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.
Design of advanced industrial furnaces using numerical modeling method
Dong, Wei
2000-01-01
This doctoral thesis describes the fundamentals ofmathematical modeling for the industrial furnaces and boilersand presents the results from the numerical simulations of sometypical applications in advanced industrial furnaces andboilers. The main objective of this thesis work is to employcomputational fluid dynamics (CFD) technology as an effectivecomputer simulation tool to study and develop the newcombustion concepts, phenomena and processes in advancedindustrial furnaces and boilers. The ...
Numerical modeling of spray combustion with an advanced VOF method
Chen, Yen-Sen; Shang, Huan-Min; Shih, Ming-Hsin; Liaw, Paul
1995-01-01
This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.
Dusan Maga
2004-01-01
Presented paper is based on authors experience on numerical methods of field solution, mostly magnetic. This paper, as the first one of prepared series, deals with mathematical apparatus and basic physical principles, as well as with possible short-comings or advantages when using the Finite Difference Method (FDM).
Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods
Directory of Open Access Journals (Sweden)
Prud’homme Christophe
2013-01-01
Full Text Available This paper presents an overview of a unified framework for finite element and spectral element methods in 1D, 2D and 3D in C++ called Feel++. The article is divided in two parts. The first part provides a digression through the design of the library as well as the main abstractions handled by it, namely, meshes, function spaces, operators, linear and bilinear forms and an embedded variational language. In every case, the closeness between the language developed in Feel++ and the equivalent mathematical objects is highlighted. In the second part, examples using the mortar, Schwartz (nonoverlapping, three fields and two fictitious domain-like methods (the Fat Boundary Method and the Penalty Method are presented and numerically solved in the scope of the library.
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
Yoshida, Hiroyuki; Takase, Kazuyuki
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.
Directory of Open Access Journals (Sweden)
E. Rajabi
2014-01-01
Full Text Available In this research a direct numerical simulation (DNS of turbulent flow is performed in a geometrically standard case like plane channel flow. Pseudo spectral (PS method is used due to geometry specifications and very high accuracy achieved despite relatively few grid points. A variable time-stepping algorithm is proposed which may reduce requirement of computational cost in simulation of such wall-bounded flow. Channel flow analysis is performed with both constant and varied time-step for 128 × 65×128 grid points. The time advancement is carried out by implicit third-order backward differentiation scheme for linear terms and explicit forward Euler for nonlinear convection term. PS method is used in Cartesian coordinates with Chebychev polynomial expansion in normal direction for one non-periodic boundary condition. Also Fourier series is employed in stream-wise and span-wise directions for two periodic boundary conditions. The friction Reynolds number is about Reτ=175 based on a friction velocity and channel half width. Standard common rotational form was chosen for discritization of nonlinear convective term of Navier-Stocks equation. The comparison is made between turbulent quantities such as the turbulent statistics, Reynolds stress, wall shear velocity, standard deviation of (u and total normalized energy of instantaneous velocities in both time-discretization methods. The results show that if final decision rests on economics, the proposed variable time-stepping algorithm will be proper choice which satisfies the accuracy and reduces the computational cost.
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.
Dahlquist, Germund
2003-01-01
""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.
Institute of Scientific and Technical Information of China (English)
SU JunWei; GU ZhaoLin; XU X.Yun
2009-01-01
Accurate prediction of the evolution of particle size distribution is critical to determining the dynamic flow structure of a disperse phase system.A population balance equation(PBE),a non-linear hyperbolic equation of the number density function,is usually employed to describe the micro-behavior(aggregation,breakage,growth,etc.)of a disperse phase and its effect on particle size distribution.Numerical solution is the only choice in most cases.In this paper,three different numerical methods(direct discretization methods,Monte Carlo methods,and moment methods)for the solution of a PBE are evaluated with regard to their ease of implementation,computational load and numerical accuracy.Special attention is paid to the relatively new and superior moment methods including quadrature method of moments(QMOM),direct quadrature method of moments(DQMOM),modified quadrature method of moments(M-QMOM),adaptive direct quadrature method of moments(ADOMOM),fixed pivot quadrature method of moments(FPQMOM),moving particle ensemble method(MPEM)and local fixed pivot quadrature method of moments(LFPQMOM).The prospects of these methods ere discussed in the final section,based on their individual merits and current state of development of the field.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Accurate prediction of the evolution of particle size distribution is critical to determining the dynamic flow structure of a disperse phase system.A population balance equation(PBE),a non-linear hyperbolic equation of the number density function,is usually employed to describe the micro-behavior(aggregation,breakage,growth,etc.) of a disperse phase and its effect on particle size distribution.Numerical solution is the only choice in most cases.In this paper,three different numerical methods(direct discretization methods,Monte Carlo methods,and moment methods) for the solution of a PBE are evaluated with regard to their ease of implementation,computational load and numerical accuracy.Special attention is paid to the relatively new and superior moment methods including quadrature method of moments(QMOM),direct quadrature method of moments(DQMOM),modified quadrature method of moments(M-QMOM),adaptive direct quadrature method of moments(ADQMOM),fixed pivot quadrature method of moments(FPQMOM),moving particle ensemble method(MPEM) and local fixed pivot quadrature method of moments(LFPQMOM).The prospects of these methods are discussed in the final section,based on their individual merits and current state of development of the field.
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...
International Nuclear Information System (INIS)
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
Numerical Methods - III Numerical Methods - III
Dusan Maga
2005-01-01
This contribution deals with giving a possible most simplified view on one of the most frequently used numerical methods – Boundary Element Method (BEM). However, after reading the previous related papers the reader would be able to realize the adequate model by-hand, this time the relative complicate integral formulations probably will not allow to do the same. In spite of this we hope that the principles of this method will also be presented clearly and could be understand.This contribution...
Numerical methods using Matlab
Gupta, Abhishek
2015-01-01
Numerical Methods with MATLAB provides a highly-practical reference work to assist anyone working with numerical methods. A wide range of techniques are introduced, their merits discussed and fully working MATLAB code samples supplied to demonstrate how they can be coded and applied. Numerical methods have wide applicability across many scientific, mathematical, and engineering disciplines and are most often employed in situations where working out an exact answer to the problem by another method is impractical. Numerical Methods with MATLAB presents each topic in a concise and readable
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.
Introduction to Numerical Methods
Energy Technology Data Exchange (ETDEWEB)
Schoonover, Joseph A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-06-14
These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.
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...
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 numerical simulations of selected metallurgical units
Directory of Open Access Journals (Sweden)
G. Kokot
2012-12-01
Full Text Available Purpose: of this paper is to present numerical simulations of large structures in metallurgical industry. Some examples of finite element analysis are presented. The calculations were performed for the determining the stress effort of the metallurgical units mainly blast furnace, throath’s gas pipelines, hot blast stoves, etc. during the working conditions and for the repairing purpose.Design/methodology/approach: The way of conducting simulations and analysis were the finite element method connected with the optimization process.Findings: Performing the numerical analysis the changes in the structures design were applied what extremely influenced on the state effort and the durability of considered structures.Research limitations/implications: Development of the presented approach solving the coupled field and CFD problems, the application of the parallel computing and domain decomposition methods in the large structure simulations.Practical implications: Presented results shows the possibility of application the advanced computational methods in the computer aided engineering processes of designing and analysing the large structure as the metallurgical units are. It can dramatically influence on the recognizing of the effort stets and helps in the monitoring, overhauls and redesigning process. Those methods gives the global very precise information which cannot be obtain in other ways (analytical solutions, experimental methods.Originality/value: The paper present the original research results comes from the complex numerical simulations of the main metallurgical units in the blast furnace train. The original value of the paper is the introduction of the advanced finite element simulation in the field of iron steel industry structures design and developing.
10th European Conference on Numerical Mathematics and Advanced Applications
Deparis, Simone; Kressner, Daniel; Nobile, Fabio; Picasso, Marco
2015-01-01
This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.
Jauregui, Ricardo; Silva, Ferran
2011-01-01
In the last years, numerical simulation has seen a great development thanks to costs reduction and speed increases of the computational systems. With these improvements, the mathematical algorithms are able to work properly with more realistic problems. Nowadays, the solution of a problem using numerical simulation is not just finding a result, but also to ensure the quality. However, can we say that the model results are correct regarding the behaviour of the system? In other words, how c...
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.
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
Developing numerical methods for experimental data processing
International Nuclear Information System (INIS)
Materials study implies experimental measurements the results of which are always affected by noise. To perform numerical data processing, as for instance, numerical derivation preparatory smoothing it is necessary to avoid instabilities. This implies the noise extraction from the experimental data. When obtaining great amount of data is possible, many of the noise related problems can be solved by using statistical indicators. In case of high cost experiments or problems of unique type, the task of extracting useful information referring to given materials parameters is of paramount significance. The paper presents several numerical methods for processing the experimental data developed at INR Pitesti. These were employed in treating the experimental data obtained in nuclear materials studies and which aimed at materials characterization and fabrication technology development. To refine and determine the accuracy of the real experimental data processing methods, computerized simulations were largely used. These methods refer to the transfer relations for important statistical indicators in case of mediate measurements, to increase the resolution of the measurements carried out with linear detectors as well as for numerical smoothing of experimental data. A figure is given with results obtained by applying the numerical smoothing method for the experimental data from X-ray diffraction measurements on Zircaloy-4. The numerical methods developed were applied in materials studies of the structure materials used in CANDU 600 reactor and advanced CANDU type fuels as well as for natural uranium or thorium and thorium-uranium fuel pellets. These methods helped in increasing the measurements' accuracy and confidence level
Advances in numerical and applied mathematics
South, J. C., Jr. (Editor); Hussaini, M. Y. (Editor)
1986-01-01
This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.
Numerical optimization methods in economics
Schmedders, K.
2008-01-01
Optimization problems are ubiquitous in economics. Many of these problems are sufficiently complex that they cannot be solved analytically. Instead economists need to resort to numerical methods. This article presents the most commonly used methods for both unconstrained and constrained optimization problems in economics; it emphasizes the solid theoretical foundation of these methods, illustrating them with examples. The presentation includes a summary of the most popular software packages f...
Numerical methods for ordinary differential equations
Butcher, John C
2008-01-01
In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author''s pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book includeIntroductory work on differential and difference equations.A comprehensive introduction to the theory and practice of solving ordinary differential equations numeri...
Advanced numerical techniques in core simulations
International Nuclear Information System (INIS)
The whole core simulations are one of the most CPU intensive calculations in reactor physics design and analyses. For a designer it is imperative to perform these calculations with good accuracy and in least time possible to try out various options. It is important for the code developers to use techniques involving minimum approximations and to use most recent numerical methods applied in tandem with huge computing power available today. In the presented paper, some of these methods are discussed. (author)
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 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...
International Nuclear Information System (INIS)
Numerical analysis of highly underexpanded jets was performed by using the SERAPHIM program for compressible multi-phase flows with sodium-water chemical reaction to investigate its applicability. When the pressurized water leaks from a failed heat transfer tube in a steam generator of sodium cooled fast reactors, the underexpanded jet with the chemical reaction will be formed. The role of the SERAPHIM program is to predict the profiles of velocities, temperatures and concentrations under the sodium-water reaction accident. To achieve this, validation of the numerical method to the multi-phase flow including underexpanded jets must be conducted. A multi-fluid model considering compressibility and a second-order TVD scheme were used in the present analysis. In the case of the air jet into the air, numerical results agreed with the experimental data very well. Also in the case of the air jet into the water, the comparable numerical results were obtained by our method. (author)
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...
Advances in numerical simulation of nonlinear water waves
Ma, Qingwei
2014-01-01
Most of the Earth's surface is covered by water. Our everyday lives and activities are affected by water waves in oceans, such as the tsunami that occurred in the Indian Ocean on 26 December 2004. This indicates how important it is for us to fully understand water waves, in particular the very large ones. One way to do so is to perform numerical simulation based on the nonlinear theory. Considerable research advances have been made in this area over the past decade by developing various numerical methods and applying them to emerging problems; however, until now there has been no comprehensive
Numerical methods for multibody systems
Glowinski, Roland; Nasser, Mahmoud G.
1994-01-01
This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.
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...
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.
International Nuclear Information System (INIS)
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)
Yoshida, Hiroyuki; Nagayoshi, Takuji; Takase, Kazuyuki; Akimoto, Hajime
Thermal-hydraulic design of the current boiling water reactor (BWR) is performed by correlations with empirical results of actual-size tests. However, 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. 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, detailed Two-Phase Flow simulation code using advanced Interface Tracking method: TPFIT is developed to calculate the detailed information of the two-phase flow. We tried to verify the TPFIT code by comparing it with the 2-channel air-water and steam-water mixing experimental results. The predicted result agrees well the observed results and bubble dynamics through the gap and cross flow behavior could be effectively predicted by the TPFIT code, and pressure difference between fluid channels is responsible for the fluid mixing.
Numerical methods used in fusion science numerical modeling
Yagi, M.
2015-04-01
The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.
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.
Methods for numerical conformal mapping
International Nuclear Information System (INIS)
Nonlinear integral equations for the boundary functions which determine conformal transformations in two dimensions are developed and analyzed. One of these equations has a nonsingular logarithmic kernel and is especially well suited for numerical computations of conformal maps including those which deal with regions having highly distorted boundaries. Numerical procedures based on interspersed Gaussian quadrature for approximating the integrals and a Newton--Raphson technique to solve the resulting nonlinear algebraic equations are described. The Newton--Raphson iteration converges reliably with very crude initial approximations. Numerical examples are given for the mapping of a half-infinite region with periodic boundary onto a half plane, with up to nine-figure accuracy for values of the map function on the boundary and for its first derivatives. The examples include regions bounded by ''spike'' curves characteristic of Rayleigh--Taylor instability phenomena. A differential equation is derived which relates changes of the boundary. This is relevant to potential problems for regions with time-dependent boundaries. Further nonsingular integral formulas are derived for conformal mapping in a variety of geometries and for application to the boundary-value problems of potential theory
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
OBJECTORIENTED NUMERICAL MANIFOLD METHOD
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The design and management of the objects about the numerical manifold method are studied by abstracting the finite cover system of numerical manifold method as independent data classes and the theoretical basis for the researching and expanding of numerical manifold method is also put forward. The Hammer integration of triangular area coordinates is used in the integration of the element. The calculation result shows that the program is accuracy and effective.
Numerical methods for phase retrieval
Osherovich, Eliyahu
2012-01-01
In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction imaging (CDI). Our main goal is to develop an efficient reconstruction method based on continuous optimization techniques. Unlike current reconstruction methods, which are based on alternating projections, our approach leads to a much faster and more robust method. However, all previous attempts to employ continuous optimization methods, such as Newton-type algorithms, to the phase retrieval problem failed. In this work we provide an explanation for this failure, and based on this explanation we devise a sufficient condition that allows development of new reconstruction methods---approximately known Fourier phase. We demonstrate that a rough (up to $\\pi/2$ radians) Fourier phase estimate practically guarantees successful reconstruction by any reasonable method. We also pres...
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
Numerical methods in multidimensional radiative transfer
Meinköhn, Erik
2008-01-01
Offers an overview of the numerical modelling of radiation fields in multidimensional geometries. This book covers advances and problems in the mathematical treatment of the radiative transfer equation, a partial integro-differential equation of high dimension that describes the propagation of the radiation in various fields.
Conjugate Function Method for Numerical Conformal Mappings
Hakula, Harri; Rasila, Antti
2011-01-01
We present a method for numerical computation of conformal mappings from simply or doubly connected domains onto so-called canonical domains, which in our case are rectangles or annuli. The method is based on conjugate harmonic functions and properties of quadrilaterals. Several numerical examples are given.
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.
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...
International Nuclear Information System (INIS)
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)
Advancement and prospect of short-term numerical climate prediction
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The defects of present methods of short-term numerical climate prediction are discussed in this paper, and four challenging problems are put forward. Considering our under developed computer conditions, we should innovate in the approcuch of numerical climate prediction on the basis of our own achievements and experiences in the field of short-term numerical climate prediction. It is possibly an effective way to settle the present defects of short-term numerical climate prediction.``
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...
Design of heat exchangers by numerical methods
International Nuclear Information System (INIS)
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)
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 in astrophysics an introduction
Bodenheimer, Peter; Rozyczka, Michal; Plewa, Tomasz; Yorke, Harold W; Yorke, Harold W
2006-01-01
Basic Equations The Boltzmann Equation Conservation Laws of Hydrodynamics The Validity of the Continuous Medium Approximation Eulerian and Lagrangian Formulation of Hydrodynamics Viscosity and Navier-Stokes Equations Radiation Transfer Conducting and Magnetized Media Numerical Approximations to Partial Differential Equations Numerical Modeling with Finite-Difference Equations Difference Quotient Discrete Representation of Variables, Functions, and Derivatives Stability of Finite-Difference Methods Physical Meaning of Stability Criterion A Useful Implicit Scheme Diffusion
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
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.
25 Years of Self-organized Criticality: Numerical Detection Methods
McAteer, R. T. James; Aschwanden, Markus J.; Dimitropoulou, Michaila; Georgoulis, Manolis K.; Pruessner, Gunnar; Morales, Laura; Ireland, Jack; Abramenko, Valentyna
2016-01-01
The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.
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...
Decision of numerical problems with symbolic methods
Directory of Open Access Journals (Sweden)
I. S. Kashirsky
2010-01-01
Full Text Available Modern methods for numerical decision of linear systems guarantee successful results only for good systems. Decision of bad systems (bad conditional, singular is already problem. This paper describes using symbol methods for decision of bad conditional and singular systems.
Numerical methods for nonlinear partial differential equations
Bartels, Sören
2015-01-01
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
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 power system state estimation
Energy Technology Data Exchange (ETDEWEB)
Singh Gill, J.
