-step method that is distinguished by simplicity and case of implementation, even in the case of an arbitrary non-rectangular mesh. It should therefore be useful in finite-element as well as finite-difference formulations
Numerical 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.
Iler, H. Darrell; Brown, Amber; Landis, Amanda; Schimke, Greg; Peters, George
2014-01-01
A numerical analysis of the free radical addition polymerization system is described that provides those teaching polymer, physical, or advanced organic chemistry courses the opportunity to introduce students to numerical methods in the context of a simple but mathematically stiff chemical kinetic system. Numerical analysis can lead students to an…
Introduction to numerical methods for time dependent differential equations
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
Advanced Fine Particulate Characterization Methods
Energy Technology Data Exchange (ETDEWEB)
Steven Benson; Lingbu Kong; Alexander Azenkeng; Jason Laumb; Robert Jensen; Edwin Olson; Jill MacKenzie; A.M. Rokanuzzaman
2007-01-31
The characterization and control of emissions from combustion sources are of significant importance in improving local and regional air quality. Such emissions include fine particulate matter, organic carbon compounds, and NO{sub x} and SO{sub 2} gases, along with mercury and other toxic metals. This project involved four activities including Further Development of Analytical Techniques for PM{sub 10} and PM{sub 2.5} Characterization and Source Apportionment and Management, Organic Carbonaceous Particulate and Metal Speciation for Source Apportionment Studies, Quantum Modeling, and High-Potassium Carbon Production with Biomass-Coal Blending. The key accomplishments included the development of improved automated methods to characterize the inorganic and organic components particulate matter. The methods involved the use of scanning electron microscopy and x-ray microanalysis for the inorganic fraction and a combination of extractive methods combined with near-edge x-ray absorption fine structure to characterize the organic fraction. These methods have direction application for source apportionment studies of PM because they provide detailed inorganic analysis along with total organic and elemental carbon (OC/EC) quantification. Quantum modeling using density functional theory (DFT) calculations was used to further elucidate a recently developed mechanistic model for mercury speciation in coal combustion systems and interactions on activated carbon. Reaction energies, enthalpies, free energies and binding energies of Hg species to the prototype molecules were derived from the data obtained in these calculations. Bimolecular rate constants for the various elementary steps in the mechanism have been estimated using the hard-sphere collision theory approximation, and the results seem to indicate that extremely fast kinetics could be involved in these surface reactions. Activated carbon was produced from a blend of lignite coal from the Center Mine in North Dakota and
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.)
Numerical simulation methods for phase-transitional flow
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
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
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)
Classical and modern numerical analysis theory, methods and practice
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...
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.
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
A review of recent advances in numerical modelling of local scour problems
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2014-01-01
A review is presented of recent advances in numerical modelling of local scour problems. The review is organized in five sections: Highlights of numerical modelling of local scour; Influence of turbulence on scour; Backfilling of scour holes; Scour around complex structures; and Scour protection ...
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
Numerical and adaptive grid methods for ideal magnetohydrodynamics
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.
Molecular dynamics with deterministic and stochastic numerical methods
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...
Two numerical methods for mean-field games
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.
Two numerical methods for mean-field games
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.
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
Stochastic numerical methods an introduction for students and scientists
Toral, Raul
2014-01-01
Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability ConceptsMonte Carlo IntegrationGeneration of Uniform and Non-uniformRandom Numbers: Non-correlated ValuesDynamical MethodsApplications to Statistical MechanicsIn...
Numerical methods design, analysis, and computer implementation of algorithms
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...
Advanced computational electromagnetic methods and applications
Li, Wenxing; Elsherbeni, Atef; Rahmat-Samii, Yahya
2015-01-01
This new resource covers the latest developments in computational electromagnetic methods, with emphasis on cutting-edge applications. This book is designed to extend existing literature to the latest development in computational electromagnetic methods, which are of interest to readers in both academic and industrial areas. The topics include advanced techniques in MoM, FEM and FDTD, spectral domain method, GPU and Phi hardware acceleration, metamaterials, frequency and time domain integral equations, and statistics methods in bio-electromagnetics.
Development of advanced MCR task analysis methods
International Nuclear Information System (INIS)
Na, J. C.; Park, J. H.; Lee, S. K.; Kim, J. K.; Kim, E. S.; Cho, S. B.; Kang, J. S.
2008-07-01
This report describes task analysis methodology for advanced HSI designs. Task analyses was performed by using procedure-based hierarchical task analysis and task decomposition methods. The results from the task analysis were recorded in a database. Using the TA results, we developed static prototype of advanced HSI and human factors engineering verification and validation methods for an evaluation of the prototype. In addition to the procedure-based task analysis methods, workload estimation based on the analysis of task performance time and analyses for the design of information structure and interaction structures will be necessary
Advanced Computational Methods for Monte Carlo Calculations
Energy Technology Data Exchange (ETDEWEB)
Brown, Forrest B. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2018-01-12
This course is intended for graduate students who already have a basic understanding of Monte Carlo methods. It focuses on advanced topics that may be needed for thesis research, for developing new state-of-the-art methods, or for working with modern production Monte Carlo codes.
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
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
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
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.
Numerical methods for axisymmetric and 3D nonlinear beams
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.
Numerical methods of mathematical optimization with Algol and Fortran programs
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
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....
Valve cam design using numerical step-by-step method
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.
Investigating Convergence Patterns for Numerical Methods Using Data Analysis
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…
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
Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance
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.
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
Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance
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.
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.
Advanced analysis methods in particle physics
Energy Technology Data Exchange (ETDEWEB)
Bhat, Pushpalatha C.; /Fermilab
2010-10-01
Each generation of high energy physics experiments is grander in scale than the previous - more powerful, more complex and more demanding in terms of data handling and analysis. The spectacular performance of the Tevatron and the beginning of operations of the Large Hadron Collider, have placed us at the threshold of a new era in particle physics. The discovery of the Higgs boson or another agent of electroweak symmetry breaking and evidence of new physics may be just around the corner. The greatest challenge in these pursuits is to extract the extremely rare signals, if any, from huge backgrounds arising from known physics processes. The use of advanced analysis techniques is crucial in achieving this goal. In this review, I discuss the concepts of optimal analysis, some important advanced analysis methods and a few examples. The judicious use of these advanced methods should enable new discoveries and produce results with better precision, robustness and clarity.
An advanced probabilistic structural analysis method for implicit performance functions
Wu, Y.-T.; Millwater, H. R.; Cruse, T. A.
1989-01-01
In probabilistic structural analysis, the performance or response functions usually are implicitly defined and must be solved by numerical analysis methods such as finite element methods. In such cases, the most commonly used probabilistic analysis tool is the mean-based, second-moment method which provides only the first two statistical moments. This paper presents a generalized advanced mean value (AMV) method which is capable of establishing the distributions to provide additional information for reliability design. The method requires slightly more computations than the second-moment method but is highly efficient relative to the other alternative methods. In particular, the examples show that the AMV method can be used to solve problems involving non-monotonic functions that result in truncated distributions.
International Nuclear Information System (INIS)
Hawong, Jai Sug; Lee, Dong Hun; Lee, Dong Ha; Tche, Konstantin
2004-01-01
In this research, the photoelastic experimental hybrid method with Hook-Jeeves numerical method has been developed: This method is more precise and stable than the photoelastic experimental hybrid method with Newton-Rapson numerical method with Gaussian elimination method. Using the photoelastic experimental hybrid method with Hook-Jeeves numerical method, we can separate stress components from isochromatics only and stress intensity factors and stress concentration factors can be determined. The photoelastic experimental hybrid method with Hook-Jeeves had better be used in the full field experiment than the photoelastic experimental hybrid method with Newton-Rapson with Gaussian elimination method
Numerical 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)
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
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.
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
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)
Advanced methods in diagnosis and therapy
International Nuclear Information System (INIS)
1987-01-01
This important meeting covers the following topics: use and optimization of monoclonal antibobies in oncology: - Tumor markers: Clinical follow-up of patients through tumor marker serum determinations. - Cancer and medical imaging: The use of monoclonal antibodies in immunoscintigraphy. - Immunoradiotherapy: Monoclonal antibodies as therapeutic vectors. Advanced methods in diagnosis: - Contribution of monoclonal antibodies in modern immunochemistry (RIA, EIA). - Interest of monoclonal antibody in immunohistochemical pathology diagnosis. - In vitro diagnosis future prospects: with receptors and oncogenes. - Immunofluoroassay: a new sensitive immunoanalytical procedure with broad applications. Recent advances in brachitherapy: - Interest of computer processing. Blood products irradiation: - Interest in transfusion and bone marrow transplantations [fr
Mathematics for natural scientists II advanced methods
Kantorovich, Lev
2016-01-01
This book covers the advanced mathematical techniques useful for physics and engineering students, presented in a form accessible to physics students, avoiding precise mathematical jargon and laborious proofs. Instead, all proofs are given in a simplified form that is clear and convincing for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each chapter. Mathematics for Natural Scientists II: Advanced Methods is the second of two volumes. It follows the first volume on Fundamentals and Basics.
Direct numerical methods of mathematical modeling in mechanical structural design
International Nuclear Information System (INIS)
Sahili, Jihad; Verchery, Georges; Ghaddar, Ahmad; Zoaeter, Mohamed
2002-01-01
Full text.Structural design and numerical methods are generally interactive; requiring optimization procedures as the structure is analyzed. This analysis leads to define some mathematical terms, as the stiffness matrix, which are resulting from the modeling and then used in numerical techniques during the dimensioning procedure. These techniques and many others involve the calculation of the generalized inverse of the stiffness matrix, called also the 'compliance matrix'. The aim of this paper is to introduce first, some different existing mathematical procedures, used to calculate the compliance matrix from the stiffness matrix, then apply direct numerical methods to solve the obtained system with the lowest computational time, and to compare the obtained results. The results show a big difference of the computational time between the different procedures
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.
Advances of evolutionary computation methods and operators
Cuevas, Erik; Oliva Navarro, Diego Alberto
2016-01-01
The goal of this book is to present advances that discuss alternative Evolutionary Computation (EC) developments and non-conventional operators which have proved to be eﬀective in the solution of several complex problems. The book has been structured so that each chapter can be read independently from the others. The book contains nine chapters with the following themes: 1) Introduction, 2) the Social Spider Optimization (SSO), 3) the States of Matter Search (SMS), 4) the collective animal behavior (CAB) algorithm, 5) the Allostatic Optimization (AO) method, 6) the Locust Search (LS) algorithm, 7) the Adaptive Population with Reduced Evaluations (APRE) method, 8) the multimodal CAB, 9) the constrained SSO method.
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)
Numerical methods for the Lévy LIBOR model
DEFF Research Database (Denmark)
Papapantoleon, Antonis; Skovmand, David
2010-01-01
but the methods are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure....... This enables simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.......The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the L\\'evy LIBOR model of Eberlein and \\"Ozkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates...
Numerical Methods for the Lévy LIBOR Model
DEFF Research Database (Denmark)
Papapantoleon, Antonis; Skovmand, David
are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure. This enables...... simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.......The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the Lévy LIBOR model of Eberlein and Özkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods...
Workshop on Numerical Methods for Ordinary Differential Equations
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.
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
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.
Numerical methods and computers used in elastohydrodynamic lubrication
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.
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.
NATO Advanced Study Institute on Methods in Computational Molecular Physics
Diercksen, Geerd
1992-01-01
This volume records the lectures given at a NATO Advanced Study Institute on Methods in Computational Molecular Physics held in Bad Windsheim, Germany, from 22nd July until 2nd. August, 1991. This NATO Advanced Study Institute sought to bridge the quite considerable gap which exist between the presentation of molecular electronic structure theory found in contemporary monographs such as, for example, McWeeny's Methods 0/ Molecular Quantum Mechanics (Academic Press, London, 1989) or Wilson's Electron correlation in moleeules (Clarendon Press, Oxford, 1984) and the realization of the sophisticated computational algorithms required for their practical application. It sought to underline the relation between the electronic structure problem and the study of nuc1ear motion. Software for performing molecular electronic structure calculations is now being applied in an increasingly wide range of fields in both the academic and the commercial sectors. Numerous applications are reported in areas as diverse as catalysi...
Advanced statistical methods in data science
Chen, Jiahua; Lu, Xuewen; Yi, Grace; Yu, Hao
2016-01-01
This book gathers invited presentations from the 2nd Symposium of the ICSA- CANADA Chapter held at the University of Calgary from August 4-6, 2015. The aim of this Symposium was to promote advanced statistical methods in big-data sciences and to allow researchers to exchange ideas on statistics and data science and to embraces the challenges and opportunities of statistics and data science in the modern world. It addresses diverse themes in advanced statistical analysis in big-data sciences, including methods for administrative data analysis, survival data analysis, missing data analysis, high-dimensional and genetic data analysis, longitudinal and functional data analysis, the design and analysis of studies with response-dependent and multi-phase designs, time series and robust statistics, statistical inference based on likelihood, empirical likelihood and estimating functions. The editorial group selected 14 high-quality presentations from this successful symposium and invited the presenters to prepare a fu...
Dynamical Systems Method and Applications Theoretical Developments and Numerical Examples
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
Hybrid RANS-LES using high order numerical methods
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.
Developing Teaching Material Software Assisted for Numerical Methods
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.
Editorial: Latest methods and advances in biotechnology.