1987-01-01
Power System State Estimation (PSSE) plays a vital role in the modern operation of electric power systems. Its function is to process redundant, noise-corrupted, telemetered measurements in order to provide a real-time data base with reliable estimates of the current state and structure of the network. The information provided by PSSE is used in a number of other on-line programs, such as the routines that assess the security of the power system. The strucutre of an electrical power network is such that there is a number of nodes where the injection is known to be exactly zero. These zero injections can be treated as equality constraints in the power system state estimation problem. The various numerical methods for solving the PSSE problem are examined. The problem is usually formulated as a weighted least squares optimization. The conventional normal equation method usually employed in PSSE, is prone to numerical ill-conditioning problems. To avoid this, the use of numerically stable orthogonal methods is proposed. Two orthogonal methods are investigated: a batch-processing technique known as Householder transformations and a general row merging procedure based on the use of Given rotations. Details of the methods' implementation for PSSE are discussed. A hybrid method, which enjoys the numerical robustness of the orthogonal methods and is capable of significantly reducing total execution time for PSSE, is also investigated. Finally, three different methods for solving the constrained PSSE problem are discussed. A modified weighting technique to obtain an acceptable solution is also presented. A comparison of the various methods presented in the thesis is given based on results from two power systems networks, including a real size network. 59 refs., 15 figs., 12 tabs.
Numerical methods in electron magnetic resonance
International Nuclear Information System (INIS)
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)
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.
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.
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.
An introduction to numerical methods and analysis
Epperson, J F
2007-01-01
Praise for the First Edition "". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.""-Zentrablatt Math "". . . carefully structured with many detailed worked examples . . .""-The Mathematical Gazette "". . . an up-to-date and user-friendly account . . .""-Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or d
The TAB method for numerical calculation of spray droplet breakup
Orourke, P. J.; Amsden, A. A.
A short history is given of the major milestones in the development of the stochastic particle method for calculating liquid fuel sprays. The most recent advance has been the discovery of the importance of drop breakup in engine sprays. A new method, called TAB, for calculating drop breakup is presented. Some theoretical properties of the method are derived; its numerical implementation in the computer program KIVA is described; and comparisons are presented between TAB-method calculations and experiments and calculations using another breakup model.
Numerical and analytical methods with Matlab
Bober, William; Masory, Oren
2013-01-01
Numerical and Analytical Methods with MATLAB® presents extensive coverage of the MATLAB programming language for engineers. It demonstrates how the built-in functions of MATLAB can be used to solve systems of linear equations, ODEs, roots of transcendental equations, statistical problems, optimization problems, control systems problems, and stress analysis problems. These built-in functions are essentially black boxes to students. By combining MATLAB with basic numerical and analytical techniques, the mystery of what these black boxes might contain is somewhat alleviated. This classroom-tested
Recent advances in two-phase flow numerics
International Nuclear Information System (INIS)
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.
Advanced modelling and numerical strategies in nuclear thermal-hydraulics
International Nuclear Information System (INIS)
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 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...
Numerical Methods for Stochastic Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Sharp, D.H.; Habib, S.; Mineev, M.B.
1999-07-08
This is the final report of a Laboratory Directed Research and Development (LDRD) project at the Los Alamos National laboratory (LANL). The objectives of this proposal were (1) the development of methods for understanding and control of spacetime discretization errors in nonlinear stochastic partial differential equations, and (2) the development of new and improved practical numerical methods for the solutions of these equations. The authors have succeeded in establishing two methods for error control: the functional Fokker-Planck equation for calculating the time discretization error and the transfer integral method for calculating the spatial discretization error. In addition they have developed a new second-order stochastic algorithm for multiplicative noise applicable to the case of colored noises, and which requires only a single random sequence generation per time step. All of these results have been verified via high-resolution numerical simulations and have been successfully applied to physical test cases. They have also made substantial progress on a longstanding problem in the dynamics of unstable fluid interfaces in porous media. This work has lead to highly accurate quasi-analytic solutions of idealized versions of this problem. These may be of use in benchmarking numerical solutions of the full stochastic PDEs that govern real-world problems.
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...
Numerical methods: Analytical benchmarking in transport theory
International Nuclear Information System (INIS)
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 dispersion and dissipation analysis of nodal expansion method
International Nuclear Information System (INIS)
The numerical property of nodal expansion method (NEM) is studied in the paper from the perspective of numerical dispersion and dissipation, which is brand new for nodal methods and no one else has ever tried before. Besides, the more complicated transient convection diffusion equation is chosen to be the research target so as to be as general and comprehensive as possible. First, the nature and connotation of dispersion and dissipation is presented. Then, the numerical dispersion and dissipation analysis for NEM is developed with the help of Fourier analysis and solution for complex matrix generalized eigenvalue problem. Through analyzing the numerical dispersion and dissipation of NEM with different order N basis functions as well as comparing it with the central difference (CD) and first order upwind scheme (FUS), and with numerical verification, the conclusion is drawn finally: the numerical dispersion and dissipation of NEM is of an advance in that it can simulate the rather difficult problems such as steep gradients, the high frequency analytical solution, convection dominated problems even in the coarse mesh. (author)
Hyperbolic conservation laws and numerical methods
Leveque, Randall J.
1990-01-01
The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.
Advanced numerical models - influence of partial material factors
Czech Academy of Sciences Publication Activity Database
Koudelka, Petr; Koudelka, T.
London/Leiden/New York : Taylor and Francis Group, 2007 - (Kanda, J.; Furuta, H.), s. 597-598 ISBN 978-0-415-45134-5. [IC on Applications of statistics and probability in civilengineering. Tokyo (JP), 31.07.2007-03.08.2007] R&D Projects: GA ČR(CZ) GA103/05/2130; GA AV ČR(CZ) IAA2071302 Institutional research plan: CEZ:AV0Z20710524 Keywords : advanced numerical models * stability * rock cliff * reliability * Limit State Design * partial material factors Subject RIV: BM - Solid Matter Physics ; Magnetism
International Nuclear Information System (INIS)
Two-fluid model is still useful to simulate two-phase flow in large domain such as rod bundles. However, two-fluid model include a lot of constitutive equations, and the two-fluid model has problems that the results of analyses depend on accuracy of constitutive equations. To solve these problems, we have been developing an advanced two-fluid model. In this model, an interface tracking method is combined with the two-fluid model to predict large interface structure behavior without any constitutive equations, and constitutive equations to evaluate the effects of small bubbles or droplets are only required. In this study, we modified the advanced two-fluid model to improve the stability of the numerical simulation and reduce the computational time. In this paper, we describe the modification performed in this study and the numerical results of two-phase flow in various flow conditions are shown. (author)
Advanced probabilistic method of development
Wirsching, P. H.
1987-01-01
Advanced structural reliability methods are utilized on the Probabilistic Structural Analysis Methods (PSAM) project to provide a tool for analysis and design of space propulsion system hardware. The role of the effort at the University of Arizona is to provide reliability technology support to this project. PSAM computer programs will provide a design tool for analyzing uncertainty associated with thermal and mechanical loading, material behavior, geometry, and the analysis methods used. Specifically, reliability methods are employed to perform sensitivity analyses, to establish the distribution of a critical response variable (e.g., stress, deflection), to perform reliability assessment, and ultimately to produce a design which will minimize cost and/or weight. Uncertainties in the design factors of space propulsion hardware are described by probability models constructed using statistical analysis of data. Statistical methods are employed to produce a probability model, i.e., a statistical synthesis or summary of each design variable in a format suitable for reliability analysis and ultimately, design decisions.
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.
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).
Numerical Methods for Finding Stationary Gravitational Solutions
Dias, Oscar J C; Way, Benson
2015-01-01
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly-spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small rotating black holes in AdS$_5\\times S^5$. We also include several tools and tricks that have been useful throughout the literature.
Numerical methods for finding stationary gravitational solutions
Dias, Óscar J. C.; Santos, Jorge E.; Way, Benson
2016-07-01
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory–Laflamme zero modes of small rotating black holes in AdS{}5× {S}5. We also include several tools and tricks that have been useful throughout the literature.
Advanced construction methods in ACR
International Nuclear Information System (INIS)
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
Automatic numerical integration methods for Feynman integrals through 3-loop
de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.
2015-05-01
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.
Numerical methods in dynamic fracture mechanics
International Nuclear Information System (INIS)
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
Meshless numerical method based on tensor product
Institute of Scientific and Technical Information of China (English)
2008-01-01
A normalized space constructed by tensor product is used in field function approach to give a special case of moving least squares (MLS) interpolation scheme.In the regular domain,the field function which meets homogenous boundary conditions is constructed by spanning base space to make the MLS interpolation scheme simpler and more efficient.Owing to expanded basis functions selection,some drawbacks in general MLS method,for example repeated inversion,low calculation efficiency,and complex criterions,can be avoided completely.Numerical examples illustrate that the proposed method is characterized by simple mathematical concept,convenient repeat calculations with high accuracy,good continuity,less computation and rapid convergence.
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...
Advanced median method for timing jitter compensation
Institute of Scientific and Technical Information of China (English)
Wang Chen; Zhu Jiangmiao; Jan Verspecht; Liu Mingliang; Li Yang
2008-01-01
Timing jitter is one of the main factors that influence on the accuracy of time domain precision measurement. Timing jitter compensation is one of the problems people concern. Because of the flaws of median method, PDF deconvolution method and synthetic method, we put forward a new method for timing jitter compensation, which is called advanced median method. The theory of the advanced median method based on probability and statistics is analyzed, and the process of the advanced median method is summarized in this paper. Simulation and experiment show that compared with other methods, the new method could compensate timing jitter effectively.
Development of numerical methods for reactive transport
International Nuclear Information System (INIS)
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
Deng Shuaiqi; Yue Jianhua; Cao Jing; Zhang Xin
2013-01-01
The high-order staggering grid Finite-Difference (FD) scheme based on first-order velocity-stress elastic wave equation has been deduced. The calculation method of PML boundary condition and stability condition established in this study can be used for numerical simulation of advanced detection of elastic wave in roadway, with the obtaining of high-precision seismogram. Then we systematically analyze the polarity of vector wave field in post-source observation system. The results indicate tha...
Nodal methods in numerical reactor calculations
International Nuclear Information System (INIS)
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)
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.
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....... From 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...
THEORETICAL STUDY OF THREE-DIMENSIONAL NUMERICAL MANIFOLD METHOD
Institute of Scientific and Technical Information of China (English)
LUO Shao-ming; ZHANG Xiang-wei; L(U) Wen-ge; JIANG Dong-ru
2005-01-01
The three-dimensional numerical manifold method(NMM) is studied on the basis of two-dimensional numerical manifold method. The three-dimensional cover displacement function is studied. The mechanical analysis and Hammer integral method of three-dimensional numerical manifold method are put forward. The stiffness matrix of three-dimensional manifold element is derived and the dissection rules are given. The theoretical system and the numerical realizing method of three-dimensional numerical manifold method are systematically studied. As an example, the cantilever with load on the end is calculated, and the results show that the precision and efficiency are agreeable.
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.
CEMRACS 2010: Numerical methods for fusion
International Nuclear Information System (INIS)
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.
Analytical And Numerical Methods In Beam Physics
Andrianov, S
2004-01-01
This report is devoted to discussion of numerical and symbolic computing ratio beam physics. We tray to draw attention on basic conceptual and computational problems first of all. It is known that the main problem in modern computational beam physics connected with high performance computing realization. The most of used approaches are not appropriate for computing using multiprocessing systems. Here we give some possible solutions, which based on symbolic presentation of necessary information and modern information technologies.
Advanced reliability methods - A review
Forsyth, David S.
2016-02-01
There are a number of challenges to the current practices for Probability of Detection (POD) assessment. Some Nondestructive Testing (NDT) methods, especially those that are image-based, may not provide a simple relationship between a scalar NDT response and a damage size. Some damage types are not easily characterized by a single scalar metric. Other sensing paradigms, such as structural health monitoring, could theoretically replace NDT but require a POD estimate. And the cost of performing large empirical studies to estimate POD can be prohibitive. The response of the research community has been to develop new methods that can be used to generate the same information, POD, in a form that can be used by engineering designers. This paper will highlight approaches to image-based data and complex defects, Model Assisted POD estimation, and Bayesian methods for combining information. This paper will also review the relationship of the POD estimate, confidence bounds, tolerance bounds, and risk assessment.
New numerical methods for solving convection problems
International Nuclear Information System (INIS)
New methods for solving one-dimensional convection problems, have appeared recently: VAN LEER's generalization of GODUNOV'S method, BORIS and BOOK's SHASTA-FCT method, CHORIN and SOD's scheme, using a random method due to GLIMM. Its appears in a global analysis certain analogies between these methods. All of them can be interpreted as two-step schemes: a transport step and a projection step
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 matrix method for quantum periodic potentials
Le Vot, Felipe; Meléndez, Juan J.; Yuste, Santos B.
2016-06-01
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the wave functions as finite superpositions of eigenfunctions of the infinite well. A matrix eigenvalue equation then yields the energy levels of the periodic potential within an acceptable accuracy. The methodology has been successfully used to deal with problems based on the well-known Kronig-Penney (KP) model. Besides the original model, these problems are a dimerized KP solid, a KP solid containing a surface, and a KP solid under an external field. A short list of additional problems that can be solved with this procedure is presented.
Numerical methods in Markov chain modeling
Philippe, Bernard; Saad, Youcef; Stewart, William J.
1989-01-01
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
Interpolation Method Needed for Numerical Uncertainty
Groves, Curtis E.; Ilie, Marcel; Schallhorn, Paul A.
2014-01-01
Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.
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...
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...
Application of the CATHARE advanced code to numerical benchmark exercises
International Nuclear Information System (INIS)
In this work the CATHARE V1.3 code was applied to two Numerical Benchmark Exercises proposed in the aim to test the behaviour of thermalhydraulic codes against some spurious numerical effects. In the analysis of the first exercise, which is related to a two-phase flow along a convergent-divergent nozzle, it was seen that the CATHARE code well predicts the expected physical trends in good agreement with the majority of other codes. The application of the code to the second exercise, concerning the water packing phenomenon, showed the presence of this numerical effect. From a sensitivity analysis on time step and mesh size, it was seen that the amplitude of the pressure spikes can be reduced increasing time step and decreasing the space increments
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…
Recent Advances in the Numerical Simulations of Binary Black Holes
Marronetti, Pedro
2011-01-01
Since the breakthrough papers from 2005/2006, the field of numerical relativity has experienced a growth spurt that took the two-body problem in general relativity from the category of "really-hard-problems" to the realm of "things-we-know-how-to-do". Simulations of binary black holes in circular orbits, the holy grail of numerical relativity, are now tractable problems that lead to some of the most spectacular results in general relativity in recent years. We cover here some of the latest achievements and highlight the field's next challenges.
A new numerical method on American option pricing
Institute of Scientific and Technical Information of China (English)
顾永耕; 舒继武; 邓小铁; 郑纬民
2002-01-01
Mathematically, the Black-Scholes model of American option pricing is a free boundary problem of partial differential equation. It is well known that this model is a nonlinear problem, and it has no closed form solution. We can only obtain an approximate solution by numerical method, but the precision and stability are hard to control, because the singularity at the exercise boundary near expiration date has a great effect on precision and stability for numerical method. We propose a new numerical method, FDA method, to solve the American option pricing problem, which combines advantages the Semi-Analytical Method and the Front-Fixed Difference Method. Using the FDA method overcomes the difficulty resulting from the singularity at the terminal of optimal exercise boundary. A large amount of calculation shows that the FDA method is more accurate and stable than other numerical methods.
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 determining filtration parameters for inhomogeneous oil strata
Energy Technology Data Exchange (ETDEWEB)
Golubev, G.V.; Danilaev, P.G.
1994-06-01
We describe a number of nonlocal hydrodrodynamic methods for determining filtration parameters for inhomogeneous oil strata and flow models. Numerical algorithms based on projection-difference, integral, finite-difference, and regularization methods are used to solve these problems. Numerical computations based on the algorithms are presented.
Numerical Methods, Algorithms and Tools in C#
Dos Passos, Waldemar
2009-01-01
Along with providing the C# source code online, this book presents practical, ready-to-use mathematical routines employing the C# programming language from Microsoft. It shows how to write mathematically intense object-oriented computer programs. It covers a spectrum of computational tools, including sorting algorithms and optimization methods.
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...
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 Simulations and Optimisation in Forming of Advanced Materials
Huétink, J.
2007-04-01
With the introduction of new materials as high strength steels, metastable steels and fiber reinforce composites, the need for advanced physically valid constitutive models arises. A biaxial test equipment is developed and applied for the determination of material data as well as for validation of material models. An adaptive through- thickness integration scheme for plate elements is developed, which improves the accuracy of spring back prediction at minimal costs. An optimization strategy is proposed that assists an engineer to model an optimization problem.
Modified semismooth Newton Method: Numerical example
Czech Academy of Sciences Publication Activity Database
Byczanski, Petr; Sysala, Stanislav
Liberec : TUL Liberec, 2009, s. 24-30. ISBN 978-80-7372-543-3. [SIMONA 2009- Simulace, modelování a nejrůznější aplikace . Seminář výzkumného centra „Pokročilé sanační technologie a procesy“ s otevřenou účastí. Liberec (CZ), 21.09.2009-23.09.2009] Institutional research plan: CEZ:AV0Z30860518 Keywords : Newton -like method * damping * elasto-plasticity Subject RIV: BA - General Mathematics
Advances in structure research by diffraction methods
Brill, R
1970-01-01
Advances in Structure Research by Diffraction Methods reviews advances in the use of diffraction methods in structure research. Topics covered include the dynamical theory of X-ray diffraction, with emphasis on Ewald waves in theory and experiment; dynamical theory of electron diffraction; small angle scattering; and molecular packing. This book is comprised of four chapters and begins with an overview of the dynamical theory of X-ray diffraction, especially in terms of how it explains all the absorption and propagation properties of X-rays at the Bragg setting in a perfect crystal. The next
Numerical methods for inertial confinement fusion
International Nuclear Information System (INIS)
This document deals with the modelling issues related to inertial confinement fusion and they are limited to the hydrodynamics of the implosion and the coupling with radiative transfer. The hydrodynamics of the implosion is triggered by a succession of shocks which result in Rayleigh-Taylor instabilities. As for the coupling with radiative transfer: the plasmas emit high energy radiations which heat up the core of the capsule. The first thing to do is to discretize (in time and space), the hydrodynamics part. In general, Lagrangian methods are preferred for this part. Secondly, the discretization of the radiative part implies in principle discretization of spacetime variables, and of frequency and propagation direction. Since this is costly, a common approach is to simplify the model by using diffusion approximation. Note that by doing so, one must face the problem of designing a diffusion scheme on a mesh which may be highly deformed. This is of course an important issue, which is (partly) studied here. The last chapter of the present document gives an example of simplified model for describing the evolution of the ablation front. This model may help in understanding particular phenomena, such as, for instance, the stabilization of long wavelength linear instability. The last part of this document gathers the slides of the presentation.
Numerical Solution of Perfect Plastic Problems with Contact: Part I - Theory and Numerical Methods
Czech Academy of Sciences Publication Activity Database
Čermák, Martin; Haslinger, J.; Sysala, Stanislav
Vol. 12. Barcelona: International Centre for Numerical Methods in Engineering (CIMNE), 2013 - (Onate, E.; Owen, D.; Peric, D.; Suárez, B.), s. 1-12 ISBN 978-84-941531-5-0. [International Conference on Computational Plasticity - Fundamentals and Applications /12./. Barcelona (ES), 03.09.2013-05.09.2013] Institutional support: RVO:68145535 Keywords : perfect plasticity * contact * limit analysis * numerical methods Subject RIV: BA - General Mathematics
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
Numerical methods for flow and transport in porous media
Vu Do, Huy Cuong
2014-01-01
This thesis bears on the modelling of groundwater flow and transport in porous media; we perform numerical simulations by means of finite volume methods and prove convergence results. In Chapter 1, we first apply a semi-implicit standard finite volume method and then the generalized finite volume method SUSHI for the numerical simulation of density driven flows in porous media; we solve a nonlinear convection-diffusion parabolic equation for the concentration coupled with an elliptic equation...
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.
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 ...
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.
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.
Numerical method of singular problems on singular integrals
International Nuclear Information System (INIS)
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
THE VARIATIONAL PRINCIPLE AND APPLICATION OF NUMERICAL MANIFOLD METHOD
Institute of Scientific and Technical Information of China (English)
骆少明; 张湘伟; 蔡永昌
2001-01-01
The physical-cover-oriented variational principle of numerical manifold method (NMM) for the analysis of linear elastic static problems was put forward according to the displacement model and the characters of numerical manifold method. The theoretical calculating formulations and the controlling equation of NMM were derived. As an example,the plate with a hole in the center is calculated and the results show that the solution precision and efficiency of NMM are agreeable.
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 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 c
Methods for wave equation prestack depth migration and numerical experiments
Institute of Scientific and Technical Information of China (English)
ZHANG Guanquan; ZHANG Wensheng
2004-01-01
In this paper the methods of wave theory based prestack depth migration and their implementation are studied. Using the splitting of wave operator, the wavefield extrapolation equations are deduced and the numerical schemes are presented. The numerical tests for SEG/EAEG model with MPI are performed on the PC-cluster. The numerical results show that the methods of single-shot (common-shot) migration and synthesized-shot migration are of practical values and can be applied to field data processing of 3D prestack depth migration.
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The BIE method is based on the numerical solution of a set of integral constraint equations which couple boundary tractions (stresses) to boundary displacements. Thus the dimensionality of the problem is reduced by one; only boundary geometry and data are discretized. Stresses at any set of selected interior points are computed following the boundary solution without any further numerical approximations. Thus, the BIE method has inherently greater resolution capability for stress gradients than does the finite element method. Conversely, the BIE method is not efficient for problems involving significant inhomogeneity such as in multi-thin-layered materials, or in elastoplasticity. Some progress in applying the BIE method to the latter problem has been made but much more work remains. Further, the BIE method is only optional for problems with significant stress risers, and only when boundary stresses are more important. Interior stress calculations are expensive, per point, and can drive the solution costs up rapidly. The current report summarizes some of the advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referring some of the much broader developmental effort. (Auth.)
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...
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...
A monotonic numerical method of incompressible Navier-Stokes equations
International Nuclear Information System (INIS)
A new monotonic approximate method for incompressible Navier-Stokes equations (INSE) is described in this paper. It discusses a method to construct a linear equations sequence, which approach INSE and easily be solved. After decomposing INSE into two parts: linear part and nonlinear part, and introduction of two unknowns and two equations into solver, the dimension of solver is increase, but well designed introduced linear equation will weaken the effect of nonlinear term in the numerical process so that residual errors can monotonically converge. This paper describes several laws to construct this kind of approaching linear equations sequence. Numerical practice verifies its monotonic behaviors. Driven cavity flows at Re=5000 and Re=10000 are examined by this numerical method in Compaq GS320. The numerical results exhibit the monotonic behaviors of residual errors. (author)
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.
LINEAR SYSTEMS ASSOCIATED WITH NUMERICAL METHODS FOR CONSTRAINED OPITMIZATION
Institute of Scientific and Technical Information of China (English)
Y. Yuan
2003-01-01
Linear systems associated with numerical methods for constrained optimization arediscussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods or trust region methods for constrainedoptimization can be expressed as similar systems of linear equations. All these linearsystems can be viewed as some kinds of approximation to the linear system derived by theLagrange-Newton method. Some properties of these linear systems are analyzed.
Asymptotic-induced numerical methods for conservation laws
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
Blended implicit methods for the numerical solution of DAE problems
Brugnano, Luigi; Magherini, Cecilia; Mugnai, Filippo
2006-05-01
Recently, a new approach for solving the discrete problems, generated by the application of block implicit methods for the numerical solution of initial value problems for ODEs, has been devised [L. Brugnano, Blended block BVMs (B3VMs): a family of economical implicit methods for ODEs, J. Comput. Appl. Math. 116 (2000) 41-62; L. Brugnano, C. Magherini, Blended implementation of block implicit methods for ODEs, Appl. Numer. Math. 42 (2002) 29-45; L. Brugnano, D. Trigiante, Block implicit methods for ODEs, in: D. Trigiante (Ed.), Recent Trends in Numerical Analysis, Nova Science Publishers, New York, 2001, pp. 81-105]. This approach is based on the so-called blended implementation of the methods, giving corresponding blended implicit methods. The latter have been implemented in the computational code BiM [L. Brugnano, C. Magherini, The BiM code for the numerical solution of ODEs, J. Comput. Appl. Math. 164-165 (2004) 145-158]. Blended implicit methods are here extended to handle the numerical solution of DAE problems, resulting in a straightforward generalization of the basic approach.
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...
Development and Comparison of Numerical Fluxes for LWDG Methods
Institute of Scientific and Technical Information of China (English)
Jianxian Qiu
2008-01-01
The discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The Lax-Wendroff time discretization procedure is an alternative method for time discretization to the popular total variation diminishing (TVD) Runge-Kutta time discretizations. In this paper, we develop fluxes for the method of DG with Lax-Wendroff time discretization procedure (LWDG) based on different numerical fluxes for finite volume or finite difference schemes, including the first-order monotone fluxes such as the Lax-Friedrichs flux, Godunov flux, the Engquist-Osher flux etc. And the second-order TVD fluxes. We systematically investigate the performance of the LWDG methods based on these differ-ent numerical fluxes for convection terms with the objective of obtaining better perfor-mance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one-dimensional system case, addressing the issues of CPU cost, ac-curacy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems.
Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence
Kritsuk, Alexei G; Collins, David; Padoan, Paolo; Norman, Michael L; Abel, Tom; Banerjee, Robi; Federrath, Christoph; Flock, Mario; Lee, Dongwook; Li, Pak Shing; Mueller, Wolf-Christian; Teyssier, Romain; Ustyugov, Sergey D; Vogel, Christian; Xu, Hao
2011-01-01
We employ simulations of supersonic super-Alfv\\'enic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high...
Numerical method for dam break problem using Godunov approach
Directory of Open Access Journals (Sweden)
A. Kartono
2013-03-01
Full Text Available In this study a numerical scheme was developed in order to overcome the problem of shock wave for the test case of dam break. The numerical scheme was based on Godunov approach of finite volume method to solve the shallow water equation. In order to expedite and improve the solution an approximate Roe’s Riemann solver associated with Monotone Upstream-centred Scheme for Conservation Laws (MUSCL was applied. The results were presented in one and two dimensional and verifications were made with analytical solution. The results are comparable and a good agreement is achieved between numerical and analytical.
Numerical method for impulse control of Piecewise Deterministic Markov Processes
de Saporta, Benoîte
2010-01-01
This paper presents a numerical method to calculate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying Markov chain defined by the post jump location and inter-arrival time. Convergence results are obtained and more importantly we are able to give a convergence rate of the algorithm. The paper is illustrated by a numerical example.
Numerov numerical method applied to the Schr\\"odinger equation
Caruso, F
2014-01-01
In this paper it is shown how to solve numerically eigenvalue problems associated to second order linear ordinary differential equations, containing also terms which depend on the variable. A didactic presentation of the Numerov Method is given and, in the sequel, it is applied to two quantum non-relativistic problems with well known analytical solutions: the simple harmonic oscillator and the hydrogen atom. The numerical results are compared to those obtained analytically.
Comparison of methods for numerical calculation of continuum damping
Bowden, George; Könies, Axel; Hole, Matthew; Gorelenkov, Nikolai; Dennis, Graham
2014-01-01
Continuum resonance damping is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this damping, particularly in the case of the toroidicity-induced shear Alfv\\'en eigenmode. This paper compares results obtained using an analytical perturbative approach with those found using resistive and complex contour numerical approaches. It is found that the perturbative method does not p...
Numerical modelling of solidification process using interval boundary element method
Directory of Open Access Journals (Sweden)
A. Piasecka Belkhayat
2008-12-01
Full Text Available In this paper an application of the interval boundary element method for solving problems with interval thermal parameters and interval source function in a system casting-mould is presented. The task is treated as a boundary-initial problem in which the crystallization model proposed by Mehl-Johnson-Avrami-Kolmogorov has been applied. The numerical solution of the problem discussed has been obtained on the basis of the interval boundary element method (IBEM. The interval Gauss elimination method with the decomposition procedure has been applied to solve the obtained interval system of equations. In the final part of the paper, results of numerical computations are shown.
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
Methods and advances in the study of aeroelasticity with uncertainties
Directory of Open Access Journals (Sweden)
Dai Yuting
2014-06-01
Full Text Available Uncertainties denote the operators which describe data error, numerical error and model error in the mathematical methods. The study of aeroelasticity with uncertainty embedded in the subsystems, such as the uncertainty in the modeling of structures and aerodynamics, has been a hot topic in the last decades. In this paper, advances of the analysis and design in aeroelasticity with uncertainty are summarized in detail. According to the non-probabilistic or probabilistic uncertainty, the developments of theories, methods and experiments with application to both robust and probabilistic aeroelasticity analysis are presented, respectively. In addition, the advances in aeroelastic design considering either probabilistic or non-probabilistic uncertainties are introduced along with aeroelastic analysis. This review focuses on the robust aeroelasticity study based on the structured singular value method, namely the μ method. It covers the numerical calculation algorithm of the structured singular value, uncertainty model construction, robust aeroelastic stability analysis algorithms, uncertainty level verification, and robust flutter boundary prediction in the flight test, etc. The key results and conclusions are explored. Finally, several promising problems on aeroelasticity with uncertainty are proposed for future investigation.
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The need for accuracy and detail, plus the availablity of the high speed computer has led to the development of many new modeling methods ranging from general purpose structural analysis finite element programs to special purpose research programs. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The paper summarizes some advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods. (Auth.)
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
The BIE (boundary integral equation) method is based on the numerical solution of a set of integral constraint equations which couple boundary tractions (stresses) to boundary displacements. Thus the dimensionality of the problem is reduced by one; only boundary geometry and data are discretized. Stresses at any set of selected interior points are computed following the boundary solution without any further numerical approximations. Thus, the BIE method has inherently greater resolution capability for stress gradients than does the finite element method. Conversely, the BIE method is not efficient for problems involving significant inhomogeneity such as in multi-thin-layered materials, or in elastoplasticity. Some progress in applyiing the BIE method to the latter problem has been made but much more work remains. Further, the BIE method is only optional for problems with significant stress risers, and only when boundary stresses are most important. Interior stress calculations are expensive, per point, and can drive the solution costs up rapidly. The current report summarizes some of the advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods
2-D Numerical Wave Tank by Boundary Element Method Using Different Numerical Techniques
Directory of Open Access Journals (Sweden)
Farid Habashi Aliabadi
2013-03-01
Full Text Available In this article, numerical modeling of a 2-D wave tank has been investigated by applying completely nonlinear condition for water surface elevation. This has been accomplished based on potential theory, the combined Eulerian-Lagrangian scheme for time marching and using boundary element method. Other physical and numerical attributes of the current work are: physical modeling in time domain, time integration by 4th order Runge-Kutta method, implementation of appropriate condition at the entrance boundary for wave generation, application of artificial dampers at the exit part of the wave tank, and ultimately numerical smoothing of the resulting free surface by using interpolation through spline functions. At the end, effective parameters on the generated wave have been analyzed and the generated wave has also been validated against the result of the linear wave theory.
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.
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…
Application of numerical analysis methods to thermoluminescence dosimetry
International Nuclear Information System (INIS)
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
A numerical test of the collective coordinate method
Energy Technology Data Exchange (ETDEWEB)
Dobrowolski, T. [Institute of Physics AP, Podchorazych 2, 30-084 Cracow (Poland)], E-mail: sfdobrow@cyf-kr.edu.pl; Tatrocki, P. [Institute of Physics AP, Podchorazych 2, 30-084 Cracow (Poland)
2008-04-14
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.
Griffiths, Graham
2010-01-01
Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by p
Advanced Bayesian Method for Planetary Surface Navigation
Center, Julian
2015-01-01
Autonomous Exploration, Inc., has developed an advanced Bayesian statistical inference method that leverages current computing technology to produce a highly accurate surface navigation system. The method combines dense stereo vision and high-speed optical flow to implement visual odometry (VO) to track faster rover movements. The Bayesian VO technique improves performance by using all image information rather than corner features only. The method determines what can be learned from each image pixel and weighs the information accordingly. This capability improves performance in shadowed areas that yield only low-contrast images. The error characteristics of the visual processing are complementary to those of a low-cost inertial measurement unit (IMU), so the combination of the two capabilities provides highly accurate navigation. The method increases NASA mission productivity by enabling faster rover speed and accuracy. On Earth, the technology will permit operation of robots and autonomous vehicles in areas where the Global Positioning System (GPS) is degraded or unavailable.
Directory of Open Access Journals (Sweden)
Deng Shuaiqi
2013-05-01
Full Text Available The high-order staggering grid Finite-Difference (FD scheme based on first-order velocity-stress elastic wave equation has been deduced. The calculation method of PML boundary condition and stability condition established in this study can be used for numerical simulation of advanced detection of elastic wave in roadway, with the obtaining of high-precision seismogram. Then we systematically analyze the polarity of vector wave field in post-source observation system. The results indicate that the relationship between the vector wave field and the polarity of direct wave is related to reflection coefficient on the interface, while the polarity relationship between horizontal and vertical components of vector wave field is related to vertical position of the interface. During data processing for advanced detection of elastic waves, the sign of the reflection coefficient on the interface ahead can be determined based on the polarity relationship between reflected wave and direct wave from the seismograms; the soft and hard rock and other geological information on both sides of the interface is thus be determined. In addition, the direction of source wave depends on polarity relationship between horizontal and vertical components of reflected wave and is used to achieve the separation of up going and down going waves.
Comparison of methods for numerical calculation of continuum damping
Bowden, George; Hole, Matthew; Gorelenkov, Nikolai; Dennis, Graham
2014-01-01
Continuum resonance damping is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this damping, particularly in the case of the toroidicity-induced shear Alfv\\'en eigenmode. This paper compares results obtained using an analytical perturbative approach with those found using resistive and complex contour numerical approaches. It is found that the perturbative method does not provide accurate agreement with reliable numerical methods for the range of parameters examined. This discrepancy exists even in the limit where damping approaches zero. When the perturbative technique is implemented using a standard finite element method, the damping estimate fails to converge with radial grid resolution. The finite elements used cannot accurately represent the eigenmode in the region of the continuum resonance, regardless of the number of radial grid points used.
Computations of film boiling. Part I: numerical method
Energy Technology Data Exchange (ETDEWEB)
Esmaeeli, A.; Tryggvason, G. [Worcester Polytechnic Institute, MA (United States). Mechanical Engineering Department
2004-12-01
A numerical method for direct simulations of boiling flows is presented. The method is similar to the front tracking/finite difference technique of Juric and Tryggvason [Int. J. Multiphase Flow 24 (1998) 387], where one set of conservation equations is used to represent the mass transfer, heat transfer, and fluid flow in the liquid and the vapor, but improves on their numerical technique by elimination of their iterative algorithm. The justification of the mathematical formulation is presented and the numerical method and the code is validated by comparison of the results with the exact solutions of a few analytical problems. A grid refinement test for film boiling on a horizontal surface shows the convergence of results. (author)
Numerical simulation methods of fires in nuclear power plants
International Nuclear Information System (INIS)
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)
Nonlinear vibrations of buckled plates by an asymptotic numerical method
Benchouaf, Lahcen; Boutyour, El Hassan
2016-03-01
This work deals with nonlinear vibrations of a buckled von Karman plate by an asymptotic numerical method and harmonic balance approach. The coupled nonlinear static and dynamic problems are transformed into a sequence of linear ones solved by a finite-element method. The static behavior of the plate is first computed. The fundamental frequency of nonlinear vibrations of the plate, about any equilibrium state, is obtained. To improve the validity range of the power series, Padé approximants are incorporated. A continuation technique is used to get the whole solution. To show the effectiveness of the proposed methodology, numerical tests are presented.
Numerical simulation methods for wave propagation through optical waveguides
International Nuclear Information System (INIS)
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 Analysis of Higher Order Discontinuous Galerkin Finite Element methods
Hartmann, Ralf
2008-01-01
After the introduction in Section 1 this lecture starts off with recalling well-known results from the numerical analysis of the continuous finite element methods. In particular, we recall a priori error estimates in the energy norm and the L2-norm including their proofs for higher order standard finite element methods of Poisson's equation in Section 2 and for the standard and the streamline diffusion finite element method of the linear advection equation in Section 3. ...