Lee, Sang Yup; Jungbauer, Alois
2014-01-01
The latest "Biotech Methods and Advances" special issue of Biotechnology Journal continues the BTJ tradition of featuring the latest breakthroughs in biotechnology. The special issue is edited by our Editors-in-Chief, Prof. Sang Yup Lee and Prof. Alois Jungbauer and covers a wide array of topics in biotechnology, including the perennial favorite workhorses of the biotech industry, Chinese hamster ovary (CHO) cell and Escherichia coli. Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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
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)
Numerical methods for characterization of synchrotron radiation based on the Wigner function method
Directory of Open Access Journals (Sweden)
Takashi Tanaka
2014-06-01
Full Text Available Numerical characterization of synchrotron radiation based on the Wigner function method is explored in order to accurately evaluate the light source performance. A number of numerical methods to compute the Wigner functions for typical synchrotron radiation sources such as bending magnets, undulators and wigglers, are presented, which significantly improve the computation efficiency and reduce the total computation time. As a practical example of the numerical characterization, optimization of betatron functions to maximize the brilliance of undulator radiation is discussed.
Numerical renormalization group method for entanglement negativity at finite temperature
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.
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
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)
Theoretical and applied aerodynamics and related numerical methods
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...
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
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
Numerical method for the unsteady potential flow about pitching airfoils
International Nuclear Information System (INIS)
Parrouffe, J.-M.; Paraschivoiu, I.
1985-01-01
This paper presents a numerical method for the unsteady potential flow about an aerodynamic profile and in its wake. This study has many applications such as airplane wings and propellers, guide vanes, subcavitant hydrofoils and wind turbine blades. Typical of such nonstationary configurations is the rotor of the Darrieus vertical-axis wind turbine whose blades are exposed to cyclic aerodynamic loads in the operating state
Numerical Verification Methods for Spherical $t$-Designs
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...
Development of numerical methods for thermohydraulic problems in reactor safety
International Nuclear Information System (INIS)
Chabrillac, M.; Kavenoky, A.; Le Coq, G.; L'Heriteau, J.P.; Stewart, B.; Rousseau, J.C.
1976-01-01
Numerical methods are being developed for the LOCA calculation; the first part is devoted to the BERTHA model and the associated characteristic treatment for the first seconds of the blowdown, the second part presents the problems encountered for accounting for velocity difference between phases. The FLIRA treatment of the reflooding is presented in the last part: this treatment allows the calculation of the quenching front velocity
A first course in ordinary differential equations analytical and numerical methods
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...
Numerical method for wave forces acting on partially perforated caisson
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.
The instanton method and its numerical implementation in fluid mechanics
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.
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)
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.
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)
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)
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
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.
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
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.
Advanced Analysis Methods in High Energy Physics
Energy Technology Data Exchange (ETDEWEB)
Pushpalatha C. Bhat
2001-10-03
During the coming decade, high energy physics experiments at the Fermilab Tevatron and around the globe will use very sophisticated equipment to record unprecedented amounts of data in the hope of making major discoveries that may unravel some of Nature's deepest mysteries. The discovery of the Higgs boson and signals of new physics may be around the corner. The use of advanced analysis techniques will be crucial in achieving these goals. The author discusses some of the novel methods of analysis that could prove to be particularly valuable for finding evidence of any new physics, for improving precision measurements and for exploring parameter spaces of theoretical models.
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.
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.
Applying multi-resolution numerical methods to geodynamics
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
An advanced method of heterogeneous reactor theory
International Nuclear Information System (INIS)
Kochurov, B.P.
1994-08-01
Recent approaches to heterogeneous reactor theory for numerical applications were presented in the course of 8 lectures given in JAERI. The limitations of initial theory known after the First Conference on Peacefull Uses of Atomic Energy held in Geneva in 1955 as Galanine-Feinberg heterogeneous theory:-matrix from of equations, -lack of consistent theory for heterogeneous parameters for reactor cell, -were overcome by a transformation of heterogeneous reactor equations to a difference form and by a development of a consistent theory for the characteristics of a reactor cell based on detailed space-energy calculations. General few group (G-number of groups) heterogeneous reactor equations in dipole approximation are formulated with the extension of two-dimensional problem to three-dimensions by finite Furie expansion of axial dependence of neutron fluxes. A transformation of initial matrix reactor equations to a difference form is presented. The methods for calculation of heterogeneous reactor cell characteristics giving the relation between vector-flux and vector-current on a cell boundary are based on a set of detailed space-energy neutron flux distribution calculations with zero current across cell boundary and G calculations with linearly independent currents across the cell boundary. The equations for reaction rate matrices are formulated. Specific methods were developed for description of neutron migration in axial and radial directions. The methods for resonance level's approach for numerous high-energy resonances. On the basis of these approaches the theory, methods and computer codes were developed for 3D space-time react or problems including simulation of slow processes with fuel burn-up, control rod movements, Xe poisoning and fast transients depending on prompt and delayed neutrons. As a result reactors with several thousands of channels having non-uniform axial structure can be feasibly treated. (author)
Advanced Computational Methods in Bio-Mechanics.
Al Qahtani, Waleed M S; El-Anwar, Mohamed I
2018-04-15
A novel partnership between surgeons and machines, made possible by advances in computing and engineering technology, could overcome many of the limitations of traditional surgery. By extending surgeons' ability to plan and carry out surgical interventions more accurately and with fewer traumas, computer-integrated surgery (CIS) systems could help to improve clinical outcomes and the efficiency of healthcare delivery. CIS systems could have a similar impact on surgery to that long since realised in computer-integrated manufacturing. Mathematical modelling and computer simulation have proved tremendously successful in engineering. Computational mechanics has enabled technological developments in virtually every area of our lives. One of the greatest challenges for mechanists is to extend the success of computational mechanics to fields outside traditional engineering, in particular to biology, the biomedical sciences, and medicine. Biomechanics has significant potential for applications in orthopaedic industry, and the performance arts since skills needed for these activities are visibly related to the human musculoskeletal and nervous systems. Although biomechanics is widely used nowadays in the orthopaedic industry to design orthopaedic implants for human joints, dental parts, external fixations and other medical purposes, numerous researches funded by billions of dollars are still running to build a new future for sports and human healthcare in what is called biomechanics era.
Advanced numerical simulation based on a non-local micromorphic model for metal forming processes
Directory of Open Access Journals (Sweden)
Diamantopoulou Evangelia
2016-01-01
Full Text Available An advanced numerical methodology is developed for metal forming simulation based on thermodynamically-consistent nonlocal constitutive equations accounting for various fully coupled mechanical phenomena under finite strain in the framework of micromorphic continua. The numerical implementation into ABAQUS/Explicit is made for 2D quadrangular elements thanks to the VUEL users’ subroutine. Simple examples with presence of a damaged area are made in order to show the ability of the proposed methodology to describe the independence of the solution from the space discretization.
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.)
Advances in Packaging Methods, Processes and Systems
Directory of Open Access Journals (Sweden)
Nitaigour Premchand Mahalik
2014-10-01
Full Text Available The food processing and packaging industry is becoming a multi-trillion dollar global business. The reason is that the recent increase in incomes in traditionally less economically developed countries has led to a rise in standards of living that includes a significantly higher consumption of packaged foods. As a result, food safety guidelines have been more stringent than ever. At the same time, the number of research and educational institutions—that is, the number of potential researchers and stakeholders—has increased in the recent past. This paper reviews recent developments in food processing and packaging (FPP, keeping in view the aforementioned advancements and bearing in mind that FPP is an interdisciplinary area in that materials, safety, systems, regulation, and supply chains play vital roles. In particular, the review covers processing and packaging principles, standards, interfaces, techniques, methods, and state-of-the-art technologies that are currently in use or in development. Recent advances such as smart packaging, non-destructive inspection methods, printing techniques, application of robotics and machineries, automation architecture, software systems and interfaces are reviewed.
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)
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)
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
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
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)
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)
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.
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs
Numerical simulation and performance investigation of an advanced adsorption desalination cycle
Thu, Kyaw; Chakraborty, Anutosh; Kim, Youngdeuk; Myat, Aung; Saha, Bidyut Baran; Ng, Kim Choon
2013-01-01
Low temperature waste heat-driven adsorption desalination (AD) cycles offer high potential as one of the most economically viable and environmental-friendly desalination methods. This article presents the development of an advanced adsorption
Proceedings of the fifth international symposium on numerical methods in engineering. Vol. 1 and 2
Energy Technology Data Exchange (ETDEWEB)
Gruber, R [Ecole Polytechnique Federale, Lausanne (Switzerland); Periaux, J [Avions Marcel Dassault-Breguet Aviation, 92 - Saint-Cloud (France). Aerodynamique, Methodes Numeriques; Shaw, R P [Buffalo Univ., NY (USA). Dept. of Civil Engineering; eds.
1989-01-01
The present two volumes survey the state of the art in advanced scientific computing as applied to engineering science. Many fields ranging from modelization (partial differential equations, integral equations, boundary conditions, macroscopic models, cellular automata) to numerical methods (finite elements, optimization, software engineering tools, parallel and vector computing methods, domain decomposition, multigrid) and applications (nonlinear solid mechanics, fracture mechanics, composite materials, friction and contact, fluid mechanics, chemical flows, convection, free boundaries, combustion, electromagnetics) are covered by invited papers, minisymposia and contributed papers. (orig./HP).
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.
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
Computer prediction of subsurface radionuclide transport: an adaptive numerical method
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
Problem of the Moving Boundary in Continuous Casting Solved by The Analytic-Numerical Method
Directory of Open Access Journals (Sweden)
Grzymkowski R.
2013-03-01
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 or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the 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 a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.
Problem of the Moving Boundary in Continuous Casting Solved by the Analytic-Numerical Method
Directory of Open Access Journals (Sweden)
R. Grzymkowski
2013-01-01
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 or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the 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 a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.
Dadashzadeh, N.; Duzgun, H. S. B.; Yesiloglu-Gultekin, N.
2017-08-01
While advanced numerical techniques in slope stability analysis are successfully used in deterministic studies, they have so far found limited use in probabilistic analyses due to their high computation cost. The first-order reliability method (FORM) is one of the most efficient probabilistic techniques to perform probabilistic stability analysis by considering the associated uncertainties in the analysis parameters. However, it is not possible to directly use FORM in numerical slope stability evaluations as it requires definition of a limit state performance function. In this study, an integrated methodology for probabilistic numerical modeling of rock slope stability is proposed. The methodology is based on response surface method, where FORM is used to develop an explicit performance function from the results of numerical simulations. The implementation of the proposed methodology is performed by considering a large potential rock wedge in Sumela Monastery, Turkey. The accuracy of the developed performance function to truly represent the limit state surface is evaluated by monitoring the slope behavior. The calculated probability of failure is compared with Monte Carlo simulation (MCS) method. The proposed methodology is found to be 72% more efficient than MCS, while the accuracy is decreased with an error of 24%.
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)
Advanced numerical description of the behavior of 700 C steam power plant components
Energy Technology Data Exchange (ETDEWEB)
Maile, K. [Materialpruefungsanstalt, Univ. Stuttgart (Germany); Schmidt, K.; Roos, E.; Klenk, A.; Speicher, M.
2009-07-01
To make full use of the strength potential of new boiler materials like the new 9-11% Cr steels and nickel based alloys, taking into account their specific stress-strain relaxation behavior, new design methods are required in the design of today's power plants. Highly loaded components are approaching more and more the classical design limits with regard to critical wall thicknesses and the related tolerable thermal gradients, due to planed increases of steam parameters like steam pressure and steam temperature. ''Design by analysis'' can be realized by modern state of the art Numerical Finite Element (FE) simulation codes and in some cases by the use of user defined advanced inelastic material laws. These material laws have to be adjusted to specific material behavior of new boiler materials. To model the strain and stress situation in components under high temperature loading, a constitutive equation based on a Graham-Walles approach is used in this paper. Furthermore essential steps and recommendations to implement experimental data in the user defined subroutines and the subsequent integration of the subroutines in modern FE codes like ABAQUS trademark and ANSYS trademark are given. As an example, the results of FE simulations of components like hollow cylinders and waterwall like components made of Alloy 617 or 9-11% Cr steels are discussed and verified with experimental results. In a last step, the successful application of the developed creep equation will be demonstrated by calculating the creep strains and stress relaxation of a P92 steam header under constant loading. (orig.)
Hu, Ping; Liu, Li-zhong; Zhu, Yi-guo
2013-01-01
Over the last 15 years, the application of innovative steel concepts in the automotive industry has increased steadily. Numerical simulation technology of hot forming of high-strength steel allows engineers to modify the formability of hot forming steel metals and to optimize die design schemes. Theories, Methods and Numerical Technology of Sheet Metal Cold and Hot Forming focuses on hot and cold forming theories, numerical methods, relative simulation and experiment techniques for high-strength steel forming and die design in the automobile industry. Theories, Methods and Numerical Technology of Sheet Metal Cold and Hot Forming introduces the general theories of cold forming, then expands upon advanced hot forming theories and simulation methods, including: • the forming process, • constitutive equations, • hot boundary constraint treatment, and • hot forming equipment and experiments. Various calculation methods of cold and hot forming, based on the authors’ experience in commercial CAE software f...
Numerical modeling of isothermal compositional grading by convex splitting methods
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.
Mathematical analysis and numerical methods for science and technology
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 ...
Numerical methods for Eulerian and Lagrangian conservation laws
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.
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
Advanced continuous cultivation methods for systems microbiology.
Adamberg, Kaarel; Valgepea, Kaspar; Vilu, Raivo
2015-09-01
Increasing the throughput of systems biology-based experimental characterization of in silico-designed strains has great potential for accelerating the development of cell factories. For this, analysis of metabolism in the steady state is essential as only this enables the unequivocal definition of the physiological state of cells, which is needed for the complete description and in silico reconstruction of their phenotypes. In this review, we show that for a systems microbiology approach, high-resolution characterization of metabolism in the steady state--growth space analysis (GSA)--can be achieved by using advanced continuous cultivation methods termed changestats. In changestats, an environmental parameter is continuously changed at a constant rate within one experiment whilst maintaining cells in the physiological steady state similar to chemostats. This increases the resolution and throughput of GSA compared with chemostats, and, moreover, enables following of the dynamics of metabolism and detection of metabolic switch-points and optimal growth conditions. We also describe the concept, challenge and necessary criteria of the systematic analysis of steady-state metabolism. Finally, we propose that such systematic characterization of the steady-state growth space of cells using changestats has value not only for fundamental studies of metabolism, but also for systems biology-based metabolic engineering of cell factories.