Numerical Methods for Control of Second Order Hyperbolic Equations
Kröner, Axel
2012-01-01
This thesis is devoted to the numerical treatment of optimal control problems governed by second order hyperbolic partial differential equations. Adaptive finite element methods for optimal control problems of differential equations of this type are derived using the dual weighted residual method (DWR) and separating the influences of time, space, and control discretization. Moreover, semismooth Newton methods for optimal control problems of wave equations with control constrai...
Transonic wing analysis using advanced computational methods
Henne, P. A.; Hicks, R. M.
1978-01-01
This paper discusses the application of three-dimensional computational transonic flow methods to several different types of transport wing designs. The purpose of these applications is to evaluate the basic accuracy and limitations associated with such numerical methods. The use of such computational methods for practical engineering problems can only be justified after favorable evaluations are completed. The paper summarizes a study of both the small-disturbance and the full potential technique for computing three-dimensional transonic flows. Computed three-dimensional results are compared to both experimental measurements and theoretical results. Comparisons are made not only of pressure distributions but also of lift and drag forces. Transonic drag rise characteristics are compared. Three-dimensional pressure distributions and aerodynamic forces, computed from the full potential solution, compare reasonably well with experimental results for a wide range of configurations and flow conditions.
Norman, Michael L; So, Geoffrey C; Harkness, Robsert P
2013-01-01
We describe an extension of the {\\em Enzo} code to enable the direct numerical simulation of inhomogeneous reionization in large cosmological volumes. By direct we mean all dynamical, radiative, and chemical properties are solved self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation, which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. Radiation transport is done in the grey flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the {\\em hypre} optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a gri...
Non-stationary iterative methods for solving macroeconomic numeric models
Directory of Open Access Journals (Sweden)
Bogdan OANCEA
2006-01-01
Full Text Available Macroeconometric modeling was influenced by the development of new and efficient computational techniques. Rational Expectations models, a particular class of macroeconometric models, give raise to very large systems of equations, the solution of which requires heavy computations. Therefore, such models are an interesting testing ground for the numerical methods addressed in this research. The most difficult problem is to obtain the solution of the linear system that arises during the Newton step. As an alternative to the direct methods, we propose non-stationary iterative methods, also called Krylov methods, to solve these models. Numerical experiments conducted by authors confirm the interesting features of these methods: low computational complexity and storage requirements.
Numerical methods for solving terminal optimal control problems
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
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.
International Nuclear Information System (INIS)
In the steam generator using liquid sodium, Water intensely reacts with sodium when it leaked out from a heat tube. It is important to evaluate an influence of the sodium-water reaction to, such as, heat tubes surrounding a leakage and the generator. In the past, evaluations of this phenomenon have been carried out by experiments. However it is difficult to extrapolate an effect by configuration of a heat tube or change of operating condition, etc. and experiments using sodium need incredible cost. Then quantification by a numerical method is desirable. To develop a multi component and multi phase numerical method with chemical reaction, fundamental models of a multi phase numerical method are selected with organizing previous works in this paper, as follows. Fluid model : multi fluid model, Pressure model : one pressure model, Solving method : HSMAC (Highly Simplified Maker And Cell) method. Two-dimensional two-phase flow analysis technique is developed to evaluate a validity of these models. And verification analyses are carried out shown in the following. Two-dimensional square cavity flow. Two-dimensional natural convection in a square cavity. Air blow down from a pressure vessel. Dam break-down problem. Edwards pipe blow down problem. In each verification analysis, good agreements are obtained and the validity of the models to a multi phase numerical method is confirmed. (author)
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...
Numerical methods for fluid flow in unsaturated heterogeneous tuff
International Nuclear Information System (INIS)
A numerical approach for modeling unsaturated flow is developed for heterogeneous simulations of fractured tuff generated using a geostatistical method. Cross correlations of hydrologic properties and upscaling of moisture retention curves is discussed. The approach is demonstrated for a study of infiltration at Yucca Mountain
Numerical simulation of inverse problems using LTSN method
International Nuclear Information System (INIS)
This work shows the feasibility of application of the LTSN method to solve the following inverse problems in transport theory: the determination of the incident flux knowing the scalar flux at the domain and parameter identification (cross sections). Numerical simulations are reported. (author). 8 refs, 2 tabs
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.
Advances in quantitative electroencephalogram analysis methods.
Thakor, Nitish V; Tong, Shanbao
2004-01-01
Quantitative electroencephalogram (qEEG) plays a significant role in EEG-based clinical diagnosis and studies of brain function. In past decades, various qEEG methods have been extensively studied. This article provides a detailed review of the advances in this field. qEEG methods are generally classified into linear and nonlinear approaches. The traditional qEEG approach is based on spectrum analysis, which hypothesizes that the EEG is a stationary process. EEG signals are nonstationary and nonlinear, especially in some pathological conditions. Various time-frequency representations and time-dependent measures have been proposed to address those transient and irregular events in EEG. With regard to the nonlinearity of EEG, higher order statistics and chaotic measures have been put forward. In characterizing the interactions across the cerebral cortex, an information theory-based measure such as mutual information is applied. To improve the spatial resolution, qEEG analysis has also been combined with medical imaging technology (e.g., CT, MR, and PET). With these advances, qEEG plays a very important role in basic research and clinical studies of brain injury, neurological disorders, epilepsy, sleep studies and consciousness, and brain function. PMID:15255777
Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems
Energy Technology Data Exchange (ETDEWEB)
Cai, Wei
2014-05-15
Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equations such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.
An advanced method of heterogeneous reactor theory
International Nuclear Information System (INIS)
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)
A NUMERICAL METHOD FOR FRACTIONAL INTEGRAL WITH APPLICATIONS
Institute of Scientific and Technical Information of China (English)
朱正佑; 李根国; 程昌钧
2003-01-01
A new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated. The method can be used to solve the integro-differential equation including fractional integral or fractional derivative in a long history. The difficulty of storing all history data is overcome and the error can be controlled. As application, motion equations governing the dynamical behavior of a viscoelastic Timoshenko beam with fractional derivative constitutive relation are given. The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables method Then the new numerical method is used to solve a class of weakly singular Volterra integro-differential equations which are applied to describe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmerical results are compared. It is found that they are very close.
A gyrokinetic continuum code based on the numerical Lie transform (NLT) method
Ye, Lei; Xu, Yingfeng; Xiao, Xiaotao; Dai, Zongliang; Wang, Shaojie
2016-07-01
In this work, we report a novel gyrokinetic simulation method named numerical Lie transform (NLT), which depends on a new physical model derived from the I-transform theory. In this model, the perturbed motion of a particle is decoupled from the unperturbed motion. Due to this property, the unperturbed orbit can be computed in advance and saved as numerical tables for real-time computation. A 4D tensor B-spline interpolation module is developed and applied with the semi-Lagrangian scheme to avoid operator splitting. The NLT code is verified by the Rosenbluth-Hinton test and the linear ITG Cyclone test.
Exact Boundary Derivative Formulation for Numerical Conformal Mapping Method
Wei-Lin Lo; Nan-Jing Wu; Chuin-Shan Chen; Ting-Kuei Tsay
2016-01-01
Conformal mapping is a useful technique for handling irregular geometries when applying the finite difference method to solve partial differential equations. When the mapping is from a hyperrectangular region onto a rectangular region, a specific length-to-width ratio of the rectangular region that fitted the Cauchy-Riemann equations must be satisfied. In this research, a numerical integral method is proposed to find the specific length-to-width ratio. It is conventional to employ the boundar...
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.
NUMERICAL METHODS FOR DIFFERENTIAL GAMES BASED ON PARTIAL DIFFERENTIAL EQUATIONS
Falcone, M
2006-01-01
In this paper we present some numerical methods for the solution of two-persons zero-sum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dyna...
Numerical modelling of solidification process using interval boundary element method
A. Piasecka Belkhayat
2008-01-01
In this paper an application of the interval boundary element method for solving problems with interval thermal parameters and interval source function in a system casting-mould is presented. The task is treated as a boundary-initial problem in which the crystallization model proposed by Mehl-Johnson-Avrami-Kolmogorov has been applied. The numerical solution of the problem discussed has been obtained on the basis of the interval boundary element method (IBEM). The interval Gauss elimination m...
Numerical method for dam break problem using Godunov approach
A. Kartono; Mamat, M; Ahmad, M.F.
2013-01-01
In this study a numerical scheme was developed in order to overcome the problem of shock wave for the test case of dam break. The numerical scheme was based on Godunov approach of finite volume method to solve the shallow water equation. In order to expedite and improve the solution an approximate Roe’s Riemann solver associated with Monotone Upstream-centred Scheme for Conservation Laws (MUSCL) was applied. The results were presented in one and two dimensional and verifications were made wit...
Numerical Solution of Perfect Plastic Problems with Contact: Part II - Theory and Numerical Methods
Czech Academy of Sciences Publication Activity Database
Čermák, M.; Haslinger, Jaroslav; Sysala, Stanislav
Vol. 12. Barcelona: International Centre for Numerical Methods in Engineering (CIMNE), 2013 - (Onate, E.; Owen, D.; Peric, D.; Suárez, B.), s. 1-11 ISBN 978-84-941531-5-0. [International Conference on Computational Plasticity - Fundamentals and Applications /12./. Barcelona (ES), 03.09.2013-05.09.2013] R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : perfect plasticity * contact * domain decomposition Subject RIV: BA - General Mathematics
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
Numerical method for the nonlinear Fokker-Planck equation
International Nuclear Information System (INIS)
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
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...
Stability and Accuracy Analysis for Taylor Series Numerical Method
Institute of Scientific and Technical Information of China (English)
赵丽滨; 姚振汉; 王寿梅
2004-01-01
The Taylor series numerical method (TSNM) is a time integration method for solving problems in structural dynamics. In this paper, a detailed analysis of the stability behavior and accuracy characteristics of this method is given. It is proven by a spectral decomposition method that TSNM is conditionally stable and belongs to the category of explicit time integration methods. By a similar analysis, the characteristic indicators of time integration methods, the percentage period elongation and the amplitude decay of TSNM, are derived in a closed form. The analysis plays an important role in implementing a procedure for automatic searching and finding convergence radii of TSNM. Finally, a linear single degree of freedom undamped system is analyzed to test the properties of the method.
Geometric representation for numerical stability region of linear multistep methods
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Studies the numerical stability region of linear multistep(LM) methods applied to linear test equation of the formy′(t) = ay(t) + by( t - 1), t ＞ 0, y( t ) = g( t ) - 1 ≤ t ≤ 0, a,b ∈ R, proves through delaydependent stability analysis that the intersection of stability regions of the equation and the method is not empty, in addition to approaches to the boundary of the delay differential equation(DDEs) in the limiting case of stepsize boundary of the stability region of linear multistep methods.
Numerical analysis of jet breakup behavior using particle method
International Nuclear Information System (INIS)
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 analysis of jet breakup behavior using particle method
International Nuclear Information System (INIS)
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 Waber 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 analysis of jet breakup behavior using particle method
International Nuclear Information System (INIS)
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 that 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)
A numerical predicting method on monthly seismic tendency
Institute of Scientific and Technical Information of China (English)
黎令仪; 刘德富; 康春丽; 韩延本
2004-01-01
Considering the deficiency of using vague language in predicting monthly seismic tendency, we propose a numerical predicting method in the paper, which may be more applicable to the society. The method is based on the "self-rhythm" phenomenon of earthquake activities, which calculates monthly seismic tendency through nonlinear mathematical model. The result of modeling test shows that there exists a kind of seismic cyclic process of every 7 to 8 months in Chinese mainland, and the average error from comparing monthly predicted and observed earthquake magnitudes is below 0.2. Thus the method is more applicable to the society than the experiential prediction.
Computational methods for aerodynamic design using numerical optimization
Peeters, M. F.
1983-01-01
Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.
A Numerical Method for Incompressible Flow with Heat Transfer
Sa, Jong-Youb; Kwak, Dochan
1997-01-01
A numerical method for the convective heat transfer problem is developed for low speed flow at mild temperatures. A simplified energy equation is added to the incompressible Navier-Stokes formulation by using Boussinesq approximation to account for the buoyancy force. A pseudocompressibility method is used to solve the resulting set of equations for steady-state solutions in conjunction with an approximate factorization scheme. A Neumann-type pressure boundary condition is devised to account for the interaction between pressure and temperature terms, especially near a heated or cooled solid boundary. It is shown that the present method is capable of predicting the temperature field in an incompressible flow.
Projected discrete ordinates methods for numerical transport problems
Energy Technology Data Exchange (ETDEWEB)
Larsen, E.W.
1985-01-01
A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.
Substantive provisions of Numeral-analytical boundary elements method
Directory of Open Access Journals (Sweden)
V.F. Orobey
2011-06-01
Full Text Available Substantive propositions of the new method of design calculation, that got the name "Numeral-analytical of boundary elements method", offered by authors, are brought. A method consists of development of the fundamental system of decisions (analytically and Green functions (also analytically for every examined task.For the account of certain border terms, or terms of contact between the separate modules (the separate element of the system is so named the small system of linear algebraic equalizations, that must be decided numeral, is made.Discretisation only of border of the area occupied by an object, sharply diminishes the order of the system of resolvent equalizations; there is possibility of decline of regularity of the decided task. A method is strictly reasonable mathematically, as uses the fundamental decisions of differential equalizations, and, means, within the framework of the accepted hypotheses allows to get the exact meaning of parameters of task (efforts, moving, tensions, currents, frequencies of eigentones, critical forces of loss of stability et cetera into an area.Simplicity of logic of algorithm, good convergence of decision, high stability and small accumulation of errors at numeral operations, are marked also.
A numerical method to study the dynamics of capillary fluid systems
Herrada, M. A.; Montanero, J. M.
2016-02-01
We propose a numerical approach to study both the nonlinear dynamics and linear stability of capillary fluid systems. In the nonlinear analysis, the time-dependent fluid region is mapped onto a fixed numerical domain through a coordinate transformation. The hydrodynamic equations are spatially discretized with the Chebyshev spectral collocation technique, while an implicit time advancement is performed using second-order backward finite differences. The resulting algebraic equations are solved with the iterative Newton-Raphson technique. The most novel aspect of the method is the fact that the elements of the Jacobian of the discretized system of equations are symbolic functions calculated before running the simulation. These functions are evaluated numerically in the Newton-Raphson iterations to find the solution at each time step, which reduces considerably the computing time. Besides, this numerical procedure can be easily adapted to solve the eigenvalue problem which determines the linear global modes of the capillary system. Therefore, both the nonlinear dynamics and the linear stability analysis can be conducted with essentially the same algorithm. We validate this numerical approach by studying the dynamics of a liquid bridge close to its minimum volume stability limit. The results are virtually the same as those obtained with other methods. The proposed approach proves to be much more computationally efficient than those other methods. Finally, we show the versatility of the method by calculating the linear global modes of a gravitational jet.
Second GAMM-conference on numerical methods in fluid mechanics
International Nuclear Information System (INIS)
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)
Numerical analysis of large deformation by finite element method
Directory of Open Access Journals (Sweden)
L.U. Sultanov
2013-12-01
Full Text Available In this paper a method of numerical studies of elastic-plastic bodies with finite deformations is considered. Constitutive relations obtained using the elastic potential in the flow theory. For plasticity condition Huber – Mises hardening condition criterion is applied. Incremental loading procedure is used, where allowing the variation equation is derived from the principle of virtual powers in the current configuration. For the simulation of plastic deformation the surface projection of the stress flow with iterative refinement of the current stress-strain state is applied, based on the introduction of a system of equations in resolving power of additional stresses. The numerical discretization is based on the finite element method. A solution of the test problem of elastic-plastic strain give by a circular bar, the results are compared with data, received by other authors.
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...
Spinning black hole in the puncture method: Numerical experiments
International Nuclear Information System (INIS)
The strong-field region inside a black hole needs special attention during numerical simulation. One approach for handling the problem is the moving puncture method, which has become an important tool in numerical relativity since it allows long term simulations of binary black holes. An essential component of this method is the choice of the '1+log'-slicing condition. We present an investigation of this slicing condition in rotating black hole spacetimes. We discuss how the results of the stationary Schwarzschild '1+log'-trumpet change when spin is added. This modification enables a simple and cheap algorithm for determining the spin of a non-moving black hole for this particular slicing condition. Applicability of the algorithm is verified in simulations of single black hole, binary neutron star and mixed binary simulations
Numerical methods for acquisition and analysis of vibration tests
International Nuclear Information System (INIS)
The S.I.D.E.X. is a digital computer assisted facility for Data acquisition and Data processing. It is designed for sine wave or random environment tests, mechanical or acoustical vibrations, shock waves. The mathematical principles and the system configuration have been described in the CEA file nb R-3666. The present one describes the numerical methods and the programs available up to now. Some examples of results obtained are shown at the end. (authors)
Numerical method for Darcy flow derived using Discrete Exterior Calculus
Hirani, Anil N.; Nakshatrala, Kalyana B.; Chaudhry, Jehanzeb H.
2008-01-01
We derive a numerical method for Darcy flow, hence 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 equa...
Interfacial Numerical Dispersion and New Conformal FDTD Method
Fisher, Axman
2011-01-01
This article shows the interfacial relation in electrodynamics shall be corrected in discrete grid form which can be seen as certain numerical dispersion beyond the usual bulk type. Further we construct a lossy conductor model to illustrate how to simulate more general material other than traditional PEC or simple dielectrics, by a new conformal FDTD method which main considers the effects of penetrative depth and the distribution of free bulk electric charge and current.