Miyauchi, Suguru; Takeuchi, Shintaro; Kajishima, Takeo
2017-09-01
We develop a numerical method for fluid-membrane interaction accounting for permeation of the fluid using a non-conforming mesh to the membrane shape. To represent the permeation flux correctly, the proposed finite element discretization incorporates the discontinuities in the velocity gradient and pressure on the membrane surface with specially selected base functions. The discontinuities are represented with independent variables and determined to satisfy the governing equations including the interfacial condition on the permeation. The motions of the fluid, membrane and permeation flux are coupled monolithically and time-advanced fully-implicitly. The validity and effectiveness of the proposed method are demonstrated by several two-dimensional fluid-membrane interaction problems of Stokes flows by comparing with the analytical models and numerical results obtained by other methods. The reproduced sharp discontinuities are found to be essential to suppress the non-physical permeation flux. Further, combined with the numerical treatment for the solute concentration across the membrane, the proposed method is applied to a fluid-structure interaction problem including the osmotic pressure difference.
Advancing UAS methods for monitoring coastal environments
Ridge, J.; Seymour, A.; Rodriguez, A. B.; Dale, J.; Newton, E.; Johnston, D. W.
2017-12-01
Utilizing fixed-wing Unmanned Aircraft Systems (UAS), we are working to improve coastal monitoring by increasing the accuracy, precision, temporal resolution, and spatial coverage of habitat distribution maps. Generally, multirotor aircraft are preferred for precision imaging, but recent advances in fixed-wing technology have greatly increased their capabilities and application for fine-scale (decimeter-centimeter) measurements. Present mapping methods employed by North Carolina coastal managers involve expensive, time consuming and localized observation of coastal environments, which often lack the necessary frequency to make timely management decisions. For example, it has taken several decades to fully map oyster reefs along the NC coast, making it nearly impossible to track trends in oyster reef populations responding to harvesting pressure and water quality degradation. It is difficult for the state to employ manned flights for collecting aerial imagery to monitor intertidal oyster reefs, because flights are usually conducted after seasonal increases in turbidity. In addition, post-storm monitoring of coastal erosion from manned platforms is often conducted days after the event and collects oblique aerial photographs which are difficult to use for accurately measuring change. Here, we describe how fixed wing UAS and standard RGB sensors can be used to rapidly quantify and assess critical coastal habitats (e.g., barrier islands, oyster reefs, etc.), providing for increased temporal frequency to isolate long-term and event-driven (storms, harvesting) impacts. Furthermore, drone-based approaches can accurately image intertidal habitats as well as resolve information such as vegetation density and bathymetry from shallow submerged areas. We obtain UAS imagery of a barrier island and oyster reefs under ideal conditions (low tide, turbidity, and sun angle) to create high resolution (cm scale) maps and digital elevation models to assess habitat condition
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.
Numerical methods for incompressible viscous flows with engineering applications
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.
Hitt, Fernando; Morasse, Christian
2009-01-01
Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…
Numerical Simulation of Tubular Pumping Systems with Different Regulation Methods
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.
Damped time advance methods for particles and EM fields
International Nuclear Information System (INIS)
Friedman, A.; Ambrosiano, J.J.; Boyd, J.K.; Brandon, S.T.; Nielsen, D.E. Jr.; Rambo, P.W.
1990-01-01
Recent developments in the application of damped time advance methods to plasma simulations include the synthesis of implicit and explicit ''adjustably damped'' second order accurate methods for particle motion and electromagnetic field propagation. This paper discusses this method
Advanced Aqueous Phase Catalyst Development using Combinatorial Methods, Phase II
National Aeronautics and Space Administration — Combinatorial methods are proposed to develop advanced Aqueous Oxidation Catalysts (AOCs) with the capability to mineralize organic contaminants present in effluents...
Advanced Source Deconvolution Methods for Compton Telescopes
Zoglauer, Andreas
The next generation of space telescopes utilizing Compton scattering for astrophysical observations is destined to one day unravel the mysteries behind Galactic nucleosynthesis, to determine the origin of the positron annihilation excess near the Galactic center, and to uncover the hidden emission mechanisms behind gamma-ray bursts. Besides astrophysics, Compton telescopes are establishing themselves in heliophysics, planetary sciences, medical imaging, accelerator physics, and environmental monitoring. Since the COMPTEL days, great advances in the achievable energy and position resolution were possible, creating an extremely vast, but also extremely sparsely sampled data space. Unfortunately, the optimum way to analyze the data from the next generation of Compton telescopes has not yet been found, which can retrieve all source parameters (location, spectrum, polarization, flux) and achieves the best possible resolution and sensitivity at the same time. This is especially important for all sciences objectives looking at the inner Galaxy: the large amount of expected sources, the high background (internal and Galactic diffuse emission), and the limited angular resolution, make it the most taxing case for data analysis. In general, two key challenges exist: First, what are the best data space representations to answer the specific science questions? Second, what is the best way to deconvolve the data to fully retrieve the source parameters? For modern Compton telescopes, the existing data space representations can either correctly reconstruct the absolute flux (binned mode) or achieve the best possible resolution (list-mode), both together were not possible up to now. Here we propose to develop a two-stage hybrid reconstruction method which combines the best aspects of both. Using a proof-of-concept implementation we can for the first time show that it is possible to alternate during each deconvolution step between a binned-mode approach to get the flux right and a
International Nuclear Information System (INIS)
Ohira, H.; Ara, K.
2002-11-01
Advanced electromagnetic components are investigated in Feasibility Studies on Commercialized FR Cycle System to apply to the main cooling systems of Liquid Metal Fast Reactor. Although a lot of experiments and numerical analysis were carried out on both high Reynolds numbers and high magnetic Reynolds numbers, the complex phenomena could not be evaluated in detail. As the first step of the development of the numerical methods for the liquid metal magnetohydrodynamics, we investigated numerical methods that could be applied to the electromagnetic components with both complex structures and high magnetic turbulent field. As a result, we selected GSMAC (Generalized-Simplified MArker and Cell) method for calculating the liquid metal fluid dynamics because it could be easily applied to the complex flow field. We also selected the vector-FEM for calculating the magnetic field of the large components because the method had no interaction procedure. In the high magnetic turbulent field, the dynamic-SGS models would be also a promising model for the good estimation, because it could calculate the field directly without any experimental constant. In order to verify the GSMAC and the vector-FEM, we developed the 2D numerical models and calculated the magnetohydrodynamics in the large electromagnetic pump. It was estimated from these results that the methods were basically reasonable, because the calculated pressure differences had the similar tendencies to the experimental ones. (author)
Jylhä, Liisi; Honkamo, Johanna; Jantunen, Heli; Sihvola, Ari
2005-05-01
Effective permittivity was modeled and measured for composites that consist of up to 35vol% of titanium dioxide powder dispersed in a continuous epoxy matrix. The study demonstrates a method that enables fast and accurate numerical modeling of the effective permittivity values of ceramic/polymer composites. The model requires electrostatic Monte Carlo simulations, where randomly oriented homogeneous prism-shaped inclusions occupy random positions in the background phase. The computation cost of solving the electrostatic problem by a finite-element code is decreased by the use of an averaging method where the same simulated sample is solved three times with orthogonal field directions. This helps to minimize the artificial anisotropy that results from the pseudorandomness inherent in the limited computational domains. All the required parameters for numerical simulations are calculated from the lattice structure of titanium dioxide. The results show a very good agreement between the measured and numerically calculated effective permittivities. When the prisms are approximated by oblate spheroids with the corresponding axial ratio, a fairly good prediction for the effective permittivity of the mixture can be achieved with the use of an advanced analytical mixing formula.
High accuracy mantle convection simulation through modern numerical methods
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
A method of numerically controlled machine part programming
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.
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.
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.
Review of Methods and Approaches for Deriving Numeric ...
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
Numerical simulation of flow field in the China advanced research reactor flow-guide tank
International Nuclear Information System (INIS)
Xu Changjiang
2002-01-01
The flow-guide tank in China advanced research reactor (CARR) acts as a reactor inlet coolant distributor and play an important role in reducing the flow-induced vibration of the internal components of the reactor core. Numerical simulations of the flow field in the flow-guide tank under different conceptual designing configurations are carried out using the PHOENICS3.2. It is seen that the inlet coolant is well distributed circumferentially into the flow-guide tank with the inlet buffer plate and the flow distributor barrel. The maximum cross-flow velocity within the flow-guide tank is reduced significantly, and the reduction of flow-induced vibration of reactor internals is expected
Adaptive and dynamic meshing methods for numerical simulations
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
Numerical divergence effects of equivalence theory in the nodal expansion method
International Nuclear Information System (INIS)
Zika, M.R.; Downar, T.J.
1993-01-01
Accurate solutions of the advanced nodal equations require the use of discontinuity factors (DFs) to account for the homogenization errors that are inherent in all coarse-mesh nodal methods. During the last several years, nodal equivalence theory (NET) has successfully been implemented for the Cartesian geometry and has received widespread acceptance in the light water reactor industry. The extension of NET to other reactor types has had limited success. Recent efforts to implement NET within the framework of the nodal expansion method have successfully been applied to the fast breeder reactor. However, attempts to apply the same methods to thermal reactors such as the Modular High-Temperature Gas Reactor (MHTGR) have led to numerical divergence problems that can be attributed directly to the magnitude of the DFs. In the work performed here, it was found that the numerical problems occur in the inner and upscatter iterations of the solution algorithm. These iterations use a Gauss-Seidel iterative technique that is always convergent for problems with unity DFs. However, for an MHTGR model that requires large DFs, both the inner and upscatter iterations were divergent. Initial investigations into methods for bounding the DFs have proven unsatisfactory as a means of remedying the convergence problems. Although the DFs could be bounded to yield a convergent solution, several cases were encountered where the resulting flux solution was less accurate than the solution without DFs. For the specific case of problems without upscattering, an alternate numerical method for the inner iteration, an LU decomposition, was identified and shown to be feasible
The role of numerical simulation for the development of an advanced HIFU system
Okita, Kohei; Narumi, Ryuta; Azuma, Takashi; Takagi, Shu; Matumoto, Yoichiro
2014-10-01
High-intensity focused ultrasound (HIFU) has been used clinically and is under clinical trials to treat various diseases. An advanced HIFU system employs ultrasound techniques for guidance during HIFU treatment instead of magnetic resonance imaging in current HIFU systems. A HIFU beam imaging for monitoring the HIFU beam and a localized motion imaging for treatment validation of tissue are introduced briefly as the real-time ultrasound monitoring techniques. Numerical simulations have a great impact on the development of real-time ultrasound monitoring as well as the improvement of the safety and efficacy of treatment in advanced HIFU systems. A HIFU simulator was developed to reproduce ultrasound propagation through the body in consideration of the elasticity of tissue, and was validated by comparison with in vitro experiments in which the ultrasound emitted from the phased-array transducer propagates through the acrylic plate acting as a bone phantom. As the result, the defocus and distortion of the ultrasound propagating through the acrylic plate in the simulation quantitatively agree with that in the experimental results. Therefore, the HIFU simulator accurately reproduces the ultrasound propagation through the medium whose shape and physical properties are well known. In addition, it is experimentally confirmed that simulation-assisted focus control of the phased-array transducer enables efficient assignment of the focus to the target. Simulation-assisted focus control can contribute to design of transducers and treatment planning.
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)
Numerical calculation of elastohydrodynamic lubrication methods and programs
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
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
Advanced Methods of Biomedical Signal Processing
Cerutti, Sergio
2011-01-01
This book grew out of the IEEE-EMBS Summer Schools on Biomedical Signal Processing, which have been held annually since 2002 to provide the participants state-of-the-art knowledge on emerging areas in biomedical engineering. Prominent experts in the areas of biomedical signal processing, biomedical data treatment, medicine, signal processing, system biology, and applied physiology introduce novel techniques and algorithms as well as their clinical or physiological applications. The book provides an overview of a compelling group of advanced biomedical signal processing techniques, such as mult
Advanced Method of the Elastomagnetic Sensors Calibration
Directory of Open Access Journals (Sweden)
Mikulas Prascak
2004-01-01
Full Text Available Elastomagnetic method (EM method is a highly sensitive non-contact evaluation method for measuring tensile and compressive stress in steel. The latest development of measuring devices and EM sensors has shown that the thermomagnetic phenomenon has a stron influence on th accuracy during the EM sensor calibration. To eliminate the influence of this effect a two dimensional regression method is presented.
Recent advances in boundary element methods
Manolis, GD
2009-01-01
Addresses the needs of the computational mechanics research community in terms of information on boundary integral equation-based methods and techniques applied to a variety of fields. This book collects both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the Mesh Reduction Methods (MRM).
The Navier-Stokes Equations Theory and Numerical Methods
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.
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)
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
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
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
Advanced methods in teaching reactor physics
International Nuclear Information System (INIS)
Snoj, Luka; Kromar, Marjan; Zerovnik, Gasper; Ravnik, Matjaz
2011-01-01
Modern computer codes allow detailed neutron transport calculations. In combination with advanced 3D visualization software capable of treating large amounts of data in real time they form a powerful tool that can be used as a convenient modern educational tool for (nuclear power plant) operators, nuclear engineers, students and specialists involved in reactor operation and design. Visualization is applicable not only in education and training, but also as a tool for fuel management, core analysis and irradiation planning. The paper treats the visualization of neutron transport in different moderators, neutron flux and power distributions in two nuclear reactors (TRIGA type research reactor and typical PWR). The distributions are calculated with MCNP and CORD-2 computer codes and presented using Amira software.