Thermal-hydraulics numerical analyses of Pebble Bed Advanced High Temperature Reactor hot channel
International Nuclear Information System (INIS)
Background: The thermal hydraulics behavior of the Pebble Bed Advanced High Temperature Reactor (PB-AHTR) hot channel was studied. Purpose: We aim to analyze the thermal-hydraulics behavior of the PB-AHTR, such as pressure drop, temperature distribution of coolant and pebble bed as well as thermal removal capacity in the condition of loss of partial coolant. Methods: We used a modified FLUENT code which was coupled with a local non-equilibrium porous media model by introducing a User Defined Scalar (UDS) in the calculation domain of the reactor core and subjoining different resistance terms (Ergun and KTA) to calculate the temperature of coolant, solid phase of pebble bed and pebble center in the core. Results: Computational results showed that the resistance factor has great influence on pressure drop and velocity distribution, but less impact on the temperature of coolant, solid phase of pebble bed and pebble center. We also confirmed the heat removal capacity of the PB-AHTR in the condition of nominal and loss of partial coolant conditions. Conclusion: The numerical analyses results can provide a useful proposal to optimize the design of PB-AHTR. (authors)
Numerical Method for Wave Forces Acting on Partially Perforated Caisson
Institute of Scientific and Technical Information of China (English)
姜峰; 唐晓成; 金钊; 张莉; 陈洪洲
2015-01-01
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.
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)
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 method of thermal design of power cables
Energy Technology Data Exchange (ETDEWEB)
Bryukhanov, O.N.; Trigorlyy, S.V.
1985-05-01
Increasing the accuracy of computation of permissible current loads in cables requires that thermal calculations be performed considering the actual distribution of temperatures in the cables. An analysis of methods of thermal design of cables showed that numerical methods allowing most complete consideration of various heat exchange factors are superior. The authors suggest the use of the method of finite elements to study thermal states of multiple-conductor power cables laid in various ways. As an example, thermal calculation of three-conductor cable with circular conductors is studied. For a number of cables the permissible current loads calculated by the method of finite elements are greater than those established by the standards documents of calculated according to previous methods.
Numerical computation of FCT equilibria by inverse equilibrium method
International Nuclear Information System (INIS)
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 to Predict Slip Length in Turbulent Channel Flow
Directory of Open Access Journals (Sweden)
Nowrouz Mohammad Nouri
2016-01-01
Full Text Available In the present research work, we introduce a new method for estimating the slip length on superhydrophobic surfaces. Hence, a dynamic force is added to momentum equations and velocity boundary condition is rewritten in a new form. Laminar and turbulent channel flows are considered and two force functions are used with different profiles to investigate their effects on results. The turbulent channel flow is considered at Re 180 and the Large Eddy Simulation (LES method has been applied to analyze this flow. All results indicate that this method can predict the streamwise slip length with a good accuracy, which is comparable with the Navier’s method. So, using this numerical solution and also measuring pressure drop and mass flow rate in the channel, slip length can be calculated. Consequently, the errors and difficulties of slip length measurements in typical methods such as AFM and μPIV would be eliminated.
Numerical experiment on finite element method for matching data
International Nuclear Information System (INIS)
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)
Comparison and verification of numerical reconstruction methods in digital holography
Liu, Changgeng; Wang, Dayong; Zhang, Yizhuo
2009-10-01
The expressions for the reconstructed field from the sample of the diffracted wave, which is produced by illuminating an object, are found by use of different diffraction integrals in the digital holography. The numerical reconstruction methods that truncate and sample this field are compared in overlapping quality, accuracy, pixel resolution, computation window, and speed. The fast Fourier transform (FFT)-based direct integration method for the Fresnel integral and the modified FFT-based direct integration method for the Rayleigh-Sommerfeld integral have similar overlapping quality and can flexibly control pixel resolution and computation window size. Meanwhile, the FFT-based angular spectrum method is superior to the FFT-based convolution method in accuracy and speed. The experimental results are presented to verify these consequences.
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.
Numerical Simulations of Equiaxed Dendrite Growth Using Phase Field Method
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growthin a metallic system. In this paper, the equiaxed dendrite evolution during the solidification of a pure material wasnumerically simulated using the phase field model. The equiaxed dendrite growth in a two-dimensional square domainof undercooled melt (nickel) with four-fold anisotropy was simulated. The phase field model equations was solvedusing the explicit finite difference method on a uniform mesh. The formation of various equiaxed dendrite patternswas shown by a series of simulations, and the effect of anisotropy on equiaxed dendrite morphology was investigated.
Integrated numerical methods for hypersonic aircraft cooling systems analysis
Petley, Dennis H.; Jones, Stuart C.; Dziedzic, William M.
1992-01-01
Numerical methods have been developed for the analysis of hypersonic aircraft cooling systems. A general purpose finite difference thermal analysis code is used to determine areas which must be cooled. Complex cooling networks of series and parallel flow can be analyzed using a finite difference computer program. Both internal fluid flow and heat transfer are analyzed, because increased heat flow causes a decrease in the flow of the coolant. The steady state solution is a successive point iterative method. The transient analysis uses implicit forward-backward differencing. Several examples of the use of the program in studies of hypersonic aircraft and rockets are provided.
Numerical simulation of production from tight-gas reservoirs by advanced stimulation technologies
Friedel, Torsten
2009-01-01
The present thesis focusses on two main issues: (i) the development of a multi-phase simulation tool for the characteristics of tight-gas reservoirs, and (ii) the investigation of advanced stimulation techniques. The latter mainly implies the analysis of certain damaging mechanisms, as well as the derivation of general modelling guidelines for fractured wells and underbalanced drilling. A special simulation tool is developed, realised in a Fortran-MATLAB coupling. The numerical model is based...
The Numerical Tours of Signal Processing - Advanced Computational Signal and Image Processing
Peyré, Gabriel
2011-01-01
The Numerical Tours of Signal Processing is an online collection of tutorials to learn advanced computational signal and image processing. These tours allow one to follow a step by step Matlab or Scilab implementation of many important processing algorithms. This implementation is commented and the connexions with the relevant mathematical notions are exposed. These algorithms are applied to various signal, image, movie and 3D mesh datasets. These tours are suitable for practitioners in the f...
Varma, Rajendra Kumar
2013-01-01
Tese de doutoramento em Estrutural Engenharia This work deals with material modelling and numerical implementation for nonlinear finite element analysis of reinforced concrete (RC) structures. Since the behaviour of concrete and steel being crucial for any RC structure under loading, uniaxial cyclic constitutive models for both were implemented in FEMIX, finite element software. Various advanced materials have been developed with specific purposes, like fibre reinforced c...
Numerical methods for the Poisson-Fermi equation in electrolytes
Liu, Jinn-Liang
2013-08-01
The Poisson-Fermi equation proposed by Bazant, Storey, and Kornyshev [Phys. Rev. Lett. 106 (2011) 046102] for ionic liquids is applied to and numerically studied for electrolytes and biological ion channels in three-dimensional space. This is a fourth-order nonlinear PDE that deals with both steric and correlation effects of all ions and solvent molecules involved in a model system. The Fermi distribution follows from classical lattice models of configurational entropy of finite size ions and solvent molecules and hence prevents the long and outstanding problem of unphysical divergence predicted by the Gouy-Chapman model at large potentials due to the Boltzmann distribution of point charges. The equation reduces to Poisson-Boltzmann if the correlation length vanishes. A simplified matched interface and boundary method exhibiting optimal convergence is first developed for this equation by using a gramicidin A channel model that illustrates challenging issues associated with the geometric singularities of molecular surfaces of channel proteins in realistic 3D simulations. Various numerical methods then follow to tackle a range of numerical problems concerning the fourth-order term, nonlinearity, stability, efficiency, and effectiveness. The most significant feature of the Poisson-Fermi equation, namely, its inclusion of steric and correlation effects, is demonstrated by showing good agreement with Monte Carlo simulation data for a charged wall model and an L type calcium channel model.
7 CFR 27.92 - Method of payment; advance deposit.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Method of payment; advance deposit. 27.92 Section 27... Micronaire § 27.92 Method of payment; advance deposit. Any payment or advance deposit under this subpart...,” and may not be made in cash except in cases where the total payment or deposit does not exceed...
Testing the numerical method for one-dimensional shock treatment
International Nuclear Information System (INIS)
In the early 80's the SMUP computer code was developed at the Jozef Stefan Institute for simulation of two-phase flow in steam generators. It was suitable only for steady-state problems and was unable to simulate transient behavior. In this paper, efforts are presented to find suitable numerical method to renew the old SMUP computer code. The obsolete numerical code has to be replaced with a more efficient one that would be able to treat time-dependent problems. It also has to ensure accurate solution during shock propagation. One-dimensional shock propagation in a tube were studied at zero viscosity. To simplify the equation of state the ideal gas was chosen as a working fluid. Stability margins in the form of transport matrix eigenvalues were calculated. Results were found to be close to those already published.(author)
A numerical method for calculating resonant-state wave functions
International Nuclear Information System (INIS)
An initial-value method of numerical solving of Sturm-Liouville problems is applied to find the solution to the Schroedinger equation which corresponds to a resonance situation. The depth of the nuclear potential is regarded as an eigenvalue, which is obtained by iteration. Having established the nuclear potential, the resonant wavefunction is generated by integrating numerically the Schroedinger differential equation inwards from larger radii using the initial conditions of G(r), where G is the irregular Coulomb function. Because the solution is exactly on resonance, nosearching for the phase shift is required. Consequently, the suggested procedure may be employed even if the resonance widths are extremely narrow (e.g., 10-16 MeV)
Time-dependent corona models - A numerical method
Korevaar, P.; van Leer, B.
1988-07-01
A time-dependent numerical method for calculating gas flows is described. The method is implicit and especially suitable for finding stationary flow solutions. Although the method is general in its application to ideal compressible fluids, this paper applies it to a stellar atmosphere, heated to coronal temperatures by dissipation of mechanical energy. The integration scheme is based on conservative upwind spatial differencing. The upwind switching is provided by Van Leer's method of differentiable flux-splitting. It is shown that the code can handle large differences in density: up to 14 orders of magnitude. Special attention is paid to the boundary conditions, which are made completely transparent to disturbances. Besides some test-results, converged solutions for various values of the initial mechanical flux are presented which are in good agreement with previous time-independent calculations.
Numerical methods for optimal control problems with state constraints
Pytlak, Radosław
1999-01-01
While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.
Numerical method of slope failure probability based on Bishop model
Institute of Scientific and Technical Information of China (English)
SU Yong-hua; ZHAO Ming-hua; ZHANG Yue-ying
2008-01-01
Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.
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. PMID:26220303
Initial investigations of spectral methods for numerical plasma kinetic theory
International Nuclear Information System (INIS)
Spectral methods offer an attractive method for the accurate numerical solution of problems without dissipation, but do not necessarily ensure the numerical conservation of physically conserved quantities. However, by exploiting the structure of infinite dimensional Hamiltonian systems such as the Vlasov-Maxwell equations it has proven possible to produce a new class of semi-discrete spectral methods that exactly preserve many conservation laws for such systems. In the Vlasov-Maxwell case, the Hamiltonian ∫∫ 1/2 mu2 line-integral(χ, u, t) dχ du + 1/2 ∫ E2 (χ) dχ, the total number of particles ∫∫ line-integral (χ, u, t) dχ du, and the square integral of the distribution function ∫∫ line-integral 2(χ, u, t) dχx du can all be exactly conserved in the semi-discrete model, independently of the number of modes retained in the spectral expansion. The key idea is to discretize not the governing equations of evolution-the Vlasov-Maxwell equations-themselves, but instead to discretize the Poisson bracket that generates those equations from the Hamiltonian. In this way, the semi-discrete equations that result are without dissipation and can actually be written in a Hamiltonian form. These ideas have been used to develop a spectral element code based on polynomial collocation at the Gauss-Radau-Legendre points within each phase space element; the resulting code has been used to test a variety of explicit and implicit time stepping schemes, and the numerical tests show excellent conservation for modest numbers of unknowns, for example 10-2% change in the total number of particles after 100,000 time steps of only 1,500 unknowns. Further, these methods do not suffer from any dispersion or dissipation of delicate phase space structures such as trapped particle distributions
A numerical method to compute interior transmission eigenvalues
International Nuclear Information System (INIS)
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)
Convergence and accuracy of numerical methods for trajectory calculations
International Nuclear Information System (INIS)
Computation of trajectories by a kinematic method requires the numerical solution of the differential equation by which the trajectory is defined. A widely used method is the iterative scheme of Petterssen which has second-order accuracy. The convergence and accuracy of this scheme is investigated for some simple flow types where analytical solutions are available. The results are discussed in comparison to other methods, especially a method similar to the Patterssen scheme, which has been recommended for use in semi-Lagrangian advection schemes. The truncation error in trajectory calculations should be kept about one order of magnitude smaller than the total uncertainty, which is mainly due to analysis errors and limited resolution of the wind data. It is shown that for trajectory calculations based on the typical output of current numerical weather prediction models or comparable data, this requires a time step 15% of the time step necessary to achieve convergence. If a fixed time step is used, it should not exceed about 0.5 h. Flexible time steps, based on the estimate of the truncation error which is provided by the difference between the first and the second iteration, are an attractive alternative. 26 refs., 8 figs
Key issues for numerical methods in neptune project
International Nuclear Information System (INIS)
Full text of publication follows:We will try to present herein the main issues of our investigation in numerical methods for two-phase flow modeling, within the framework of the NEPTUNE project, which benefits from both contributions of CEA and EDF. These may be recast in five work packages. The first two are devoted to the mathematical and numerical modeling of two-phase flows with interfaces and the two-fluid two-pressure approach. This in particular includes investigation of relaxation methods in order to establish correct links with standard two-fluid models, which are the core of the third work package. Computations of the interaction of shock waves with bubbles will be presented. Some new results concerning two-fluid and three-field flow modeling will also be briefly presented. Part of the work in the third work package concerns benchmarking, and comparison with several hyperbolic solvers, but also improvement of numerical treatment of source terms, multi-field models and suitable boundary conditions. The fourth one, which deals with the interfacial coupling of codes, is probably the most important one since it requires connecting all models together. Since little attention has been paid to this crucial point, part of the focus will be given in this paper on the coupling of equations of state, one-dimensional and three-dimensional codes, porous approach and free medium approach, but also on ongoing work concerning relaxed and un-relaxed hyperbolic two-phase flow models. The fifth work package gathers all classical contributions in numerical methods, including: recent applications of fictitious domain methods; preconditioning of so-called 'low Mach number' two-phase flows (with applications to the motion of rising bubbles in water); parallel and multigrid techniques (with applications to steam generators in nuclear power plants); Finite Volume Element methods (with applications to the standard two-fluid models); construction and validation of new exact or
Introduction to numerical and analytical methods with Matlab for engineers and scientists
Bober, William
2013-01-01
The text covers useful numerical methods, including interpolation, Simpson’s rule on integration, the Gauss elimination method for solving systems of linear algebraic equations, the Runge-Kutta method for solving ordinary differential equations, and the search method in combination with the bisection method for obtaining the roots of transcendental and polynomial equations. It also highlights MATLAB’s built-in functions. These include interp1 function, the quad and dblquad functions, the inv function, the ode45 function, the fzero function, and many others. The second half of the text covers more advanced topics, including the iteration method for solving pipe flow problems, the Hardy-Cross method for solving flow rates in a pipe network, separation of variables for solving partial differential equations, and the use of Laplace transforms to solve both ordinary and partial differential equations.
Numerical method of characteristics for one-dimensional blood flow
Acosta, Sebastian; Riviere, Beatrice; Penny, Daniel J; Rusin, Craig G
2014-01-01
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time-step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the ...
A fast direct numerical simulation method for characterising hydraulic roughness
Chung, Daniel; MacDonald, Michael; Hutchins, Nicholas; Ooi, Andrew
2015-01-01
We describe a fast direct numerical simulation (DNS) method that promises to directly characterise the hydraulic roughness of any given rough surface, from the hydraulically smooth to the fully rough regime. The method circumvents the unfavourable computational cost associated with simulating high-Reynolds-number flows by employing minimal-span channels (Jimenez & Moin 1991). Proof-of-concept simulations demonstrate that flows in minimal-span channels are sufficient for capturing the downward velocity shift, that is, the Hama roughness function, predicted by flows in full-span channels. We consider two sets of simulations, first with modelled roughness imposed by body forces, and second with explicit roughness described by roughness-conforming grids. Owing to the minimal cost, we are able to conduct DNSs with increasing roughness Reynolds numbers while maintaining a fixed blockage ratio, as is typical in full-scale applications. The present method promises a practical, fast and accurate tool for character...
Numerical methods for high-dimensional probability density function equations
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016-01-01
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Numerical Iterative Methods Solving three-phase Multilevel Voltage Converter
Czech Academy of Sciences Publication Activity Database
Kujan, Petr
Vol. IEEE CACSC CFP10CAC-CDR. Yokohama: IEEE, 2010, s. 1801-1806. ISBN 978-1-4244-5355-9. [The 10th IEEE International Symposium on Computer - Aided Control System Design . Yokohama, Kanagawa (JP), 08.09.2010-10.09.2010] R&D Projects: GA MŠk(CZ) 1M0567 Grant ostatní: GA ČR(CZ) GPP103/10/P323 Institutional research plan: CEZ:AV0Z10750506 Keywords : multilevel converter * numerical methods * optimal PWM * selective harmonic elimination Subject RIV: BC - Control Systems Theory
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.
First Numerical Implementation of the Loop-Tree Duality Method
Buchta, Sebastian
2015-01-01
The Loop-Tree Duality (LTD) is a novel perturbative method in QFT that establishes a relation between loop-level and tree-level amplitudes, which gives rise to the idea of treating them simultaneously in a common Monte Carlo. Initially introduced for one-loop scalar integrals, the applicability of the LTD has been expanded to higher order loops and Feynman graphs beyond simple poles. For the first time, a numerical implementation relying on the LTD was realized in the form of a computer program that calculates one-loop scattering amplitudes. We present details on the employed contour deformation as well as results for scalar and tensor integrals.
"Advanced Manufacturing Methods for Systems of Nanospacecrafts".
Rochus, Pierre
2014-01-01
Space instrumentation and Space Environmental testing activities at CSL Dreams, a priori expectations and space specificities Advanced Manufacturing Techniques considered in our studies First steps realizations 15 years ago More concrete and more recent examples Conclusions and future activities
Various numerical simulation methods for acoustic emission in rock
International Nuclear Information System (INIS)
Acoustic Emission (AE) or Microseismicity (MS) is a very useful method to understand fracture mechanism and to predict serious rock fracture like rockburst. This method can be applied to monitor reservoirs where water and gas are injected, for example, in underground sequestration of carbon dioxide and in Enhanced Oil Recovery (EOR) of petroleum industry. If a numerical simulation helps to interpret AE monitoring results, AE monitoring would become much more powerful tool for the rock engineering. Thus, in this paper, the authors review various methods that can simulate occurrence of AE events incorporating inhomogeneity of rock. A code of Finite Element Method (FEM) developed by Tang et al., those of Boundary Element Method (BEM) by Napier's and Stephansson's groups and those of Distinct Element Method (DEM) by Shimizu et. al., Fakhimi et al. and Cai et al. are briefly introduced as simulation methods of brittle fracture like rockburst. For simulation of AE events induced by water or gas injection, DEM incorporating Fluid Flow Algorism by Shimizu et al. are introduced, with showing their simulation results of hydraulic fracturing. (author)
International Nuclear Information System (INIS)
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
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.
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 METHOD AND RANDOM ANALYSIS OF CEMENT CONCRETE EXPANSION
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The numerical method and random analysis of cement concrete expansion are given. A mathematical procedure is presented which includes the nonlinear characteristics of the concrete. An expression is presented to predict the linear restrained expansion of expansive concrete bar restrained by a steel rod. The results indicate a rapid change in strains and stresses within initial days, after which the change gradually decreases. A reliable and accurate method of predicting the behavior of the concrete bulkheads in drifts is presented here. Extensive sensitivity and parametric studies have been performed. The random density distributions of expansive concrete are given based on the restricted or unrestricted condition. These studies show that the bulkhead stress fields are largely influenced by the early modulus of the concrete and the randomness of the ultimate unrestrained expansion of the concrete.
A NUMERICAL METHOD BASED ENCRYPTION ALGORITHM WITH STEGANOGRAPHY
Directory of Open Access Journals (Sweden)
Amartya Ghosh
2013-02-01
Full Text Available Now-a-days many encryption algorithms have been proposed for network security. In this paper, a new cryptographic algorithm for network security is proposed to assist the effectiveness of network security. Here symmetric key concept instead of public key is considered to develop the encryption – decryption algorithm. Also, to give more security in the algorithm, the idea of one way function alongwith Newton’s method is applied as a secret key to the proposed work as well as Digital Signature Standard (DSS technology is used to send the key. Moreover, steganography is used to hide the cipher within a picture in encryption algorithm. In brief, a numerical method based secret key encryption – decryption algorithm is developed using steganography to enhance the network security.
New numerical methods for nuclear cross section processing
International Nuclear Information System (INIS)
Nuclear data allow to describe how a particle interacts with matter. These data are therefore at the basis of neutron transport and reactor physics calculations. Once measured and evaluated, they are given in libraries as a list of parameters. Before they can be used in neutron transport calculations, processing is required which includes taking into account several physical phenomena. This can be done by several softwares, such as NJOY, which all have the drawback to use old numerical methods derived from the same algorithms. For nuclear safety applications, it is important to rely on independent methods, to have a comparison point and to isolate the effects of the treatment on the final results. Moreover, it is important to properly master processing accuracy during its different steps. The objective of this PhD is then to develop independent numerical methods that can guarantee nuclear data processing within a given precision and to implement them practically, with the creation of the GAIA software. Our first step was the reconstruction of cross sections from the parameters given in libraries, with different approximations of the R-matrix theory. Reconstruction using the general formalism, without any approximation, has also been implemented, which has required the development of a new method to calculate the R-matrix. Tests have been performed on all existing formalisms, including the newest one. They have shown a good agreement between GAIA and NJOY. Reconstruction of angular differential cross sections directly from R-matrix parameters, using the Blatt-Biedenharn formula, has also been implemented and tested. The cross sections we have obtained at this point correspond to a target nucleus at absolute zero temperature. Because of thermal agitation, these cross sections are subject to a Doppler effect that is taken into account by integrating them with Solbrig's kernel. Our second step was then to calculate this integral. First, we have elaborated and
Damped time advance methods for particles and EM fields
International Nuclear Information System (INIS)
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 Project
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...
A method for improving time-stepping numerics
Williams, P. D.
2012-04-01
In contemporary numerical simulations of the atmosphere, evidence suggests that time-stepping errors may be a significant component of total model error, on both weather and climate time-scales. This presentation will review the available evidence, and will then suggest a simple but effective method for substantially improving the time-stepping numerics at no extra computational expense. The most common time-stepping method is the leapfrog scheme combined with the Robert-Asselin (RA) filter. This method is used in the following atmospheric models (and many more): ECHAM, MAECHAM, MM5, CAM, MESO-NH, HIRLAM, KMCM, LIMA, SPEEDY, IGCM, PUMA, COSMO, FSU-GSM, FSU-NRSM, NCEP-GFS, NCEP-RSM, NSEAM, NOGAPS, RAMS, and CCSR/NIES-AGCM. Although the RA filter controls the time-splitting instability in these models, it also introduces non-physical damping and reduces the accuracy. This presentation proposes a simple modification to the RA filter. The modification has become known as the RAW filter (Williams 2011). When used in conjunction with the leapfrog scheme, the RAW filter eliminates the non-physical damping and increases the amplitude accuracy by two orders, yielding third-order accuracy. (The phase accuracy remains second-order.) The RAW filter can easily be incorporated into existing models, typically via the insertion of just a single line of code. Better simulations are obtained at no extra computational expense. Results will be shown from recent implementations of the RAW filter in various atmospheric models, including SPEEDY and COSMO. For example, in SPEEDY, the skill of weather forecasts is found to be significantly improved. In particular, in tropical surface pressure predictions, five-day forecasts made using the RAW filter have approximately the same skill as four-day forecasts made using the RA filter (Amezcua, Kalnay & Williams 2011). These improvements are encouraging for the use of the RAW filter in other models.
Numerical study of Alfvén eigenmodes in the Experimental Advanced Superconducting Tokamak
International Nuclear Information System (INIS)
Alfvén eigenmodes in up-down asymmetric tokamak equilibria are studied by a new magnetohydrodynamic eigenvalue code. The code is verified with the NOVA code for the Solovév equilibrium and then is used to study Alfvén eigenmodes in a up-down asymmetric equilibrium of the Experimental Advanced Superconducting Tokamak. The frequency and mode structure of toroidicity-induced Alfvén eigenmodes are calculated. It is demonstrated numerically that up-down asymmetry induces phase variation in the eigenfunction across the major radius on the midplane
Verifying an advanced non-linear numerical model for retaining structures
Czech Academy of Sciences Publication Activity Database
Koudelka, Petr; Koudelka, T.
The Netherlands : Taylor & Francis/Balkema, 2006 - (Schweiger, H.), s. 51-58 ISBN 0-415-40477-0. [IC Physical modelling in geotechnics 2006/6./. Hong Kong (HK), 28.07.2006-02.08.2006] R&D Projects: GA AV ČR(CZ) IAA2071302; GA ČR(CZ) GA103/05/2130 Institutional research plan: CEZ:AV0Z20710524 Keywords : advanced numerical model * physical experiment * verifying constitutive relations * passive lateral pressure of granular material Subject RIV: BM - Solid Matter Physics ; Magnetism
Shock Simulation of the Optics Mirror Assembly By Numerical Method
Directory of Open Access Journals (Sweden)
Mr. Brijeshkumar Patel
2015-09-01
Full Text Available Satellite faces many extreme types of loading throughout their life time from the harsh launch environment to the critical space environment. Launch load mainly dynamic is the main design concern for space structure. Shocks are the one of the most critical dynamic load occurs in spacecraft. Optics Mirror Assembly (OMA is used in the telescope of the satellite. The telescope performance relies on dimensional control & the geometric positioning of the mirror, pointing accuracy and controlled surface deformation of the mirror; Mirror fixation device (MFD is used for controlling all these factors. It should not distort due to launch loads mainly shocks as well as loads during operation of the telescope. In the present work an attempt has been made to perform experimental and computational analysis of the shock load on Optics Mirror Assembly. The FE modal for Shock Analysis purpose has been analysed with a specific Linear Transient Response Analysis in order to obtain the time history of acceleration in several output points. The analysis has been conducted over the time interval 0 to 62 ms and frequency band between 10 - 10 KHz. In order to verify the feasibility and reliability of the numerical (Implicit Finite Element Code, Nastran analysis, the numerical results obtained by Nastran have been compared with those obtained experimentally in the form of SRS. The overall outcome of the simulation method has proven its reliability in simulating Satellite payloads subjected to shocks.
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
A reduced complexity numerical method for optimal gate synthesis
Sridharan, Srinivas; James, Matthew R; McEneaney, William M; 10.1103/PhysRevA.82.042319}
2010-01-01
Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate design problem is equivalent to the solution of an associated optimal control problem, the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality free techniques) that determine the optimal control thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, used in previous literature. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on $SU(4)$- a problem that is com...
The Numerical Simulation of Ship Waves using Cartesian Grid Methods
Sussman, Mark
2014-01-01
Two different cartesian-grid methods are used to simulate the flow around the DDG 5415. The first technique uses a "coupled level-set and volume-of-fluid" (CLS) technique to model the free-surface interface. The no-flux boundary condition on the hull is imposed using a finite-volume technique. The second technique uses a level-set technique (LS) to model the free-surface interface. A body-force technique is used to impose the hull boundary condition. The predictions of both numerical techniques are compared to whisker-probe measurements of the DDG 5415. The level-set technique is also used to investigate the breakup of a two-dimensional spray sheet.
Intelligent numerical methods II applications to multivariate fractional calculus
Anastassiou, George A
2016-01-01
In this short monograph Newton-like and other similar numerical methods with applications to solving multivariate equations are developed, which involve Caputo type fractional mixed partial derivatives and multivariate fractional Riemann-Liouville integral operators. These are studied for the first time in the literature. The chapters are self-contained and can be read independently. 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 short monograph is suitable for researchers, graduate students, to be used in graduate classes and seminars of the above subjects, also to be in all science and engineering libraries.
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...... accuracy, also they lack the potential to predict the pore pressure developed in the soil. Therefore, it is necessary to carry out a ground response analysis to obtain pore pressures and shear stresses in the soil due to earthquake loading. Using soil historical, geological and compositional criteria, a...... zone of the corridor of Tabriz urban railway line 2 susceptible to liquefaction was recognized. Then, using numerical analysis and cyclic stress method using QUAKE/W finite element code, soil liquefaction potential in susceptible zone was evaluated based on design earthquake....
Methods testing electrodes for advanced batteries
Czech Academy of Sciences Publication Activity Database
Novák, V.; Vondrák, Jiří
Vol. 2. Brno: Akademické nakladatelství CERM, 2000 - (Vondrák, J.; Sedlaříková, M.), s. 13.1-13.4 ISBN 80-214-1615-7. [Advanced Batteries and Accumulators /1./. Brno (CZ), 28.08.2000-01.09.2000] R&D Projects: GA AV ČR IAA4032002 Institutional research plan: CEZ:AV0Z4032918 Keywords : electrodes * batteries * electrochemistry Subject RIV: CG - Electrochemistry
a Numerical Method for Stability Analysis of Pinned Flexible Mechanisms
Beale, D. G.; Lee, S. W.
1996-05-01
A technique is presented to investigate the stability of mechanisms with pin-jointed flexible members. The method relies on a special floating frame from which elastic link co-ordinates are defined. Energies are easily developed for use in a Lagrange equation formulation, leading to a set of non-linear and mixed ordinary differential-algebraic equations of motion with constraints. Stability and bifurcation analysis is handled using a numerical procedure (generalized co-ordinate partitioning) that avoids the tedious and difficult task of analytically reducing the system of equations to a number equalling the system degrees of freedom. The proposed method was then applied to (1) a slider-crank mechanism with a flexible connecting rod and crank of constant rotational speed, and (2) a four-bar linkage with a flexible coupler with a constant speed crank. In both cases, a single pinned-pinned beam bending mode is employed to develop resonance curves and stability boundaries in the crank length-crank speed parameter plane. Flip and fold bifurcations are common occurrences in both mechanisms. The accuracy of the proposed method was also verified by comparison with previous experimental results [1].
Introduction to finite-difference methods for numerical fluid dynamics
Energy Technology Data Exchange (ETDEWEB)
Scannapieco, E.; Harlow, F.H.
1995-09-01
This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.
International Nuclear Information System (INIS)
The weather is a chaotic system. Small errors in the initial conditions of a forecast grow rapidly and predictability is limited by model errors due to the approximate simulation of atmospheric processes of the state-of-the-art numerical models. These two sources of uncertainties limit the skill of single, deterministic forecasts in an unpredictable way, with days of high/poor quality forecasts randomly followed by days of high/poor quality forecasts. Two recent advances in numerical weather prediction, the operational implementation of ensemble prediction systems and the development of objective procedures to target adaptive observations are discussed. These advances have been thought and designed to reduce forecast errors and to provide forecasters with more complete weather predictions. Ensemble prediction is a feasible method to estimate the probability distribution function of forecast states. Ensemble systems can provide forecasters with an objective way to predict the skill of single deterministic forecasts. Adaptive observations targeted in sensitive regions can reduce the initial conditions' uncertainties, and thus decrease forecast errors. Singular vectors that identify unstable regions of the atmospheric flow can be used to identify optimal ways to adapt the atmospheric observing system. The European Centre for Medium-Range Weather Forecasts Ensemble Prediction System is described, and targeting experiments are discussed
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
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).
Class of numerical methods for differential-algebraic systems with discontinuous right-hand sides
Institute of Scientific and Technical Information of China (English)
Leng Xin; Song Xiaoqiu; Liu Degui
2005-01-01
Numerical methods for Differential-Algebraic systems with discontinuous right-hand sides is discussed. A class of continuous Rosenbrock methods are constructed, and numerical experiments show that the continuous Rosenbrock methods are effective. Applying the methods, a fast and high-precision numerical algorithm is given to deal with typical discontinuous parts, which occur frequently in differential-algebraic systems(DAS).
Numerical Weather Predictions Evaluation Using Spatial Verification Methods
Tegoulias, I.; Pytharoulis, I.; Kotsopoulos, S.; Kartsios, S.; Bampzelis, D.; Karacostas, T.
2014-12-01
During the last years high-resolution numerical weather prediction simulations have been used to examine meteorological events with increased convective activity. Traditional verification methods do not provide the desired level of information to evaluate those high-resolution simulations. To assess those limitations new spatial verification methods have been proposed. In the present study an attempt is made to estimate the ability of the WRF model (WRF -ARW ver3.5.1) to reproduce selected days with high convective activity during the year 2010 using those feature-based verification methods. Three model domains, covering Europe, the Mediterranean Sea and northern Africa (d01), the wider area of Greece (d02) and central Greece - Thessaly region (d03) are used at horizontal grid-spacings of 15km, 5km and 1km respectively. By alternating microphysics (Ferrier, WSM6, Goddard), boundary layer (YSU, MYJ) and cumulus convection (Kain--Fritsch, BMJ) schemes, a set of twelve model setups is obtained. The results of those simulations are evaluated against data obtained using a C-Band (5cm) radar located at the centre of the innermost domain. Spatial characteristics are well captured but with a variable time lag between simulation results and radar data. Acknowledgements: This research is cofinanced by the European Union (European Regional Development Fund) and Greek national funds, through the action "COOPERATION 2011: Partnerships of Production and Research Institutions in Focused Research and Technology Sectors" (contract number 11SYN_8_1088 - DAPHNE) in the framework of the operational programme "Competitiveness and Entrepreneurship" and Regions in Transition (OPC II, NSRF 2007--2013).
International Nuclear Information System (INIS)
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)
Energy Technology Data Exchange (ETDEWEB)
Pember, R.B. (Lawrence Livermore National Lab., CA (United States))
1993-07-01
A higher-order Godunov method is presented for hyperbolic systems of conservation laws with stiff, relaxing source terms. The goal is to develop a Godunov method that produces higher-order accurate solutions using time and space increments governed solely by the nonstiff part of the system, i.e., without fully resolving the effect of the stiff source terms. It is assumed that the system satisfies a certain subcharacteristic'' condition. The method is a semi-implicit form of a method developed by Colella for hyperbolic conservation laws with nonstiff source terms. In addition to being semi-implicit, the method differs from the method for nonstiff systems in its treatment of the characteristic form of the equations. The method is applied to a model system of equations and to a system of equations for gas flow with heat transfer. The analytical and numerical results show that the modifications to the nonstiff method are necessary for obtaining second-order accuracy as the relaxation time tends to zero. The numerical results also suggest that certain modifications to the Riemann solver used by the Godunov method would help reduce numerical oscillations produced by the scheme near discontinuities. The development of a modified Riemann solver is a topic of future work.
Advanced methods in teaching reactor physics
International Nuclear Information System (INIS)
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.
Catalytic Methods in Asymmetric Synthesis Advanced Materials, Techniques, and Applications
Gruttadauria, Michelangelo
2011-01-01
This book covers advances in the methods of catalytic asymmetric synthesis and their applications. Coverage moves from new materials and technologies to homogeneous metal-free catalysts and homogeneous metal catalysts. The applications of several methodologies for the synthesis of biologically active molecules are discussed. Part I addresses recent advances in new materials and technologies such as supported catalysts, supports, self-supported catalysts, chiral ionic liquids, supercritical fluids, flow reactors and microwaves related to asymmetric catalysis. Part II covers advances and milesto
Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Verner Method
Jayakumar, T; T. Muthukumar; K. Kanagarajan
2015-01-01
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.