Advanced methods in teaching reactor physics
Energy Technology Data Exchange (ETDEWEB)
Snoj, Luka, E-mail: luka.snoj@ijs.s [Jozef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Kromar, Marjan, E-mail: marjan.kromar@ijs.s [Jozef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Zerovnik, Gasper, E-mail: gasper.zerovnik@ijs.s [Jozef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Ravnik, Matjaz [Jozef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia)
2011-04-15
Modern computer codes allow detailed neutron transport calculations. In combination with advanced 3D visualization software capable of treating large amounts of data in real time they form a powerful tool that can be used as a convenient modern educational tool for (nuclear power plant) operators, nuclear engineers, students and specialists involved in reactor operation and design. Visualization is applicable not only in education and training, but also as a tool for fuel management, core analysis and irradiation planning. The paper treats the visualization of neutron transport in different moderators, neutron flux and power distributions in two nuclear reactors (TRIGA type research reactor and typical PWR). The distributions are calculated with MCNP and CORD-2 computer codes and presented using Amira software.
Lee, Chany; Jung, Young-Jin; Lee, Sang Jun; Im, Chang-Hwan
2017-02-01
Since there is no way to measure electric current generated by transcranial direct current stimulation (tDCS) inside the human head through in vivo experiments, numerical analysis based on the finite element method has been widely used to estimate the electric field inside the head. In 2013, we released a MATLAB toolbox named COMETS, which has been used by a number of groups and has helped researchers to gain insight into the electric field distribution during stimulation. The aim of this study was to develop an advanced MATLAB toolbox, named COMETS2, for the numerical analysis of the electric field generated by tDCS. COMETS2 can generate any sizes of rectangular pad electrodes on any positions on the scalp surface. To reduce the large computational burden when repeatedly testing multiple electrode locations and sizes, a new technique to decompose the global stiffness matrix was proposed. As examples of potential applications, we observed the effects of sizes and displacements of electrodes on the results of electric field analysis. The proposed mesh decomposition method significantly enhanced the overall computational efficiency. We implemented an automatic electrode modeler for the first time, and proposed a new technique to enhance the computational efficiency. In this paper, an efficient toolbox for tDCS analysis is introduced (freely available at http://www.cometstool.com). It is expected that COMETS2 will be a useful toolbox for researchers who want to benefit from the numerical analysis of electric fields generated by tDCS. Copyright © 2016. Published by Elsevier B.V.
Advances in iterative methods for nonlinear equations
Busquier, Sonia
2016-01-01
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...
Some variance reduction methods for numerical stochastic homogenization.
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).
Advanced undergraduate quantum mechanics methods and applications
Deych, Lev I
2018-01-01
This introduction to quantum mechanics is intended for undergraduate students of physics, chemistry, and engineering with some previous exposure to quantum ideas. Following in Heisenberg’s and Dirac’s footsteps, this book is centered on the concept of the quantum state as an embodiment of all experimentally available information about a system, and its representation as a vector in an abstract Hilbert space. This conceptual framework and formalism are introduced immediately, and developed throughout the first four chapters, while the standard Schrödinger equation does not appear until Chapter 5. The book grew out of lecture notes developed by the author over fifteen years of teaching at the undergraduate level. In response to numerous requests by students, material is presented with an unprecedented level of detail in both derivation of technical results and discussion of their physical significance. The book is written for students to enjoy reading it, rather than to use only as a source of formulas a...
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
Advanced repair methods for enhanced reactor safety
International Nuclear Information System (INIS)
Kornfeldt, H.
1993-01-01
A few innovative concepts are described of the ABB Atom Service Division for repair and mitigation techniques for primary systems in nuclear power plants. The concepts are based on Shape Memory Alloy (SMA) technology. A basic feature of all methods is that welding and component replacement is being avoided and the radiation dose imposed on maintenance personnel reduced. The SMA-based repair methods give plant operators new ways to meet increased safety standards and rising maintenance costs. (Z.S.) 4 figs
Advanced verification methods for OVI security ink
Coombs, Paul G.; McCaffery, Shaun F.; Markantes, Tom
2006-02-01
OVI security ink +, incorporating OVP security pigment* microflakes, enjoys a history of effective document protection. This security feature provides not only first-line recognition by the person on the street, but also facilitates machine-readability. This paper explores the evolution of OVI reader technology from proof-of-concept to miniaturization. Three different instruments have been built to advance the technology of OVI machine verification. A bench-top unit has been constructed which allows users to automatically verify a multitude of different banknotes and OVI images. In addition, high speed modules were fabricated and tested in a state of the art banknote sorting machine. Both units demonstrate the ability of modern optical components to illuminate and collect light reflected from the interference platelets within OVI ink. Electronic hardware and software convert and process the optical information in milliseconds to accurately determine the authenticity of the security feature. Most recently, OVI ink verification hardware has been miniaturized and simplified providing yet another platform for counterfeit protection. These latest devices provide a tool for store clerks and bank tellers to unambiguously determine the validity of banknotes in the time period it takes the cash drawer to be opened.
Core design methods for advanced LMFBRs
International Nuclear Information System (INIS)
Chandler, J.C.; Marr, D.R.; McCurry, D.C.; Cantley, D.A.
1977-05-01
The multidiscipline approach to advanced LMFBR core design requires an iterative design procedure to obtain a closely-coupled design. HEDL's philosophy requires that the designs should be coupled to the extent that the design limiting fuel pin, the design limiting duct and the core reactivity lifetime should all be equal and should equal the fuel residence time. The design procedure consists of an iterative loop involving three stages of the design sequence. Stage 1 consists of general mechanical design and reactor physics scoping calculations to arrive at an initial core layout. Stage 2 consists of detailed reactor physics calculations for the core configuration arrived at in Stage 1. Based upon the detailed reactor physics results, a decision is made either to alter the design (Stage 1) or go to Stage 3. Stage 3 consists of core orificing and detailed component mechanical design calculations. At this point, an assessment is made regarding design adequacy. If the design is inadequate the entire procedure is repeated until the design is acceptable
Striking against bioterrorism with advanced proteomics and reference methods.
Armengaud, Jean
2017-01-01
The intentional use by terrorists of biological toxins as weapons has been of great concern for many years. Among the numerous toxins produced by plants, animals, algae, fungi, and bacteria, ricin is one of the most scrutinized by the media because it has already been used in biocrimes and acts of bioterrorism. Improving the analytical toolbox of national authorities to monitor these potential bioweapons all at once is of the utmost interest. MS/MS allows their absolute quantitation and exhibits advantageous sensitivity, discriminative power, multiplexing possibilities, and speed. In this issue of Proteomics, Gilquin et al. (Proteomics 2017, 17, 1600357) present a robust multiplex assay to quantify a set of eight toxins in the presence of a complex food matrix. This MS/MS reference method is based on scheduled SRM and high-quality standards consisting of isotopically labeled versions of these toxins. Their results demonstrate robust reliability based on rather loose scheduling of SRM transitions and good sensitivity for the eight toxins, lower than their oral median lethal doses. In the face of an increased threat from terrorism, relevant reference assays based on advanced proteomics and high-quality companion toxin standards are reliable and firm answers. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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.
Recent advances in coupled-cluster methods
Bartlett, Rodney J
1997-01-01
Today, coupled-cluster (CC) theory has emerged as the most accurate, widely applicable approach for the correlation problem in molecules. Furthermore, the correct scaling of the energy and wavefunction with size (i.e. extensivity) recommends it for studies of polymers and crystals as well as molecules. CC methods have also paid dividends for nuclei, and for certain strongly correlated systems of interest in field theory.In order for CC methods to have achieved this distinction, it has been necessary to formulate new, theoretical approaches for the treatment of a variety of essential quantities
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.
Achieving better cooling of turbine blades using numerical simulation methods
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.
Advanced method for making vitreous waste forms
International Nuclear Information System (INIS)
Pope, J.M.; Harrison, D.E.
1980-01-01
A process is described for making waste glass that circumvents the problems of dissolving nuclear waste in molten glass at high temperatures. Because the reactive mixing process is independent of the inherent viscosity of the melt, any glass composition can be prepared with equal facility. Separation of the mixing and melting operations permits novel glass fabrication methods to be employed
Advanced Testing Method for Ground Thermal Conductivity
Energy Technology Data Exchange (ETDEWEB)
Liu, Xiaobing [ORNL; Clemenzi, Rick [Geothermal Design Center Inc.; Liu, Su [University of Tennessee (UT)
2017-04-01
A new method is developed that can quickly and more accurately determine the effective ground thermal conductivity (GTC) based on thermal response test (TRT) results. Ground thermal conductivity is an important parameter for sizing ground heat exchangers (GHEXs) used by geothermal heat pump systems. The conventional GTC test method usually requires a TRT for 48 hours with a very stable electric power supply throughout the entire test. In contrast, the new method reduces the required test time by 40%–60% or more, and it can determine GTC even with an unstable or intermittent power supply. Consequently, it can significantly reduce the cost of GTC testing and increase its use, which will enable optimal design of geothermal heat pump systems. Further, this new method provides more information about the thermal properties of the GHEX and the ground than previous techniques. It can verify the installation quality of GHEXs and has the potential, if developed, to characterize the heterogeneous thermal properties of the ground formation surrounding the GHEXs.
Theory of difference equations numerical methods and applications
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
Advance of core design method for ATR
International Nuclear Information System (INIS)
Maeda, Seiichirou; Ihara, Toshiteru; Iijima, Takashi; Seino, Hideaki; Kobayashi, Tetsurou; Takeuchi, Michio; Sugawara, Satoru; Matsumoto, Mitsuo.
1995-01-01
Core characteristics of ATR demonstration plant has been revised such as increasing the fuel burnup and the channel power, which is achieved by changing the number of fuel rod per fuel assembly from 28 to 36. The research and development concerning the core design method for ATR have been continued. The calculational errors of core analysis code have been evaluated using the operational data of FUGEN and the full scale simulated test results in DCA (Deuterium Critical Assembly) and HTL (Heat Transfer Loop) at O-arai engineering center. It is confirmed that the calculational error of power distribution is smaller than the design value of ATR demonstration plant. Critical heat flux correlation curve for 36 fuel rod cluster has been developed and the probability evaluation method based on its curve, which is more rational to evaluate the fuel dryout, has been adopted. (author)
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.
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
Advances on geometric flux optical design method
García-Botella, Ángel; Fernández-Balbuena, Antonio Álvarez; Vázquez, Daniel
2017-09-01
Nonimaging optics is focused on the study of methods to design concentrators or illuminators systems. It can be included in the area of photometry and radiometry and it is governed by the laws of geometrical optics. The field vector method, which starts with the definition of the irradiance vector E, is one of the techniques used in nonimaging optics. Called "Geometrical flux vector" it has provide ideal designs. The main property of this model is, its ability to estimate how radiant energy is transferred by the optical system, from the concepts of field line, flux tube and pseudopotential surface, overcoming traditional raytrace methods. Nevertheless this model has been developed only at an academic level, where characteristic optical parameters are ideal not real and the studied geometries are simple. The main objective of the present paper is the application of the vector field method to the analysis and design of real concentration and illumination systems. We propose the development of a calculation tool for optical simulations by vector field, using algorithms based on Fermat`s principle, as an alternative to traditional tools for optical simulations by raytrace, based on reflection and refraction law. This new tool provides, first, traditional simulations results: efficiency, illuminance/irradiance calculations, angular distribution of light- with lower computation time, photometrical information needs about a few tens of field lines, in comparison with million rays needed nowadays. On the other hand the tool will provides new information as vector field maps produced by the system, composed by field lines and quasipotential surfaces. We show our first results with the vector field simulation tool.
Improved methods for computing masses from numerical simulations
Energy Technology Data Exchange (ETDEWEB)
Kronfeld, A.S.
1989-11-22
An important advance in the computation of hadron and glueball masses has been the introduction of non-local operators. This talk summarizes the critical signal-to-noise ratio of glueball correlation functions in the continuum limit, and discusses the case of (q{bar q} and qqq) hadrons in the chiral limit. A new strategy for extracting the masses of excited states is outlined and tested. The lessons learned here suggest that gauge-fixed momentum-space operators might be a suitable choice of interpolating operators. 15 refs., 2 tabs.
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
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)
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.
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)
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
Advanced Topology Optimization Methods for Conceptual Architectural Design
DEFF Research Database (Denmark)
Aage, Niels; Amir, Oded; Clausen, Anders
2015-01-01
This paper presents a series of new, advanced topology optimization methods, developed specifically for conceptual architectural design of structures. The proposed computational procedures are implemented as components in the framework of a Grasshopper plugin, providing novel capacities...
Advanced Topology Optimization Methods for Conceptual Architectural Design
DEFF Research Database (Denmark)
Aage, Niels; Amir, Oded; Clausen, Anders
2014-01-01
This paper presents a series of new, advanced topology optimization methods, developed specifically for conceptual architectural design of structures. The proposed computational procedures are implemented as components in the framework of a Grasshopper plugin, providing novel capacities...
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
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
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
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....
Energy Technology Data Exchange (ETDEWEB)
Seignole, V
2005-07-01
This report presents the work of thesis realized under the direction of Jean-Michel Ghidaglia (thesis director, ENS-Cachan) and of Anela Kumbaro (tutor, CEA) within the framework of the modeling of two-phase flows with OAP code. The report consists of two parts of unequal size: the first part concentrates on aspects related exclusively to two-phase flows, while the second one is devoted to the study of a numerical problem inherent to the resolution of two-phase flow systems, but whose action has a broader framework. (author)
Energy Technology Data Exchange (ETDEWEB)
Seignole, V
2005-07-01
This report presents the work of thesis realized under the direction of Jean-Michel Ghidaglia (thesis director, ENS-Cachan) and of Anela Kumbaro (tutor, CEA) within the framework of the modeling of two-phase flows with OAP code. The report consists of two parts of unequal size: the first part concentrates on aspects related exclusively to two-phase flows, while the second one is devoted to the study of a numerical problem inherent to the resolution of two-phase flow systems, but whose action has a broader framework. (author)
Polarization control method for UV writing of advanced bragg gratings
DEFF Research Database (Denmark)
Deyerl, Hans-Jürgen; Plougmann, Nikolai; Jensen, Jesper Bo Damm
2002-01-01
We report the application of the polarization control method for the UV writing of advanced fiber Bragg gratings (FBG). We demonstrate the strength of the new method for different apodization profiles, including the Sinc-profile and two designs for dispersion-free square filters. The method has...