Advanced mathematical methods in science and engineering
Hayek, SI
2010-01-01
Ordinary Differential EquationsDEFINITIONS LINEAR DIFFERENTIAL EQUATIONS OF FIRST ORDER LINEAR INDEPENDENCE AND THE WRONSKIAN LINEAR HOMOGENEOUS DIFFERENTIAL EQUATION OF ORDER N WITH CONSTANT COEFFICIENTS EULER'S EQUATION PARTICULAR SOLUTIONS BY METHOD OF UNDETERMINED COEFFICIENTS PARTICULAR SOLUTIONS BY THE METHOD OF VARIATIONS OF PARAMETERS ABEL'S FORMULA FOR THE WRONSKIAN INITIAL VALUE PROBLEMSSeries Solutions of Ordinary Differential EquationsINTRODUCTION POWER SERIES SOLUTIONS CLASSIFICATION
Water hammer analysis using characteristics method and numerical simulation
International Nuclear Information System (INIS)
Sudden change in the velocity of fluid induces substantial increase or decrease of pressure which are transmitted through the system with speed equal to the speed of sound. When it comes to incompressible fluid flow, pressure surges and consequences are described with process called water hammer. Water hammer can be result of normal system operation, such as valves closure, pumps and turbines turning off, turbine regulation, as well as abnormal system operation such as electrical defect or emergency shutdown of operating elements (turbine runaway). Characteristic of water hammer is dull humming sound and can result in catastrophic component effect. Because of this, possibility of water hammer appearance in the system has to be considered during the system design and determine the normal operation conditions of elements. The main aim of this paper is to analyse and to determine conditions for water hammer appearance in hydraulic systems. Mathematical model of system is presented and solution of water hammer is made in conditions of quicker closure the valve and turbine guide vanes closure. Several solution are performed according to method of characteristics and numerical simulation with specialized software packages. Also, analysis and validation of results obtained is made. (Author)
Reduced-complexity numerical method for optimal gate synthesis
International Nuclear Information System (INIS)
Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate-design problem is equivalent to the solution of an associated optimal-control problem; the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality-free techniques) that determine the optimal control, thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control-set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, which is used in previous research. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on SU(4) - a problem that is computationally intractable by grid-based approaches.
Numerical Analysis of Maneuvering Rotorcraft Using Moving Overlapped Grid Method
Yang, Choongmo; Aoyama, Takashi
In transient flight, rotor wakes and tip vortex generated by unsteady blade air-loads and blade motions are fully unsteady and 3-dimensionally-aperiodic, giving rise to significant complicity in accurate analysis compared to steady flight. We propose a hybrid approach by splitting the motions of a maneuvering helicopter into translation and rotation. Translation is simulated using a non-inertial moving (translating) coordinate for which new governing equations are derived, and rotations are simulated by moving each grid in the frame. A flow simulation (CFD) code is constructed by using the hybrid approach, then two simple cases (accelerating/decelerating flight and right-turn flight) for maneuvering helicopter are calculated using the moving overlapped grid method, which is now one of the most advanced techniques for tip-vortex capture. The vortex bundling phenomena, which is a main characteristic of right-turn flight, is well captured by the simulation code. The results of the present study provide better understanding of the characteristics for maneuvering rotorcraft, which can be valuable in full helicopter design.
Energy Technology Data Exchange (ETDEWEB)
Fansi, Joseph, E-mail: jfansi@doct.ulg.ac.be [University of Liège, Departement ArGEnCo, Division MS2F, Chemin des Chevreuils 1, Liège 4000 (Belgium); Arts et Métiers ParisTech, LEM3, UMR CNRS 7239, 4 rue A. Fresnel, 57078 Metz cedex 03 (France); ArcelorMittal R and D Global Maizières S.A., voie Romaine, Maizières-Lès-Metz 57238 (France); Balan, Tudor [Arts et Métiers ParisTech, LEM3, UMR CNRS 7239, 4 rue A. Fresnel, 57078 Metz cedex 03 (France); Lemoine, Xavier [Arts et Métiers ParisTech, LEM3, UMR CNRS 7239, 4 rue A. Fresnel, 57078 Metz cedex 03 (France); ArcelorMittal R and D Global Maizières S.A., voie Romaine, Maizières-Lès-Metz 57238 (France); Maire, Eric; Landron, Caroline [INSA de Lyon, MATEIS CNRS UMR5510, 7 Avenue Jean Capelle, Villeurbanne 69621 (France); Bouaziz, Olivier [ArcelorMittal R and D Global Maizières S.A., voie Romaine, Maizières-Lès-Metz 57238 (France); Ecole des Mines de Paris, Centre des Matériaux, CNRS UMR 7633, BP 87, Evry Cedex 91003 (France); Ben Bettaieb, Mohamed [Ensicaen, 6 Boulevard du Maréchal Juin, 14050 CAEN Cedex 4 (France); Marie Habraken, Anne [University of Liège, Departement ArGEnCo, Division MS2F, Chemin des Chevreuils 1, Liège 4000 (Belgium)
2013-05-01
This numerical investigation of an advanced Gurson–Tvergaard–Needleman (GTN) model is an extension of the original work of Ben Bettaiebet al. (2011 [18]). The model has been implemented as a user-defined material model subroutine (VUMAT) in the Abaqus/explicit FE code. The current damage model extends the previous version by integrating the three damage mechanisms: nucleation, growth and coalescence of voids. Physically based void nucleation and growth laws are considered, including an effect of the kinematic hardening. These new contributions are based and validated on experimental results provided by high-resolution X-ray absorption tomography measurements. The current damage model is applied to predict the damage evolution and the stress state in a tensile notched specimen experiment.
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 spectral methods for climatic time series
Ghil, M.; Allen, M.R.; Dettinger, M.D.; Ide, K.; Kondrashov, D.; Mann, M.E.; Robertson, A.W.; Saunders, A.; Tian, Y.; Varadi, F.; Yiou, P.
2002-01-01
The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal- to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.
International Nuclear Information System (INIS)
In the modern nodal methods of the analytic function expansion nodal method (AFEN) and the analytic nodal method (ANM), analytic functions are used to describe the flux distribution in a node. AFEN uses analytic solutions of the diffusion equation in multidimensional geometry without transverse integration, while ANM uses analytic solutions of the one-dimensional equations resulting from transverse integration with quadratic leakage approximation. The analytic functions used in these methods are explicit functions of keff of the core. There was some concern about the numerical stability in these methods, when the core contains nearly no-net-leakage nodes; i.e., k∞ of a node approaches keff of the core. Reference 5 discusses this instability problem in the two-node ANM nonlinear solution and describes an approximate method that is equivalent to a Taylor series expansion of the analytic solution, truncated in the first order. The present paper provides an exact method that avoids this problem without any approximation. This numerical singularity removal method decomposes the highly ill conditioned system into singular and nonsingular parts and cancels out the singular part. The method is applied to the formulation of AFEN, and tests are performed in both rectangular and hexagonal geometries. The singularity removal method was implemented in AFEN to solve no-net-leakage node embedded problems in both rectangular and hexagonal geometries. To test the method in rectangular geometry, the fast and thermal fission cross sections of a fuel assembly in the EPRI-9R core were modified such that a small eigenvalue of Λ=-3.56146x10-8 is generated. AFEN solves the problem accurately in the presence of a highly singular node. In hexagonal geometry, the VVER- 440 core was tested with an eigenvalue of -1.14308 x 10-8, and similarly accurate results were obtained. In the analytical nodal methods such as AFEN and ANM, the numerical instability problem may occur in the presence of
Advances in the homotopy analysis method
Liao, Shijun
2013-01-01
Unlike other analytic techniques, the Homotopy Analysis Method (HAM) is independent of small/large physical parameters. Besides, it provides great freedom to choose equation type and solution expression of related linear high-order approximation equations. The HAM provides a simple way to guarantee the convergence of solution series. Such uniqueness differentiates the HAM from all other analytic approximation methods. In addition, the HAM can be applied to solve some challenging problems with high nonlinearity. This book, edited by the pioneer and founder of the HAM, describes the current ad
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
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.
Advances in direct numerical simulation for MHD modeling of free surface flows
International Nuclear Information System (INIS)
The utilization of FLiBe (LiF-BeF2) free-surface flow as a chamber protection scheme is considered in advanced nuclear fusion reactor. At the design of the nuclear fusion reactor from the viewpoint of thermofluid research, it would be very important to understand the influence of a magnetic field in turbulent free surface flow. On the other hand, turbulent free surface flow (called open channel flow) by direct numerical simulation (DNS) with non-deformable surface was first succeeded by imposing free-slip and non-slip conditions as velocity boundary conditions at the upper and lower, respectively. After that, the research by DNS has been advanced more, it has been clarified that turbulent structures generated from the lower wall travels to the free surface and affected the mechanism of heat and mass transfer at the free surface. The behavior of the structures is affected by the strong magnetic field in the nuclear fusion reactor. Therefore, a DNS of liquid film cooling in the nuclear fusion reactor is performed by authors, and the relations between a magnetic orientation and turbulent flow statistics are clearly observed. In this paper, the DNS result is introduced, and the trial turbulence modeling for MHD free-surface flow by using the DNS database is also discussed
Institute of Scientific and Technical Information of China (English)
Baoshan Zhu; Kyoji Kamemoto
2005-01-01
In this study, an advanced Lagrangian vortexboundary element method is applied to simulate the unsteady impeller-diffuser interactions in a diffuser pump not only for design but also for off-design considerations. In velocity calculations based on the Biot-Savart law we do not have to grid large portions of the flow field and the calculation points are concentrated in the regions where vorticity is present.Lagrangian representation of the evolving vorticity field is well suited to moving boundaries. An integral pressure equation shows that the pressure distribution can be estimated directly from the instantaneous velocity and vorticity field.The numerical results are compared with the experimental data and the comparisons show that the method used in this study can provide us insight into the complicated unsteady impeller-diffuser interaction phenomena in a diffuser pump.
Advanced Bayesian Methods for Lunar Surface Navigation Project
National Aeronautics and Space Administration — The key innovation of this project is the application of advanced Bayesian methods to integrate real-time dense stereo vision and high-speed optical flow with an...
Advanced Bayesian Methods for Lunar Surface Navigation Project
National Aeronautics and Space Administration — The key innovation of this project will be the application of advanced Bayesian methods to integrate real-time dense stereo vision and high-speed optical flow with...
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 in...
Advanced Aqueous Phase Catalyst Development using Combinatorial Methods Project
National Aeronautics and Space Administration — The use of combinatorial methods is proposed to rapidly screen catalyst formulations for the advanced development of aqueous phase oxidation catalysts with greater...
Numerical divergence effects of equivalence theory in the nodal expansion method
International Nuclear Information System (INIS)
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
Advanced methods of treatment of hypophysis adenoma
Directory of Open Access Journals (Sweden)
Kan Ya.A.
2011-03-01
Full Text Available Hypophysis adenomas are mostly spread in the chiasmatic cellular area. They account 18% of all new brain formations, the structure of pituitary adenomas includes prolactinomas in a large number of cases which are manifested by the syndrome of hyperprolactinemia and hormone inactive hypophysis tumours (35%. Somatotropins (13-15% are lower in frequency, the main clinical feature is acromegalia. One can rarely reveal corticotropins (8-10%, gonadotro-pins (7-9% and thyrotropins (1% and their mixed forms. Transsphenoidal surgical interventions are considered to be methods of choice treatment of hypophysis adenomas and other formations in the chiasmatic cellular area. Alternative methods of treatment are conservative. They can be as an addition to microsurgery (radiotherapy
Advanced diagnostic methods for human brucellosis
Taleski, Vaso; Kunguloski, Dzoko
2011-01-01
Brucellosis is a typical zoonotic disease caused by organisms of genus brucella. Humans become infected by ingestion of animal food products, direct contact with infected animals or inhalation of infectious aerosols. Variable symptoms, sub-clinical and atypical infections make diagnosis of human brucellosis difficult. Objective of this paper is to evaluate specificity and sensitivity of different diagnostic methods, on large number of samples, in patients at different stages of...
Advanced CFD methods for wind turbine analysis
Lynch, C. Eric
2011-12-01
Horizontal-axis wind turbines operate in a complex, inherently unsteady aerodynamic environment. Even when the rotor is not stalled, the flow over the blades is dominated by three-dimensional (3-D) effects. Stall is accompanied by massive flow separation and vortex shedding over the suction surface of the blades. Under yawed conditions, dynamic stall may be present as well. In all operating conditions, there is bluff-body shedding from the turbine nacelle and support structure which interacts with the rotor wake. In addition, the high aspect ratios of wind turbine blades make them very flexible, leading to substantial aeroelastic deformation of the blades, altering the aerodynamics. Finally, when situated in a wind farm, turbines must operate in the unsteady wake of upstream neighbors. Though computational fluid dynamics (CFD) has made significant inroads as a research tool, simple, inexpensive methods, such as blade element momentum (BEM) theory, are still the workhorses in wind turbine design and aeroelasticity applications. These methods generally assume a quasi-steady flowfield and use two-dimensional aerodynamic approximations with very limited empirical 3-D corrections. As a result, they are unable to accurately predict rotor loads near the edges of the operating envelope. CFD methods make very few limiting assumptions about the flowfield, and thus have much greater potential for predicting these flows. In this work, a range of unstructured grid CFD techniques for predicting wind turbine loads and aeroelasticity has been developed and applied to a wind turbine configuration of interest. First, a nearest neighbor search algorithm based on a k-dimensional tree data structure was used to improve the computational efficiency of an approximate unsteady actuator blade method. This method was then shown to predict root and tip vortex locations and strengths similar to an overset method on the same background mesh, but without the computational expense of modeling
Dielectric Boundary Forces in Numerical Poisson-Boltzmann Methods: Theory and Numerical Strategies
Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray
2011-01-01
Continuum modeling of electrostatic interactions based upon the numerical solutions of the Poisson-Boltzmann equation has been widely adopted in biomolecular applications. To extend their applications to molecular dynamics and energy minimization, robust and efficient methodologies to compute solvation forces must be developed. In this study, we have first reviewed the theory for the computation of dielectric boundary forces based on the definition of the Maxwell stress tensor. This is follow...
Advances in organometallic synthesis with mechanochemical methods.
Rightmire, Nicholas R; Hanusa, Timothy P
2016-02-14
Solvent-based syntheses have long been normative in all areas of chemistry, although mechanochemical methods (specifically grinding and milling) have been used to good effect for decades in organic, and to a lesser but growing extent, inorganic coordination chemistry. Organometallic synthesis, in contrast, represents a relatively underdeveloped area for mechanochemical research, and the potential benefits are considerable. From access to new classes of unsolvated complexes, to control over stoichiometries that have not been observed in solution routes, mechanochemical (or 'M-chem') approaches have much to offer the synthetic chemist. It has already become clear that removing the solvent from an organometallic reaction can change reaction pathways considerably, so that prediction of the outcome is not always straightforward. This Perspective reviews recent developments in the field, and describes equipment that can be used in organometallic synthesis. Synthetic chemists are encouraged to add mechanochemical methods to their repertoire in the search for new and highly reactive metal complexes and novel types of organometallic transformations. PMID:26763151
Advancements in Research Synthesis Methods: From a Methodologically Inclusive Perspective
Suri, Harsh; Clarke, David
2009-01-01
The dominant literature on research synthesis methods has positivist and neo-positivist origins. In recent years, the landscape of research synthesis methods has changed rapidly to become inclusive. This article highlights methodologically inclusive advancements in research synthesis methods. Attention is drawn to insights from interpretive,…
Current methods and advances in bone densitometry
Energy Technology Data Exchange (ETDEWEB)
Guglielmi, G. [Dept. of Radiology, Scientific Inst. ``CSS``, San Giovanni Rotondo (Italy); Glueer, C.C. [Dept. of Radiology, Musculoskeletal Section and Osteoporosis Research Group, Univ. of California, San Francisco, CA (United States); Majumdar, S. [Dept. of Radiology, Musculoskeletal Section and Osteoporosis Research Group, Univ. of California, San Francisco, CA (United States); Blunt, B.A. [Dept. of Radiology, Musculoskeletal Section and Osteoporosis Research Group, Univ. of California, San Francisco, CA (United States); Genant, H.K. [Dept. of Radiology, Musculoskeletal Section and Osteoporosis Research Group, Univ. of California, San Francisco, CA (United States)
1995-08-01
Bone mass is the primary, although not the only, determinant of fracture. Over the past few years a number of noninvasive techniques have been developed to more sensitively quantitate bone mass. These include single and dual photon absorptiometry (SPA and DPA), single and dual X-ray absorptiometry (SXA and DXA) and quantitative computed tomography (QCT). While differing in anatomic sites measured and in their estimates of precision, accuracy, and fracture discrimination, all of these methods provide clinically useful measurements of skeletal status. It is the intent of this review to discuss the pros and cons of these techniques and to present the new applications of ultrasound (US) and magnetic resonance (MRI) in the detection and management of osteoporosis. (orig.)
Current methods and advances in bone densitometry
Guglielmi, G.; Gluer, C. C.; Majumdar, S.; Blunt, B. A.; Genant, H. K.
1995-01-01
Bone mass is the primary, although not the only, determinant of fracture. Over the past few years a number of noninvasive techniques have been developed to more sensitively quantitate bone mass. These include single and dual photon absorptiometry (SPA and DPA), single and dual X-ray absorptiometry (SXA and DXA) and quantitative computed tomography (QCT). While differing in anatomic sites measured and in their estimates of precision, accuracy, and fracture discrimination, all of these methods provide clinically useful measurements of skeletal status. It is the intent of this review to discuss the pros and cons of these techniques and to present the new applications of ultrasound (US) and magnetic resonance (MRI) in the detection and management of osteoporosis.
Advanced Methods and Applications in Computational Intelligence
Nikodem, Jan; Jacak, Witold; Chaczko, Zenon; ACASE 2012
2014-01-01
This book offers an excellent presentation of intelligent engineering and informatics foundations for researchers in this field as well as many examples with industrial application. It contains extended versions of selected papers presented at the inaugural ACASE 2012 Conference dedicated to the Applications of Systems Engineering. This conference was held from the 6th to the 8th of February 2012, at the University of Technology, Sydney, Australia, organized by the University of Technology, Sydney (Australia), Wroclaw University of Technology (Poland) and the University of Applied Sciences in Hagenberg (Austria). The book is organized into three main parts. Part I contains papers devoted to the heuristic approaches that are applicable in situations where the problem cannot be solved by exact methods, due to various characteristics or dimensionality problems. Part II covers essential issues of the network management, presents intelligent models of the next generation of networks and distributed systems ...