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)
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)
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.
Numerical methods in image processing for applications in jewellery industry
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 ...
A Numerical Matrix-Based method in Harmonic Studies in Wind Power Plants
DEFF Research Database (Denmark)
Dowlatabadi, Mohammadkazem Bakhshizadeh; Hjerrild, Jesper; Kocewiak, Łukasz Hubert
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...
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.)
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.)
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.
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.
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.)
Assessment of Soil Liquefaction Potential Based on Numerical Method
DEFF Research Database (Denmark)
Choobasti, A. Janalizadeh; Vahdatirad, Mohammad Javad; Torabi, M.
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...
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
Hybrid Particle-Continuum Numerical Methods for Aerospace Applications
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
Fast Numerical Methods for Stochastic Partial Differential Equations
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
Deformation of two-phase aggregates using standard numerical methods
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.
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.
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.
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.
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....
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.
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)
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....
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.
Energy Technology Data Exchange (ETDEWEB)
Doessing, M.
2011-05-15
During the last decades the annual energy produced by wind turbines has increased dramatically and wind turbines are now available in the 5MW range. Turbines in this range are constantly being developed and it is also being investigated whether turbines as large as 10-20MW are feasible. The design of very large machines introduces new problems in the practical design, and optimization tools are necessary. These must combine the dynamic effects of both aerodynamics and structure in an integrated optimization environment. This is referred to as aeroelastic optimization. The Risoe DTU optimization software HAWTOPT has been used in this project. The quasi-steady aerodynamic module have been improved with a corrected blade element momentum method. A structure module has also been developed which lays out the blade structural properties. This is done in a simplified way allowing fast conceptual design studies and with focus on the overall properties relevant for the aeroelastic properties. Aeroelastic simulations in the time domain were carried out using the aeroelastic code HAWC2. With these modules coupled to HAWTOPT, optimizations have been made. In parallel with the developments of the mentioned numerical modules, focus has been on analysis and a fundamental understanding of the key parameters in wind turbine design. This has resulted in insight and an effective design methodology is presented. Using the optimization environment a 5MW wind turbine rotor has been optimized for reduced fatigue loads due to apwise bending moments. Among other things this has indicated that airfoils for wind turbine blades should have a high lift coefficient. The design methodology proved to be stable and a help in the otherwise challenging task of numerical aeroelastic optimization. (Author)
Method of independent timesteps in the numerical solution of initial value problems
International Nuclear Information System (INIS)
Porter, A.P.
1976-01-01
In the numerical solution of initial-value problems in several independent variables, the timestep is controlled, especially in the presence of shocks, by a small portion of the logical mesh, what one may call the crisis zone. One is frustrated by the necessity of doing in the whole mesh frequent calculations required by only a small part of the mesh. It is shown that it is possible to choose different timesteps natural to different parts of the mesh and to advance each zone in time only as often as is appropriate to that zone's own natural timestep. Prior work is reviewed and for the first time an investigation of the conditions for well-posedness, consistency and stability in independent timesteps is presented; a new method results. The prochronic and parachronic Cauchy surfaces are identified; and the reasons (well-posedness) for constraining the Cauchy surfaces to be prochronic (as distinct from the method of Grandey), that is, to lie prior to the time of the crisis zone (the zone of least timestep), are indicated. Stability (in the maximum norm) of parabolic equations and (in the L2 norm) of hyperbolic equations is reviewed, without restricting the treatment to linear equations or constant coefficients, and stability of the new method is proven in this framework. The details of the method of independent timesteps, the rules for choosing timesteps and for deciding when to update and when to skip zones, and the method of joining adjacent regions of differing timestep are described. The stability of independent timestep difference schemes is analyzed and exhibited. The economic advantages of the method, which often amount to an order-of-magnitude decrease in running time relative to conventional or implicit difference methods, are noted
Method of independent timesteps in the numerical solution of initial value problems
Energy Technology Data Exchange (ETDEWEB)
Porter, A.P.
1976-07-21
In the numerical solution of initial-value problems in several independent variables, the timestep is controlled, especially in the presence of shocks, by a small portion of the logical mesh, what one may call the crisis zone. One is frustrated by the necessity of doing in the whole mesh frequent calculations required by only a small part of the mesh. It is shown that it is possible to choose different timesteps natural to different parts of the mesh and to advance each zone in time only as often as is appropriate to that zone's own natural timestep. Prior work is reviewed and for the first time an investigation of the conditions for well-posedness, consistency and stability in independent timesteps is presented; a new method results. The prochronic and parachronic Cauchy surfaces are identified; and the reasons (well-posedness) for constraining the Cauchy surfaces to be prochronic (as distinct from the method of Grandey), that is, to lie prior to the time of the crisis zone (the zone of least timestep), are indicated. Stability (in the maximum norm) of parabolic equations and (in the L2 norm) of hyperbolic equations is reviewed, without restricting the treatment to linear equations or constant coefficients, and stability of the new method is proven in this framework. The details of the method of independent timesteps, the rules for choosing timesteps and for deciding when to update and when to skip zones, and the method of joining adjacent regions of differing timestep are described. The stability of independent timestep difference schemes is analyzed and exhibited. The economic advantages of the method, which often amount to an order-of-magnitude decrease in running time relative to conventional or implicit difference methods, are noted.
Numerical integration methods and layout improvements in the context of dynamic RNA visualization.
Shabash, Boris; Wiese, Kay C
2017-05-30
RNA visualization software tools have traditionally presented a static visualization of RNA molecules with limited ability for users to interact with the resulting image once it is complete. Only a few tools allowed for dynamic structures. One such tool is jViz.RNA. Currently, jViz.RNA employs a unique method for the creation of the RNA molecule layout by mapping the RNA nucleotides into vertexes in a graph, which we call the detailed graph, and then utilizes a Newtonian mechanics inspired system of forces to calculate a layout for the RNA molecule. The work presented here focuses on improvements to jViz.RNA that allow the drawing of RNA secondary structures according to common drawing conventions, as well as dramatic run-time performance improvements. This is done first by presenting an alternative method for mapping the RNA molecule into a graph, which we call the compressed graph, and then employing advanced numerical integration methods for the compressed graph representation. Comparing the compressed graph and detailed graph implementations, we find that the compressed graph produces results more consistent with RNA drawing conventions. However, we also find that employing the compressed graph method requires a more sophisticated initial layout to produce visualizations that would require minimal user interference. Comparing the two numerical integration methods demonstrates the higher stability of the Backward Euler method, and its resulting ability to handle much larger time steps, a high priority feature for any software which entails user interaction. The work in this manuscript presents the preferred use of compressed graphs to detailed ones, as well as the advantages of employing the Backward Euler method over the Forward Euler method. These improvements produce more stable as well as visually aesthetic representations of the RNA secondary structures. The results presented demonstrate that both the compressed graph representation, as well as the Backward
Advanced methods of solid oxide fuel cell modeling
Milewski, Jaroslaw; Santarelli, Massimo; Leone, Pierluigi
2011-01-01
Fuel cells are widely regarded as the future of the power and transportation industries. Intensive research in this area now requires new methods of fuel cell operation modeling and cell design. Typical mathematical models are based on the physical process description of fuel cells and require a detailed knowledge of the microscopic properties that govern both chemical and electrochemical reactions. ""Advanced Methods of Solid Oxide Fuel Cell Modeling"" proposes the alternative methodology of generalized artificial neural networks (ANN) solid oxide fuel cell (SOFC) modeling. ""Advanced Methods
Efficient Numerical Methods for Nonequilibrium Re-Entry Flows
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
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....
Strategy to Promote Active Learning of an Advanced Research Method
McDermott, Hilary J.; Dovey, Terence M.
2013-01-01
Research methods courses aim to equip students with the knowledge and skills required for research yet seldom include practical aspects of assessment. This reflective practitioner report describes and evaluates an innovative approach to teaching and assessing advanced qualitative research methods to final-year psychology undergraduate students. An…
Numerical method for IR background and clutter simulation
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.
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)
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)
Numerical methods in finance and economics a MATLAB-based introduction
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...
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.
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
Advanced Corrections for InSAR Using GPS and Numerical Weather Models
Cossu, F.; Foster, J. H.; Amelung, F.; Varugu, B. K.; Businger, S.; Cherubini, T.
2017-12-01
We present results from an investigation into the application of numerical weather models for generating tropospheric correction fields for Interferometric Synthetic Aperture Radar (InSAR). We apply the technique to data acquired from a UAVSAR campaign as well as from the CosmoSkyMed satellites. The complex spatial and temporal changes in the atmospheric propagation delay of the radar signal remain the single biggest factor limiting InSAR's potential for hazard monitoring and mitigation. A new generation of InSAR systems is being built and launched, and optimizing the science and hazard applications of these systems requires advanced methodologies to mitigate tropospheric noise. We use the Weather Research and Forecasting (WRF) model to generate a 900 m spatial resolution atmospheric models covering the Big Island of Hawaii and an even higher, 300 m resolution grid over the Mauna Loa and Kilauea volcanoes. By comparing a range of approaches, from the simplest, using reanalyses based on typically available meteorological observations, through to the "kitchen-sink" approach of assimilating all relevant data sets into our custom analyses, we examine the impact of the additional data sets on the atmospheric models and their effectiveness in correcting InSAR data. We focus particularly on the assimilation of information from the more than 60 GPS sites in the island. We ingest zenith tropospheric delay estimates from these sites directly into the WRF analyses, and also perform double-difference tomography using the phase residuals from the GPS processing to robustly incorporate heterogeneous information from the GPS data into the atmospheric models. We assess our performance through comparisons of our atmospheric models with external observations not ingested into the model, and through the effectiveness of the derived phase screens in reducing InSAR variance. Comparison of the InSAR data, our atmospheric analyses, and assessments of the active local and mesoscale
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
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.
Continuum-Kinetic Models and Numerical Methods for Multiphase Applications
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.
Study on pipe deflection by using numerical method
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.
A conservative finite difference method for the numerical solution of plasma fluid equations
International Nuclear Information System (INIS)
Colella, P.; Dorr, M.R.; Wake, D.D.
1999-01-01
This paper describes a numerical method for the solution of a system of plasma fluid equations. The fluid model is similar to those employed in the simulation of high-density, low-pressure plasmas used in semiconductor processing. The governing equations consist of a drift-diffusion model of the electrons, together with an internal energy equation, coupled via Poisson's equation to a system of Euler equations for each ion species augmented with electrostatic force, collisional, and source/sink terms. The time integration of the full system is performed using an operator splitting that conserves space charge and avoids dielectric relaxation timestep restrictions. The integration of the individual ion species and electrons within the time-split advancement is achieved using a second-order Godunov discretization of the hyperbolic terms, modified to account for the significant role of the electric field in the propagation of acoustic waves, combined with a backward Euler discretization of the parabolic terms. Discrete boundary conditions are employed to accommodate the plasma sheath boundary layer on underresolved grids. The algorithm is described for the case of a single Cartesian grid as the first step toward an implementation on a locally refined grid hierarchy in which the method presented here may be applied on each refinement level
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
Methods for studying fuel management in advanced gas cooled reactors
International Nuclear Information System (INIS)
Buckler, A.N.; Griggs, C.F.; Tyror, J.G.
1971-07-01
The methods used for studying fuel and absorber management problems in AGRs are described. The basis of the method is the use of ARGOSY lattice data in reactor calculations performed at successive time steps. These reactor calculations may be quite crude but for advanced design calculations a detailed channel-by-channel representation of the whole core is required. The main emphasis of the paper is in describing such an advanced approach - the ODYSSEUS-6 code. This code evaluates reactor power distributions as a function of time and uses the information to select refuelling moves and determine controller positions. (author)
Sotiropoulos, F.; Kang, S.; Chamorro, L. P.; Hill, C.
2011-12-01
The field of MHK energy is still in its infancy lagging approximately a decade or more behind the technology and development progress made in wind energy engineering. Marine environments are characterized by complex topography and three-dimensional (3D) turbulent flows, which can greatly affect the performance and structural integrity of MHK devices and impact the Levelized Cost of Energy (LCoE). Since the deployment of multi-turbine arrays is envisioned for field applications, turbine-to-turbine interactions and turbine-bathymetry interactions need to be understood and properly modeled so that MHK arrays can be optimized on a site specific basis. Furthermore, turbulence induced by MHK turbines alters and interacts with the nearby ecosystem and could potentially impact aquatic habitats. Increased turbulence in the wake of MHK devices can also change the shear stress imposed on the bed ultimately affecting the sediment transport and suspension processes in the wake of these structures. Such effects, however, remain today largely unexplored. In this work a science-based approach integrating state-of-the-art experimentation with high-resolution computational fluid dynamics is proposed as a powerful strategy for optimizing the performance of MHK devices and assessing environmental impacts. A novel numerical framework is developed for carrying out Large-Eddy Simulation (LES) in arbitrarily complex domains with embedded MHK devices. The model is able to resolve the geometrical complexity of real-life MHK devices using the Curvilinear Immersed Boundary (CURVIB) method along with a wall model for handling the flow near solid surfaces. Calculations are carried out for an axial flow hydrokinetic turbine mounted on the bed of rectangular open channel on a grid with nearly 200 million grid nodes. The approach flow corresponds to fully developed turbulent open channel flow and is obtained from a separate LES calculation. The specific case corresponds to that studied
Advances in computational methods for Quantum Field Theory calculations
Ruijl, B.J.G.
2017-01-01
In this work we describe three methods to improve the performance of Quantum Field Theory calculations. First, we simplify large expressions to speed up numerical integrations. Second, we design Forcer, a program for the reduction of four-loop massless propagator integrals. Third, we extend the R*
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
Advanced Semi-Implicit Method (ASIM) for hyperbolic two-fluid model
International Nuclear Information System (INIS)
Lee, Sung Jae; Chung, Moon Sun
2003-01-01
Introducing the interfacial pressure jump terms based on the surface tension into the momentum equations of two-phase two-fluid model, the system of governing equations is turned mathematically into the hyperbolic system. The eigenvalues of the equation system become always real representing the void wave and the pressure wave propagation speeds as shown in the previous manuscript. To solve the interfacial pressure jump terms with void fraction gradients implicitly, the conventional semi-implicit method should be modified as an intermediate iteration method for void fraction at fractional time step. This Advanced Semi-Implicit Method (ASIM) then becomes stable without conventional additive terms. As a consequence, including the interfacial pressure jump terms with the advanced semi-implicit method, the numerical solutions of typical two-phase problems can be more stable and sound than those calculated exclusively by using any other terms like virtual mass, or artificial viscosity
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
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.
International Nuclear Information System (INIS)
Shimooka, Hiroshi
1982-01-01
The disposal of high-level radioactive waste should result in temperature rises and thermal stresses which change the hydraulic conductivity of the rock around the repository. For safety analysis on disposal of high-level radioactive waste into hard rock, it is necessary to find the temperature rises and thermal stresses distributions around the repository. In this paper, these distribution changes are analyzed by the use of the finite difference method. In advance of numerical analysis, it is required to simplify the shapes and properties of the repository and the rock. Several kinds of numerical models are prepared, and the results of this analysis are examined. And, the waste disposal methods are discussed from the stand-points of the temperature rise and thermal stress analysis. (author)
Teaching numerical methods with IPython notebooks and inquiry-based learning
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.
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.
Numerical simulation and performance investigation of an advanced adsorption desalination cycle
Thu, Kyaw
2013-01-01
Low temperature waste heat-driven adsorption desalination (AD) cycles offer high potential as one of the most economically viable and environmental-friendly desalination methods. This article presents the development of an advanced adsorption desalination cycle that employs internal heat recovery between the evaporator and the condenser, utilizing an encapsulated evaporator-condenser unit for effective heat transfer. A simulation model has been developed based on the actual sorption characteristics of the adsorbent-adsorbate pair, energy and mass balances applied to the components of the AD cycle. With an integrated design, the temperature in the evaporator and the vapor pressurization of the adsorber are raised due to the direct heat recovery from the condenser, resulting in the higher water production rates, typically improved by as much as three folds of the conventional AD cycle. In addition, the integrated design eliminates two pumps, namely, the condenser cooling water and the chilled water pumps, lowering the overall electricity consumption. The performance of the cycle is analyzed at assorted heat source and cooling water temperatures, and different cycle times as well as the transient heat transfer coefficients of the evaporation and condensation. © 2012 Elsevier B.V.
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...
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.
Numerical Simulation of Partially-Coherent Broadband Optical Imaging Using the FDTD Method
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
Advanced Numerical Integration Techniques for HighFidelity SDE Spacecraft Simulation
National Aeronautics and Space Administration — Classic numerical integration techniques, such as the ones at the heart of several NASA GSFC analysis tools, are known to work well for deterministic differential...
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
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.
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.
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...
Method and Tools for Development of Advanced Instructional Systems
Arend, J. van der; Riemersma, J.B.J.
1994-01-01
The application of advanced instructional systems (AISs), like computer-based training systems, intelligent tutoring systems and training simulators, is widely spread within the Royal Netherlands Army. As a consequence there is a growing interest in methods and tools to develop effective and
METHODS ADVANCEMENT FOR MILK ANALYSIS: THE MAMA STUDY
The Methods Advancement for Milk Analysis (MAMA) study was designed by US EPA and CDC investigators to provide data to support the technological and study design needs of the proposed National Children=s Study (NCS). The NCS is a multi-Agency-sponsored study, authorized under the...
Advances in the Analytical Methods for Determining the Antioxidant ...
African Journals Online (AJOL)
Advances in the Analytical Methods for Determining the Antioxidant Properties of Honey: A Review. M Moniruzzaman, MI Khalil, SA Sulaiman, SH Gan. Abstract. Free radicals and reactive oxygen species (ROS) have been implicated in contributing to the processes of aging and disease. In an effort to combat free radical ...
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
On nitrogen condensation in hypersonic nozzle flows: Numerical method and parametric study
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
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.)
Advanced Measuring (Instrumentation Methods for Nuclear Installations: A Review
Directory of Open Access Journals (Sweden)
Wang Qiu-kuan
2012-01-01
Full Text Available The nuclear technology has been widely used in the world. The research of measurement in nuclear installations involves many aspects, such as nuclear reactors, nuclear fuel cycle, safety and security, nuclear accident, after action, analysis, and environmental applications. In last decades, many advanced measuring devices and techniques have been widely applied in nuclear installations. This paper mainly introduces the development of the measuring (instrumentation methods for nuclear installations and the applications of these instruments and methods.
Second order numerical method of two-fluid model of air-water flow
International Nuclear Information System (INIS)
Tiselj, I.; Petelin, S.
1995-01-01
Model considered in this paper is six-equation two-fluid model used in computer code RELAP5. Air-water equations were taken in a code named PDE to avoid additional problems caused by condensation or vaporization. Terms with space derivatives were added in virtual mass term in momentum equations to ensure the hyperbolicity of the equations. Numerical method in PDE code is based on approximate Riemann solvers. Equations are solved on non-staggered grid with explicit time advancement and with upwind discretization of the convective terms in characteristic form of the equations. Flux limiters are used to find suitable combinations of the first (upwind) and the second order (Lax-Wendroff) discretization s which ensure second order accuracy on smooth solutions and damp oscillations around the discontinuities. Because of the small time steps required and because of its non-dissipative nature the scheme is suitable for the prediction of the fast transients: pressure waves, shock and rarefaction waves, water hammer or critical flow. Some preliminary results are presented for a shock tube problem and for Water Faucet problem - problems usually used as benchmarks for two-fluid computer codes. (author)
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.
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.
Geothermal-Related Thermo-Elastic Fracture Analysis by Numerical Manifold Method
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 ...
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.
Higher geometry an introduction to advanced methods in analytic geometry
Woods, Frederick S
2005-01-01
For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study
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
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.)
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.
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
Balancing of linkages and robot manipulators advanced methods with illustrative examples
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.
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.
Advanced non-destructive methods for an efficient service performance
International Nuclear Information System (INIS)
Rauschenbach, H.; Clossen-von Lanken Schulz, M.; Oberlin, R.
2015-01-01
Due to the power generation industry's desire to decrease outage time and extend inspection intervals for highly stressed turbine parts, advanced and reliable Non-destructive methods were developed by Siemens Non-destructive laboratory. Effective outage performance requires the optimized planning of all outage activities as well as modern Non-destructive examination methods, in order to examine the highly stressed components (turbine rotor, casings, valves, generator rotor) reliably and in short periods of access. This paper describes the experience of Siemens Energy with an ultrasonic Phased Array inspection technique for the inspection of radial entry pinned turbine blade roots. The developed inspection technique allows the ultrasonic inspection of steam turbine blades without blade removal. Furthermore advanced Non-destructive examination methods for joint bolts will be described, which offer a significant reduction of outage duration in comparison to conventional inspection techniques. (authors)
Advanced airflow distribution methods for reducing exposure of indoor pollution
DEFF Research Database (Denmark)
Cao, Guangyu; Nielsen, Peter Vilhelm; Melikov, Arsen
2017-01-01
The adverse effect of various indoor pollutants on occupants’ health have been recognized. In public spaces flu viruses may spread from person to person by airflow generated by various traditional ventilation methods, like natural ventilation and mixing ventilation (MV Personalized ventilation (PV......) supplies clean air close to the occupant and directly into the breathing zone. Studies show that it improves the inhaled air quality and reduces the risk of airborne cross-infection in comparison with total volume (TV) ventilation. However, it is still challenging for PV and other advanced air distribution...... methods to reduce the exposure to gaseous and particulate pollutants under disturbed conditions and to ensure thermal comfort at the same time. The objective of this study is to analyse the performance of different advanced airflow distribution methods for protection of occupants from exposure to indoor...
Advanced airflow distribution methods for reducing exposure of indoor pollution
DEFF Research Database (Denmark)
Cao, Guangyu; Nielsen, Peter Vilhelm; Melikov, Arsen Krikor
methods to reduce the exposure to gaseous and particulate pollutants under disturbed conditions and to ensure thermal comfort at the same time. The objective of this study is to analyse the performance of different advanced airflow distribution methods for protection of occupants from exposure to indoor......The adverse effect of various indoor pollutants on occupants’ health have been recognized. In public spaces flu viruses may spread from person to person by airflow generated by various traditional ventilation methods, like natural ventilation and mixing ventilation (MV Personalized ventilation (PV......) supplies clean air close to the occupant and directly into the breathing zone. Studies show that it improves the inhaled air quality and reduces the risk of airborne cross-infection in comparison with total volume (TV) ventilation. However, it is still challenging for PV and other advanced air distribution...
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)
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
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.
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
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
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)
International Nuclear Information System (INIS)
Marxen, Olaf; Magin, Thierry E.; Shaqfeh, Eric S.G.; Iaccarino, Gianluca
2013-01-01
A new numerical method is presented here that allows to consider chemically reacting gases during the direct numerical simulation of a hypersonic fluid flow. The method comprises the direct coupling of a solver for the fluid mechanical model and a library providing the physio-chemical model. The numerical method for the fluid mechanical model integrates the compressible Navier–Stokes equations using an explicit time advancement scheme and high-order finite differences. This Navier–Stokes code can be applied to the investigation of laminar-turbulent transition and boundary-layer instability. The numerical method for the physio-chemical model provides thermodynamic and transport properties for different gases as well as chemical production rates, while here we exclusively consider a five species air mixture. The new method is verified for a number of test cases at Mach 10, including the one-dimensional high-temperature flow downstream of a normal shock, a hypersonic chemical reacting boundary layer in local thermodynamic equilibrium and a hypersonic reacting boundary layer with finite-rate chemistry. We are able to confirm that the diffusion flux plays an important role for a high-temperature boundary layer in local thermodynamic equilibrium. Moreover, we demonstrate that the flow for a case previously considered as a benchmark for the investigation of non-equilibrium chemistry can be regarded as frozen. Finally, the new method is applied to investigate the effect of finite-rate chemistry on boundary layer instability by considering the downstream evolution of a small-amplitude wave and comparing results with those obtained for a frozen gas as well as a gas in local thermodynamic equilibrium
CNC Turning Center Advanced Operations. Computer Numerical Control Operator/Programmer. 444-332.
Skowronski, Steven D.; Tatum, Kenneth
This student guide provides materials for a course designed to introduce the student to the operations and functions of a two-axis computer numerical control (CNC) turning center. The course consists of seven units. Unit 1 presents course expectations and syllabus, covers safety precautions, and describes the CNC turning center components, CNC…
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
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
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.
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.
Advanced Markov chain Monte Carlo methods learning from past samples
Liang, Faming; Carrol, Raymond J
2010-01-01
This book provides comprehensive coverage of simulation of complex systems using Monte Carlo methods. Developing algorithms that are immune to the local trap problem has long been considered as the most important topic in MCMC research. Various advanced MCMC algorithms which address this problem have been developed include, the modified Gibbs sampler, the methods based on auxiliary variables and the methods making use of past samples. The focus of this book is on the algorithms that make use of past samples. This book includes the multicanonical algorithm, dynamic weighting, dynamically weight
Numerical simulation of single bubbles rising through subchannels with interface tracking method
International Nuclear Information System (INIS)
Hiroyuki Yoshida; Takuji Nagayoshi; Hidesada Tamai; Tazuyuki Takase; Hajime Akimoto
2005-01-01
Full text of publication follows: Although the sub-channel codes are used for the thermal-hydraulic analysis of fuel bundles in nuclear reactors from the former, many compositions and empirical equations based on experimental results are needed to predict the two-phase flow behavior in details. When there are no experimental data such as the reduced-moderation light water reactor (RMWR) which is studied by the Japan Atomic Energy Research Institute (JAERI), therefore, it is very difficult to obtain highly precise predictions. The RMWR core has remarkably narrow gap spacing between fuel rods (i.e., around 1 mm) which are arranged at a triangular tight-lattice configuration. To evaluate the feasibility and to optimize the thermal design of the RMWR core, a full-scale bundle test is required. However, several systematic full-scale tests are difficult to perform during an initial design phase from economic and temporal reason. Thus, we made a plan to develop a mechanistic BT model to evaluate the effects of the geometry configuration by a two-phase flow numerical simulation. In the plan of the mechanistic BT model development, three dimensional two-phase flow simulation codes with the interface tracking method, the moving particle semi-implicit method and the advanced two-fluid model are developed. In this study, as a part of this model development, detailed two-phase flow simulation code using interface tracking method (named TPFIT) is developed. In this paper, the results of TPFIT code with the advanced interface tracking method applied to single bubbles behavior through subchannels) to verify TPFIT code performance in complicated flow channel as rod bundles. In the simulation, the flow channel is composed of a square duct and four tubes with outside diameters D = 12 mm. The width and height of the duct are 27.2 mm and 192 mm, respectively. In the flow channel, the tubes are used to simulate fuel rods. One center subchannel and four periphery subchannels exist in the
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.
Numerical simulation of compressible two-phase flow using a diffuse interface method
International Nuclear Information System (INIS)
Ansari, M.R.; Daramizadeh, A.
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
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)
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.
Numerical simulation of interface movement in gas-liquid two-phase flows with Level Set method
International Nuclear Information System (INIS)
Li Huixiong; Chinese Academy of Sciences, Beijing; Deng Sheng; Chen Tingkuan; Zhao Jianfu; Wang Fei
2005-01-01
Numerical simulation of gas-liquid two-phase flow and heat transfer has been an attractive work for a quite long time, but still remains as a knotty difficulty due to the inherent complexities of the gas-liquid two-phase flow resulted from the existence of moving interfaces with topology changes. This paper reports the effort and the latest advances that have been made by the authors, with special emphasis on the methods for computing solutions to the advection equation of the Level set function, which is utilized to capture the moving interfaces in gas-liquid two-phase flows. Three different schemes, i.e. the simple finite difference scheme, the Superbee-TVD scheme and the 5-order WENO scheme in combination with the Runge-Kutta method are respectively applied to solve the advection equation of the Level Set. A numerical procedure based on the well-verified SIMPLER method is employed to numerically calculate the momentum equations of the two-phase flow. The above-mentioned three schemes are employed to simulate the movement of four typical interfaces under 5 typical flowing conditions. Analysis of the numerical results shows that the 5-order WENO scheme and the Superbee-TVD scheme are much better than the simple finite difference scheme, and the 5-order WENO scheme is the best to compute solutions to the advection equation of the Level Set. The 5-order WENO scheme will be employed as the main scheme to get solutions to the advection equations of the Level Set when gas-liquid two-phase flows are numerically studied in the future. (authors)
Kettle, L. M.; Mora, P.; Weatherley, D.; Gross, L.; Xing, H.
2006-12-01
Simulations using the Finite Element method are widely used in many engineering applications and for the solution of partial differential equations (PDEs). Computational models based on the solution of PDEs play a key role in earth systems simulations. We present numerical modelling of crustal fault systems where the dynamic elastic wave equation is solved using the Finite Element method. This is achieved using a high level computational modelling language, escript, available as open source software from ACcESS (Australian Computational Earth Systems Simulator), the University of Queensland. Escript is an advanced geophysical simulation software package developed at ACcESS which includes parallel equation solvers, data visualisation and data analysis software. The escript library was implemented to develop a flexible Finite Element model which reliably simulates the mechanism of faulting and the physics of earthquakes. Both 2D and 3D elastodynamic models are being developed to study the dynamics of crustal fault systems. Our final goal is to build a flexible model which can be applied to any fault system with user-defined geometry and input parameters. To study the physics of earthquake processes, two different time scales must be modelled, firstly the quasi-static loading phase which gradually increases stress in the system (~100years), and secondly the dynamic rupture process which rapidly redistributes stress in the system (~100secs). We will discuss the solution of the time-dependent elastic wave equation for an arbitrary fault system using escript. This involves prescribing the correct initial stress distribution in the system to simulate the quasi-static loading of faults to failure; determining a suitable frictional constitutive law which accurately reproduces the dynamics of the stick/slip instability at the faults; and using a robust time integration scheme. These dynamic models generate data and information that can be used for earthquake forecasting.
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.
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
New or improved computational methods and advanced reactor design
International Nuclear Information System (INIS)
Nakagawa, Masayuki; Takeda, Toshikazu; Ushio, Tadashi
1997-01-01
Nuclear computational method has been studied continuously up to date, as a fundamental technology supporting the nuclear development. At present, research on computational method according to new theory and the calculating method thought to be difficult to practise are also continued actively to find new development due to splendid improvement of features of computer. In Japan, many light water type reactors are now in operations, new computational methods are induced for nuclear design, and a lot of efforts are concentrated for intending to more improvement of economics and safety. In this paper, some new research results on the nuclear computational methods and their application to nuclear design of the reactor were described for introducing recent trend of the nuclear design of the reactor. 1) Advancement of the computational method, 2) Reactor core design and management of the light water reactor, and 3) Nuclear design of the fast reactor. (G.K.)
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.
Advanced symbolic analysis for VLSI systems methods and applications
Shi, Guoyong; Tlelo Cuautle, Esteban
2014-01-01
This book provides comprehensive coverage of the recent advances in symbolic analysis techniques for design automation of nanometer VLSI systems. The presentation is organized in parts of fundamentals, basic implementation methods and applications for VLSI design. Topics emphasized include statistical timing and crosstalk analysis, statistical and parallel analysis, performance bound analysis and behavioral modeling for analog integrated circuits . Among the recent advances, the Binary Decision Diagram (BDD) based approaches are studied in depth. The BDD-based hierarchical symbolic analysis approaches, have essentially broken the analog circuit size barrier. In particular, this book • Provides an overview of classical symbolic analysis methods and a comprehensive presentation on the modern BDD-based symbolic analysis techniques; • Describes detailed implementation strategies for BDD-based algorithms, including the principles of zero-suppression, variable ordering and canonical reduction; • Int...
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.
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.
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.
NUMERICAL MODELLING OF THE SOIL BEHAVIOUR BY USING NEWLY DEVELOPED ADVANCED MATERIAL MODEL
Directory of Open Access Journals (Sweden)
Jan Veselý
2017-02-01
Full Text Available This paper describes a theoretical background, implementation and validation of the newly developed Jardine plastic hardening-softening model (JPHS model, which can be used for numerical modelling of the soils behaviour. Although the JPHS model is based on the elasto-plastic theory, like the Mohr-Coulomb model that is widely used in geotechnics, it contains some improvements, which removes the main disadvantages of the MC model. The presented model is coupled with an isotopically hardening and softening law, non-linear elastic stress-strain law, non-associated elasto-plastic material description and a cap yield surface. The validation of the model is done by comparing the numerical results with real measured data from the laboratory tests and by testing of the model on the real project of the tunnel excavation. The 3D numerical analysis is performed and the comparison between the JPHS, Mohr-Coulomb, Modified Cam-Clay, Hardening small strain model and monitoring in-situ data is done.
Numerical comparison of robustness of some reduction methods in rough grids
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.
Advanced soft computing diagnosis method for tumour grading.
Papageorgiou, E I; Spyridonos, P P; Stylios, C D; Ravazoula, P; Groumpos, P P; Nikiforidis, G N
2006-01-01
To develop an advanced diagnostic method for urinary bladder tumour grading. A novel soft computing modelling methodology based on the augmentation of fuzzy cognitive maps (FCMs) with the unsupervised active Hebbian learning (AHL) algorithm is applied. One hundred and twenty-eight cases of urinary bladder cancer were retrieved from the archives of the Department of Histopathology, University Hospital of Patras, Greece. All tumours had been characterized according to the classical World Health Organization (WHO) grading system. To design the FCM model for tumour grading, three experts histopathologists defined the main histopathological features (concepts) and their impact on grade characterization. The resulted FCM model consisted of nine concepts. Eight concepts represented the main histopathological features for tumour grading. The ninth concept represented the tumour grade. To increase the classification ability of the FCM model, the AHL algorithm was applied to adjust the weights of the FCM. The proposed FCM grading model achieved a classification accuracy of 72.5%, 74.42% and 95.55% for tumours of grades I, II and III, respectively. An advanced computerized method to support tumour grade diagnosis decision was proposed and developed. The novelty of the method is based on employing the soft computing method of FCMs to represent specialized knowledge on histopathology and on augmenting FCMs ability using an unsupervised learning algorithm, the AHL. The proposed method performs with reasonably high accuracy compared to other existing methods and at the same time meets the physicians' requirements for transparency and explicability.
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)
Hajipour, Mojtaba; Jajarmi, Amin
2018-02-01
Using the Pontryagin's maximum principle for a time-delayed optimal control problem results in a system of coupled two-point boundary-value problems (BVPs) involving both time-advance and time-delay arguments. The analytical solution of this advance-delay two-point BVP is extremely difficult, if not impossible. This paper provides a discrete general form of the numerical solution for the derived advance-delay system by applying a finite difference θ-method. This method is also implemented for the infinite-time horizon time-delayed optimal control problems by using a piecewise version of the θ-method. A matrix formulation and the error analysis of the suggested technique are provided. The new scheme is accurate, fast and very effective for the optimal control of linear and nonlinear time-delay systems. Various types of finite- and infinite-time horizon problems are included to demonstrate the accuracy, validity and applicability of the new technique.
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.
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
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.
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.)
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)
Solutions manual to accompany An introduction to numerical methods and analysis
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
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
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
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...
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...
Digital spectral analysis parametric, non-parametric and advanced methods
Castanié, Francis
2013-01-01
Digital Spectral Analysis provides a single source that offers complete coverage of the spectral analysis domain. This self-contained work includes details on advanced topics that are usually presented in scattered sources throughout the literature.The theoretical principles necessary for the understanding of spectral analysis are discussed in the first four chapters: fundamentals, digital signal processing, estimation in spectral analysis, and time-series models.An entire chapter is devoted to the non-parametric methods most widely used in industry.High resolution methods a
Advanced method of double contrast examination of the stomach
International Nuclear Information System (INIS)
Vlasov, P.V.; Yakimenko, V.F.
1981-01-01
An advanced method of double contrast examination of the stomach with the use of high concentrated barium suspension is described. It is shown that concentration of barium suspension must be not less than 200 mass/volume per cent to obtain the sharp image of the mucosal microrelief 6 standard position are recommended for the double contrast examination of all stomach walls. 200 patients with different digestive system diseases are examined with the help of developed methods. The sharp image of the mucosal microrelief is obtained in 70% cases [ru
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)
Advances in Statistical Methods for Substance Abuse Prevention Research
MacKinnon, David P.; Lockwood, Chondra M.
2010-01-01
The paper describes advances in statistical methods for prevention research with a particular focus on substance abuse prevention. Standard analysis methods are extended to the typical research designs and characteristics of the data collected in prevention research. Prevention research often includes longitudinal measurement, clustering of data in units such as schools or clinics, missing data, and categorical as well as continuous outcome variables. Statistical methods to handle these features of prevention data are outlined. Developments in mediation, moderation, and implementation analysis allow for the extraction of more detailed information from a prevention study. Advancements in the interpretation of prevention research results include more widespread calculation of effect size and statistical power, the use of confidence intervals as well as hypothesis testing, detailed causal analysis of research findings, and meta-analysis. The increased availability of statistical software has contributed greatly to the use of new methods in prevention research. It is likely that the Internet will continue to stimulate the development and application of new methods. PMID:12940467
Vectorization on the star computer of several numerical methods for a fluid flow problem
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.
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
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.
Development of a set of benchmark problems to verify numerical methods for solving burnup equations
International Nuclear Information System (INIS)
Lago, Daniel; Rahnema, Farzad
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.
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.
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.
A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.
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.
An analytically based numerical method for computing view factors in real urban environments
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.
Katsuro-Hopkins, Oksana; Sabbagh, S. A.; Bialek, J. M.; Park, H. K.; Kim, J. Y.; You, K.-I.; Glasser, A. H.; Lao, L. L.
2007-11-01
Stability to ideal MHD kink/ballooning modes and the resistive wall mode (RWM) is investigated for the KSTAR tokamak. Free-boundary equilibria that comply with magnetic field coil current constraints are computed for monotonic and reversed shear safety factor profiles and H-mode tokamak pressure profiles. Advanced tokamak operation at moderate to low plasma internal inductance shows that a factor of two improvement in the plasma beta limit over the no-wall beta limit is possible for toroidal mode number of unity. The KSTAR conducting structure, passive stabilizers, and in-vessel control coils are modeled by the VALEN-3D code and the active RWM stabilization performance of the device is evaluated using both standard and advanced feedback algorithms. Steady-state power and voltage requirements for the system are estimated based on the expected noise on the RWM sensor signals. Using NSTX experimental RWM sensors noise data as input, a reduced VALEN state-space LQG controller is designed to realistically assess KSTAR stabilization system performance.
1984-01-01
That there have been remarkable advances in the field of molecular electronic structure during the last decade is clear not only to those working in the field but also to anyone else who has used quantum chemical results to guide their own investiga tions. The progress in calculating the electronic structures of molecules has occurred through the truly ingenious theoretical and methodological developments that have made computationally tractable the underlying physics of electron distributions around a collection of nuclei. At the same time there has been consider able benefit from the great advances in computer technology. The growing sophistication, declining costs and increasing accessibi lity of computers have let theorists apply their methods to prob lems in virtually all areas of molecular science. Consequently, each year witnesses calculations on larger molecules than in the year before and calculations with greater accuracy and more com plete information on molecular properties. We can surel...
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
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.
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.)
Bahrami, Saeed; Doulati Ardejani, Faramarz; Aslani, Soheyla; Baafi, Ernest
2014-12-01
The groundwater inflow into a mine during its life and after ceasing operations is one of the most important concerns of the mining industry. This paper presents a hydrogeological assessment of the Irankuh Zn-Pb mine at 20 km south of Esfahan and 1 km northeast of Abnil in west-Central Iran. During mine excavation, the upper impervious bed of a confined aquifer was broken and water at high-pressure flowed into an open pit mine associated with the Kolahdarvazeh deposit. The inflow rates were 6.7 and 1.4 m(3)/s at the maximum and minimum quantities, respectively. Permeability, storage coefficient, thickness and initial head of the fully saturated confined aquifer were 3.5 × 10(-4) m/s, 0.2, 30 m and 60 m, respectively. The hydraulic heads as a function of time were monitored at four observation wells in the vicinity of the pit over 19 weeks and at an observation well near a test well over 21 h. In addition, by measuring the rate of pumping out from the pit sump, at a constant head (usually equal to height of the pit floor), the real inflow rates to the pit were monitored. The main innovations of this work were to make comparison between numerical modelling using a finite element software called SEEP/W and actual data related to inflow and extend the applicability of the numerical model. This model was further used to estimate the hydraulic heads at the observation wells around the pit over 19 weeks during mining operations. Data from a pump-out test and observation wells were used for model calibration and verification. In order to evaluate the model efficiency, the modelling results of inflow quantity and hydraulic heads were compared to those from analytical solutions, as well as the field data. The mean percent error in relation to field data for the inflow quantity was 0.108. It varied between 1.16 and 1.46 for hydraulic head predictions, which are much lower values than the mean percent errors resulted from the analytical solutions (from 1.8 to 5
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
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.
Monotone numerical methods for finite-state mean-field games
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.
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)
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)
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.
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.
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION
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...
Monotone numerical methods for finite-state mean-field games
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.
Numerical flow simulation and efficiency prediction for axial turbines by advanced turbulence models
International Nuclear Information System (INIS)
Jošt, D; Škerlavaj, A; Lipej, A
2012-01-01
Numerical prediction of an efficiency of a 6-blade Kaplan turbine is presented. At first, the results of steady state analysis performed by different turbulence models for different operating regimes are compared to the measurements. For small and optimal angles of runner blades the efficiency was quite accurately predicted, but for maximal blade angle the discrepancy between calculated and measured values was quite large. By transient analysis, especially when the Scale Adaptive Simulation Shear Stress Transport (SAS SST) model with zonal Large Eddy Simulation (ZLES) in the draft tube was used, the efficiency was significantly improved. The improvement was at all operating points, but it was the largest for maximal discharge. The reason was better flow simulation in the draft tube. Details about turbulent structure in the draft tube obtained by SST, SAS SST and SAS SST with ZLES are illustrated in order to explain the reasons for differences in flow energy losses obtained by different turbulence models.
Numerical flow simulation and efficiency prediction for axial turbines by advanced turbulence models
Jošt, D.; Škerlavaj, A.; Lipej, A.
2012-11-01
Numerical prediction of an efficiency of a 6-blade Kaplan turbine is presented. At first, the results of steady state analysis performed by different turbulence models for different operating regimes are compared to the measurements. For small and optimal angles of runner blades the efficiency was quite accurately predicted, but for maximal blade angle the discrepancy between calculated and measured values was quite large. By transient analysis, especially when the Scale Adaptive Simulation Shear Stress Transport (SAS SST) model with zonal Large Eddy Simulation (ZLES) in the draft tube was used, the efficiency was significantly improved. The improvement was at all operating points, but it was the largest for maximal discharge. The reason was better flow simulation in the draft tube. Details about turbulent structure in the draft tube obtained by SST, SAS SST and SAS SST with ZLES are illustrated in order to explain the reasons for differences in flow energy losses obtained by different turbulence models.
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)
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)
Energy Technology Data Exchange (ETDEWEB)
Andre, Carlos de [PETROBRAS, Rio de Janeiro, RJ (Brazil); Canas, Jesus A.; Low, Steven; Barreto, Wesley [Schlumberger, Houston, TX (United States)
2004-07-01
This paper describes an integrated and rigorous approach for viscous and middle oil reservoir productivity evaluation using petrophysical models calibrated with permeability derived from mini tests (Dual Packer) and Vertical Interference Tests (VIT) from open hole wire line testers (MDT SLB TM). It describes the process from Dual Packer Test and VIT pre-job design, evaluation via analytical and inverse simulation modeling, calibration and up scaling of petrophysical data into a numerical model, history matching of Dual Packer Tests and VIT with numerical simulation modeling. Finally, after developing a dynamic calibrated model, we perform productivity forecasts of different well configurations (vertical, horizontal and multilateral wells) for several deep offshore oil reservoirs in order to support well testing activities and future development strategies. The objective was to characterize formation static and dynamic properties early in the field development process to optimize well testing design, extended well test (EWT) and support the development strategies in deep offshore viscous oil reservoirs. This type of oil has limitations to flow naturally to surface and special lifting equipment is required for smooth optimum well testing/production. The integrated analysis gave a good overall picture of the formation, including permeability anisotropy and fluid dynamics. Subsequent analysis of different well configurations and lifting schemes allows maximizing formation productivity. The simulation and calibration results are compared to measured well test data. Results from this work shows that if the various petrophysical and fluid properties sources are integrated properly an accurate well productivity model can be achieved. If done early in the field development program, this time/knowledge gain could reduce the risk and maximize the development profitability of new blocks (value of the information). (author)
Study on numerical methods for transient flow induced by speed-changing impeller of fluid machinery
International Nuclear Information System (INIS)
Wu, Dazhuan; Chen, Tao; Wang, Leqin; Cheng, Wentao; Sun, Youbo
2013-01-01
In order to establish a reliable numerical method for solving the transient rotating flow induced by a speed-changing impeller, two numerical methods based on finite volume method (FVM) were presented and analyzed in this study. Two-dimensional numerical simulations of incompressible transient unsteady flow induced by an impeller during starting process were carried out respectively by using DM and DSR methods. The accuracy and adaptability of the two methods were evaluated by comprehensively comparing the calculation results. Moreover, an intensive study on the application of DSR method was conducted subsequently. The results showed that transient flow structure evolution and transient characteristics of the starting impeller are obviously affected by the starting process. The transient flow can be captured by both two methods, and the DSR method shows a higher computational efficiency. As an application example, the starting process of a mixed-flow pump was simulated by using DSR method. The calculation results were analyzed by comparing with the experiment data.
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)
Varnhagen, Scott; Same, Adam; Remillard, Jesse; Park, Jae Wan
2011-03-01
Series plug-in hybrid electric vehicles of varying engine configuration and battery capacity are modeled using Advanced Vehicle Simulator (ADVISOR). The performance of these vehicles is analyzed on the bases of energy consumption and greenhouse gas emissions on the tank-to-wheel and well-to-wheel paths. Both city and highway driving conditions are considered during the simulation. When simulated on the well-to-wheel path, it is shown that the range extender with a Wankel rotary engine consumes less energy and emits fewer greenhouse gases compared to the other systems with reciprocating engines during many driving cycles. The rotary engine has a higher power-to-weight ratio and lower noise, vibration and harshness compared to conventional reciprocating engines, although performs less efficiently. The benefits of a Wankel engine make it an attractive option for use as a range extender in a plug-in hybrid electric vehicle.
A different approach to estimate nonlinear regression model using numerical methods
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].
Numerical solution of the Navier-Stokes equations by discontinuous Galerkin method
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.
Advanced codes and methods supporting improved fuel cycle economics - 5493
International Nuclear Information System (INIS)
Curca-Tivig, F.; Maupin, K.; Thareau, S.
2015-01-01
AREVA's code development program was practically completed in 2014. The basic codes supporting a new generation of advanced methods are the followings. GALILEO is a state-of-the-art fuel rod performance code for PWR and BWR applications. Development is completed, implementation started in France and the U.S.A. ARCADIA-1 is a state-of-the-art neutronics/ thermal-hydraulics/ thermal-mechanics code system for PWR applications. Development is completed, implementation started in Europe and in the U.S.A. The system thermal-hydraulic codes S-RELAP5 and CATHARE-2 are not really new but still state-of-the-art in the domain. S-RELAP5 was completely restructured and re-coded such that its life cycle increases by further decades. CATHARE-2 will be replaced in the future by the new CATHARE-3. The new AREVA codes and methods are largely based on first principles modeling with an extremely broad international verification and validation data base. This enables AREVA and its customers to access more predictable licensing processes in a fast evolving regulatory environment (new safety criteria, requests for enlarged qualification databases, statistical applications, uncertainty propagation...). In this context, the advanced codes and methods and the associated verification and validation represent the key to avoiding penalties on products, on operational limits, or on methodologies themselves
Advances in product family and product platform design methods & applications
Jiao, Jianxin; Siddique, Zahed; Hölttä-Otto, Katja
2014-01-01
Advances in Product Family and Product Platform Design: Methods & Applications highlights recent advances that have been made to support product family and product platform design and successful applications in industry. This book provides not only motivation for product family and product platform design—the “why” and “when” of platforming—but also methods and tools to support the design and development of families of products based on shared platforms—the “what”, “how”, and “where” of platforming. It begins with an overview of recent product family design research to introduce readers to the breadth of the topic and progresses to more detailed topics and design theory to help designers, engineers, and project managers plan, architect, and implement platform-based product development strategies in their companies. This book also: Presents state-of-the-art methods and tools for product family and product platform design Adopts an integrated, systems view on product family and pro...
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.
Combinatorial methods for advanced materials research and development
Energy Technology Data Exchange (ETDEWEB)
Cremer, R.; Dondorf, S.; Hauck, M.; Horbach, D.; Kaiser, M.; Krysta, S.; Kyrylov, O.; Muenstermann, E.; Philipps, M.; Reichert, K.; Strauch, G. [Rheinisch-Westfaelische Technische Hochschule Aachen (Germany). Lehrstuhl fuer Theoretische Huettenkunde
2001-10-01
The applicability of combinatorial methods in developing advanced materials is illustrated presenting four examples for the deposition and characterization of one- and two-dimensionally laterally graded coatings, which were deposited by means of (reactive) magnetron sputtering and plasma-enhanced chemical vapor deposition. To emphasize the advantages of combinatorial approaches, metastable hard coatings like (Ti,Al)N and (Ti,Al,Hf)N respectively, as well as Ge-Sb-Te based films for rewritable optical data storage were investigated with respect to the relations between structure, composition, and the desired materials properties. (orig.)
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.
Numerical and experimental validation of a particle Galerkin method for metal grinding simulation
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.
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.
International Nuclear Information System (INIS)
Kobayashi, Yasuhiro; Takamoto, Masanori; Nonaka, Hisanori; Yamada, Naoyuki
1994-01-01
A scheduling system has been developed by integrating symbolic processing functions for constraint handling and modification guidance, with numeric processing functions for schedule optimization and evaluation. The system is composed of an automatic schedule generation module, interactive schedule revision module and schedule evaluation module. The goal of the problem solving is the flattening of the daily resources requirement throughout the scheduling period. The automatic schedule generation module optimizes the initial schedule according to the formulatable portion of requirement description specified in a predicate-like language. A planning engineer refines the near-goal schedule through a knowledge-based interactive optimization process to obtain the goal schedule which fully covers the requirement description, with the interactive schedule revision module and schedule evaluation module. A scheduling system has been implemented on the basis of the proposed problem solving framework and experimentally applied to real-world sized scheduling problems for plant construction. With a result of the overall plant construction scheduling, a section schedule optimization process is described with the emphasis on the symbolic processing functions. (author)
Bisetti, Fabrizio
2014-07-14
Combustion of fossil fuels is likely to continue for the near future due to the growing trends in energy consumption worldwide. The increase in efficiency and the reduction of pollutant emissions from combustion devices are pivotal to achieving meaningful levels of carbon abatement as part of the ongoing climate change efforts. Computational fluid dynamics featuring adequate combustion models will play an increasingly important role in the design of more efficient and cleaner industrial burners, internal combustion engines, and combustors for stationary power generation and aircraft propulsion. Today, turbulent combustion modelling is hindered severely by the lack of data that are accurate and sufficiently complete to assess and remedy model deficiencies effectively. In particular, the formation of pollutants is a complex, nonlinear and multi-scale process characterized by the interaction of molecular and turbulent mixing with a multitude of chemical reactions with disparate time scales. The use of direct numerical simulation (DNS) featuring a state of the art description of the underlying chemistry and physical processes has contributed greatly to combustion model development in recent years. In this paper, the analysis of the intricate evolution of soot formation in turbulent flames demonstrates how DNS databases are used to illuminate relevant physico-chemical mechanisms and to identify modelling needs. © 2014 The Author(s) Published by the Royal Society.
Advances in Applications of Hierarchical Bayesian Methods with Hydrological Models
Alexander, R. B.; Schwarz, G. E.; Boyer, E. W.
2017-12-01
Mechanistic and empirical watershed models are increasingly used to inform water resource decisions. Growing access to historical stream measurements and data from in-situ sensor technologies has increased the need for improved techniques for coupling models with hydrological measurements. Techniques that account for the intrinsic uncertainties of both models and measurements are especially needed. Hierarchical Bayesian methods provide an efficient modeling tool for quantifying model and prediction uncertainties, including those associated with measurements. Hierarchical methods can also be used to explore spatial and temporal variations in model parameters and uncertainties that are informed by hydrological measurements. We used hierarchical Bayesian methods to develop a hybrid (statistical-mechanistic) SPARROW (SPAtially Referenced Regression On Watershed attributes) model of long-term mean annual streamflow across diverse environmental and climatic drainages in 18 U.S. hydrological regions. Our application illustrates the use of a new generation of Bayesian methods that offer more advanced computational efficiencies than the prior generation. Evaluations of the effects of hierarchical (regional) variations in model coefficients and uncertainties on model accuracy indicates improved prediction accuracies (median of 10-50%) but primarily in humid eastern regions, where model uncertainties are one-third of those in arid western regions. Generally moderate regional variability is observed for most hierarchical coefficients. Accounting for measurement and structural uncertainties, using hierarchical state-space techniques, revealed the effects of spatially-heterogeneous, latent hydrological processes in the "localized" drainages between calibration sites; this improved model precision, with only minor changes in regional coefficients. Our study can inform advances in the use of hierarchical methods with hydrological models to improve their integration with stream
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.
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
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.
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
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
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.
Evaluating Blended and Flipped Instruction in Numerical Methods at Multiple Engineering Schools
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…
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.
Implementing a Flipped Classroom Approach in a University Numerical Methods Mathematics Course
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…
Numerical simulation of pseudoelastic shape memory alloys using the large time increment method
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.