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
Numerical method for two-phase flow discontinuity propagation calculation
International Nuclear Information System (INIS)
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
Analytical and numerical methods for wave propagation in fluid media
Murawski, K
2002-01-01
This book surveys analytical and numerical techniques appropriate to the description of fluid motion with an emphasis on the most widely used techniques exhibiting the best performance.Analytical and numerical solutions to hyperbolic systems of wave equations are the primary focus of the book. In addition, many interesting wave phenomena in fluids are considered using examples such as acoustic waves, the emission of air pollutants, magnetohydrodynamic waves in the solar corona, solar wind interaction with the planet venus, and ion-acoustic solitons.
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
A PERTURBATION METHOD FOR THE NUMERICAL SOLUTION OF THE BERNOULLI PROBLEM
Institute of Scientific and Technical Information of China (English)
Fran(c)ois bouchon; Stéphane Clain; Rachid Touzani
2008-01-01
We consider the numerical solution of the free boundary Bernoulli problem by employing level set formulations.Using a perturbation technique,we derive a second order method that leads to a fast iteration solver.The iteration procedure is adapted in order to work in the case of topology changes.Various numerical experiments confirm the efficiency of the derived numerical method.
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)
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)
Studying approximating method and numerical computation of heat transfer of a fuel rod in PWR
International Nuclear Information System (INIS)
Based on the differential form of the general heat conduction equation, the approximating expression for a nu clear fuel rod was derived through integral. The fuel rod has asymmetrical heat resource distribution. Bessel function distribution is in radial direction and Cosine function distribution is in axis direction. Also, using the model of the advanced pressure water reactor 600, and taking an iterative calculation between tangential and normal diffusion terms in every control cell, temperature distribution of the fuel rod was computed by the finite volume method (FVM) in the unstructured grids. Comparing the approximate solutions with the numerical results, there was a good agreement between them. On this condition, we derived the location and size of maximum temperature by analysis the temperature distribution and variation. All of these can provide a useful reference for the pressure water reactor thermal design and thermal protection of nuclear engineering. (authors)
Methods of Celestial Mechanics Volume I: Physical, Mathematical, and Numerical Principles
Beutler, Gerhard
2005-01-01
G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students in physics, mathematics and engineering as well as an excellent reference for practitioners. This Volume I gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. After a brief review of the history of celestial mechanics, the equations of motion (Newtonian and relativistic versions) are developed for planetary systems (N-body-problem), for artificial Earth satellites, and for extended bodies (which includes the problem of Earth and lunar rotation). Perturbation theory is outlined in an elementary way from generally known mathematical principles without making use of the advanced tools of analytical mechanics. The variational equations associated with orbital motion - of fundamental importance for parameter estimation (e.g., orbit determination), numerical error propagation, and stability considerations - are introduced and their properties discussed in ...
Directory of Open Access Journals (Sweden)
Michael eNivala
2012-05-01
Full Text Available Intracellular calcium (Ca cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR, mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a varient of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain and the myoplasm domain in each CRU are modeled by 5x5x5 voxels to maintain proper Ca diffusion. Advanced numerical algorithms implemented on graphical processing units were used for fast computational simulations. For a myocyte containing 100x20x10 CRUs, a one-second heart time simulation takes about 10 minutes of machine time on a single NVIDIA Tesla C2050. Examples of simulated Ca cycling dynamics, such as Ca sparks, Ca waves, and Ca alternans, are shown.
The Advanced Computational Methods Center, University of Georgia
Nute, Donald; Covington, Michael; Rankin, Terry
1986-01-01
The Advanced Computational Methods Center (ACMC) established at the University of Georgia in 1984, supports several research projects in artificial intelligence. The primary goal of AI research at ACMC is the design and installation of a logic-programming environment with advanced natural language processing and knowledge-acquisition capabilities on the university's highly parallel CYBERPLUS system from Control Data Corporation. This article briefly describes current research projects in arti...
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
Numerical strategies for the Galerkin–proper generalized decomposition method
Falcó Montesinos, Antonio; Hilario Pérez, Lucía; Montes Sánchez, Nicolás; Mora Aguilar, Marta Covadonga
2013-01-01
The Proper Generalized Decomposition or, for short, PGD is a tensor decomposition based technique to solve PDE problems. It reduces calculation and storage cost drastically and presents some similarities with the Proper Orthogonal Decomposition, for short POD. In this work, we propose an efficient implementation to improve the convergence of the PGD, toward the numerical solution of a discretized PDE problem, when the associated matrix is Laplacian-like.
Numerical methods for solving the planar vacuum Einstein equations
International Nuclear Information System (INIS)
We describe a numerical code developed as a tool to investigate fully nonlinear behavior in the one-dimensional vacuum Einstein equations in plane symmetry. We use the York splitting into free and constrained variables to solve the initial-value equations. These data are then propagated in time using a fully constrained evolution scheme. We carry out a perturbative treatment of the Einstein equations and use the results as test-bed calculations for the code
Numerical methods for solving the planar vacuum Einstein equations
Energy Technology Data Exchange (ETDEWEB)
Anninos, P.; Centrella, J. (Department of Physics and Atmospheric Science, Drexel University, Philadelphia, Pennsylvania 19104 (USA)); Matzner, R.A. (Department of Physics and Center for Relativity, The University of Texas at Austin, Austin, Texas 78712 (USA))
1991-03-15
We describe a numerical code developed as a tool to investigate fully nonlinear behavior in the one-dimensional vacuum Einstein equations in plane symmetry. We use the York splitting into free and constrained variables to solve the initial-value equations. These data are then propagated in time using a fully constrained evolution scheme. We carry out a perturbative treatment of the Einstein equations and use the results as test-bed calculations for the code.
Improved Numerical Method for Calculation of 4-Body Transition Amplitudes
Harris, A. L.
2013-01-01
In order to study 4-body atomic collisions such as excitation-ionization, transfer with target excitation, and double electron capture, the calculation of a nine-dimensional numerical integral is often required. This calculation can become computationally expensive, especially when calculating fully differential cross sections (FDCS), where the positions and momenta of all the particles are known. We have developed a new technique for calculating FDCS using fewer computing hours, but more mem...
Visual numerical steering in 3D AGENT code system for advanced nuclear reactor modeling and design
International Nuclear Information System (INIS)
Highlights: ► Numerical steering framework developed for deterministic neutron transport code AGENT to speed up the solution. ► Resulting speed up is on the order of 50%. ► Use of the steering framework is demonstrated modeling a TRIGA reactor. ► Numerical steering framework showed to be well suited for the deterministic neutron transport methods. - Abstract: The AGENT simulation system is used for detailed three-dimensional modeling of neutron transport and corresponding properties of nuclear reactors of any design. Numerical solution to the neutron transport equation in the AGENT system is based on the Method of Characteristics (MOCs) and the theory of R-functions. The latter of which is used for accurately describing current and future heterogeneous lattices of reactor core configurations. The AGENT code has been extensively verified to assure a high degree of accuracy for predicting neutron three-dimensional point-wise flux spatial distributions, power peaking factors, reaction rates, and eigenvalues. In this paper, a new AGENT code feature, a computational steering, is presented. This new feature provides a novel way for using deterministic codes for fast evaluation of reactor core parameters, at no loss to accuracy. The computational steering framework as developed at the Technische Universität München is smoothly integrated into the AGENT solver. This framework allows for an arbitrary interruption of AGENT simulation, allowing the solver to restart with updated parameters. One possible use of this is to accelerate the convergence of the final values resulting in significantly reduced simulation times. Using this computational steering in the AGENT system, coarse MOC resolution parameters can initially be selected and later update them – while the simulation is actively running – into fine resolution parameters. The utility of the steering framework is demonstrated using the geometry of a research reactor at the University of Utah: this new
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.
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…
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)
Path Integrals and Exotic Options:. Methods and Numerical Results
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
Advanced Numerical Imaging Procedure Accounting for Non-Ideal Effects in GPR Scenarios
Comite, Davide; Galli, Alessandro; Catapano, Ilaria; Soldovieri, Francesco
2015-04-01
advanced implementation have also been tested by introducing 'errors' on the knowledge of the background medium permittivity, by simulating the presence of one or more layers, and by choosing different models of the surface roughness. The impact of these issues on the performance of both the conventional procedure and the advanced one will be extensively highlighted and discussed at the conference. [1] G. Valerio et al., "GPR detectability of rocks in a Martian-like shallow subsoil: A numerical approach," Plan. Sp. Sci., vol. 62, pp. 31-40, 2012. [2] A. Galli et al., "3D imaging of buried dielectric targets with a tomographic microwave approach applied to GPR synthetic data," Int. J. Antennas Propag., art. ID 610389, 10 pp., 2013 [3] F. Soldovieri et al., "A linear inverse scattering algorithm for realistic GPR applications," Near Surface Geophysics, 5 (1), pp. 29-42, 2007.
Projection methods for the numerical solution of Markov chain models
Saad, Youcef
1989-01-01
Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.
Viscous-Inviscid Coupling Methods for Advanced Marine Propeller Applications
Martin Greve; Katja Wöckner-Kluwe; Moustafa Abdel-Maksoud; Thomas Rung
2012-01-01
The paper reports the development of coupling strategies between an inviscid direct panel method and a viscous RANS method and their application to complex propeller ows. The work is motivated by the prohibitive computational cost associated to unsteady viscous flow simulations using geometrically resolved propellers to analyse the dynamics of ships in seaways. The present effort aims to combine the advantages of the two baseline methods in order to reduce the numerical effort without comprom...
Extending Abstract Acceleration Methods to Data-Flow Programs with Numerical Inputs
Schrammel, Peter; Jeannet, Bertrand
2010-01-01
Acceleration methods are commonly used for computing precisely the effects of loops in the reachability analysis of counter machine models. Applying these methods on synchronous data-flow programs with Boolean and numerical variables, e.g. Lustre programs, firstly requires the enumeration of the Boolean states in order to obtain a control graph with numerical variables only. Secondly, acceleration methods have to deal with the non-determinism introduced by numerical input variables. In this a...
Extending abstract acceleration methods to data-flow programs with numerical inputs
Schrammel, Peter; Jeannet, Bertrand
2010-01-01
Acceleration methods are commonly used for computing precisely the effects of loops in the reachability analysis of counter machine models. Applying these methods on synchronous data-flow programs with Boolean and numerical variables, e.g. Lustre programs, firstly requires the enumeration of the Boolean states in order to obtain a control graph with numerical variables only. Secondly, acceleration methods have to deal with the non-determinism introduced by numerical input variables. In this a...
Higher-order Godunov methods for reducing numerical dispersion in reservoir simulation
Energy Technology Data Exchange (ETDEWEB)
Bell, J.B.; Shubin, G.R.
1985-02-01
Standard finite difference methods used in reservoir simulation employ large amounts of numerical dispersion. This inherent numerical dispersion causes sharp fronts to be smeared over many grid blocks, and can cause their shapes to be wildly distorted. In this paper we discuss a new method that substantially reduces the effects of numerical dispersion. The new method significantly improves the resolution of fronts, and is specifically constructed to be essentially free of grid orientation effects.
Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods
International Nuclear Information System (INIS)
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 extending the
Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods
Energy Technology Data Exchange (ETDEWEB)
Ernst, Frederick J [FJE Enterprises, 511 County Route 59, Potsdam, NY 13676 (United States)
2007-06-18
source can be represented by discontinuities in the 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
Methods for studying fuel management in advanced gas cooled reactors
International Nuclear Information System (INIS)
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)
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.
Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing
Directory of Open Access Journals (Sweden)
R. Company
2014-01-01
analysis of the method is provided. The method preserves positivity and monotonicity of the numerical solution. Consistency and stability properties of the scheme are studied. Explicit calculations avoid iterative algorithms for solving nonlinear systems. Theoretical results are confirmed by numerical experiments. Comparison with other approaches shows that the proposed method is accurate and competitive.
Recent advances in theoretical and numerical studies of wire array Z-pinch in the IAPCM
International Nuclear Information System (INIS)
Fast Z-pinch has produced the most powerful X-ray radiation source in laboratory and also shows the possibility to drive inertial confinement fusion (ICF). Recent advances in wire-array Z-pinch researches at the Institute of Applied Physics and Computational Mathematics are presented in this paper. A typical wire array Z-pinch process has three phases: wire plasma formation and ablation, implosion and the MRT instability development, stagnation and radiation. A mass injection model with azimuthal modulation coefficient is used to describe the wire initiation, and the dynamics of ablated plasmas of wire-array Z-pinches in (r, θ) geometry is numerically studied. In the implosion phase, a two-dimensional(r, z) three temperature radiation MHD code MARED has been developed to investigate the development of the Magneto-Rayleigh-Taylor(MRT) instability. We also analyze the implosion modes of nested wire-array and find that the inner wire-array is hardly affected before the impaction of the outer wire-array. While the plasma accelerated to high speed in the implosion stage stagnates on the axis, abundant x-ray radiation is produced. The energy spectrum of the radiation and the production mechanism are investigated. The computational x-ray pulse shows a reasonable agreement with the experimental result. We also suggest that using alloyed wire-arrays can increase multi-keV K-shell yield by decreasing the opacity of K-shell lines. In addition, we use a detailed circuit model to study the energy coupling between the generator and the Z-pinch implosion. Recently, we are concentrating on the problems of Z-pinch driven ICF, such as dynamic hohlraum and capsule implosions. Our numerical investigations on the interaction of wire-array Z-pinches on foam convertors show qualitative agreements with experimental results on the “Qiangguang I” facility. An integrated two-dimensional simulation of dynamic hohlraum driven capsule implosion provides us the physical insights of wire
Numerical Methods as an Integrated Part of Physics Education
Vistnes, A I; Vistnes, Arnt Inge
2005-01-01
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on mainframe machines and written in computing languages such as Fortran or C/C++, can now easily be solved on standard PCs with the bonus of immediate visualizations of the results. In our undergraduate programs an often posed question is how to incorporate and exploit efficiently these advances in the standard physics and mathematics curriculum, without detracting the attention from the classical and basic theoretical and experimental topics to be covered. Furthermore, if students are trained to use such tools at early stages in their education, do such tools really enhance and improve the learning environment? And, perhaps even more important, does it lead to a better physics understanding? Here we present one possible approach, where computational topics are gradually baked into ...
A numerical method for solving heat equations involving interfaces
Directory of Open Access Journals (Sweden)
Zhilin Li
2000-07-01
Full Text Available In 1993, Li and Mayo [3] gave a finite-difference method with second order accuracy for solving the heat equations involving interfaces with constant coefficients and discontinuous sources. In this paper, we expand their result by presenting a finite-difference method which allows each coefficient to take different values in different sub-regions of the interface. Our method is useful in physical applications, and has also second order accuracy.
GENETIC ALGORITHM IN REDUCTION OF NUMERICAL DISPERSION OF 3-D ADI-FDTD METHOD
Institute of Scientific and Technical Information of China (English)
Zhang Yan; Lǖ Shanwei; Gao Wenjun
2007-01-01
A new method to reduce the numerical dispersion of the three-dimensional Alternating Direction Implicit Finite-Difference Time-Domain(3-D ADI-FDTD)method is proposed.Firstly,the numerical formulations of the 3-D ADI-FDTD method are modified with the artificial anisotropy,and the new numerical dispersion relation is derived.Secondly,the relative permittivity tensor of the artificial anisotropy can be obtained by the Adaptive Genetic Algorithm(AGA).In order to demonstrate the accuracy and efficiency of this new method,a monopole antenna is simulated as an example.And the numerical results and the computational requirements of the proposed method are cornpared with those of the conventional ADI-FDTD method and the measured data.In addition the reduction of the numerical dispersion is investigated as the objective function of the AGA.It is found that this new method is accurate and efficient by choosing proper objective function.
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 partial differential equations an Overview and Applications
Jaun, A
This is the web edition of the 3-4 weeks course F2A5076 taught 1997-2001 at the Royal Institute of Technology in Stockholm (Sweden). The main target is to provide a robust introduction in computational methods to graduate- and lifelong learning students, using a distance learning method that can easily be tailored to professional schedules.
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...
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 efficie
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 Stability and Convergence of Approximate Methods for Conservation Laws
Galkin, V. A.
We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.
International Nuclear Information System (INIS)
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.)
Shadow boundary effects in hybrid numerical-asymptotic methods for high frequency scattering
Hewett, David P.
2014-01-01
The hybrid numerical-asymptotic (HNA) approach aims to reduce the computational cost of conventional numerical methods for high frequency wave scattering problems by enriching the numerical approximation space with oscillatory basis functions, chosen based on partial knowledge of the high frequency solution asymptotics. In this paper we propose a new methodology for the treatment of shadow boundary effects in HNA boundary element methods, using the classical geometrical theory of diffraction ...
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.
Schuster, Jonathan
Infrared (IR) detectors are well established as a vital sensor technology for military, defense and commercial applications. Due to the expense and effort required to fabricate pixel arrays, it is imperative to develop numerical simulation models to perform predictive device simulations which assess device characteristics and design considerations. Towards this end, we have developed a robust three-dimensional (3D) numerical simulation model for IR detector pixel arrays. We used the finite-difference time-domain technique to compute the optical characteristics including the reflectance and the carrier generation rate in the device. Subsequently, we employ the finite element method to solve the drift-diffusion equations to compute the electrical characteristics including the I(V) characteristics, quantum efficiency, crosstalk and modulation transfer function. We use our 3D numerical model to study a new class of detector based on the nBn-architecture. This detector is a unipolar unity-gain barrier device consisting of a narrow-gap absorber layer, a wide-gap barrier layer, and a narrow-gap collector layer. We use our model to study the underlying physics of these devices and to explain the anomalously long lateral collection lengths for photocarriers measured experimentally. Next, we investigate the crosstalk in HgCdTe photovoltaic pixel arrays employing a photon-trapping (PT) structure realized with a periodic array of pillars intended to provide broadband operation. The PT region drastically reduces the crosstalk; making the use of the PT structures not only useful to obtain broadband operation, but also desirable for reducing crosstalk, especially in small pitch detector arrays. Then, the power and flexibility of the nBn architecture is coupled with a PT structure to engineer spectrally filtering detectors. Last, we developed a technique to reduce the cost of large-format, high performance HgCdTe detectors by nondestructively screen-testing detector arrays prior
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.
Method of independent timesteps in the numerical solution of initial value problems
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
Full text: The Gyrokinetic Vlasov equation describes the evolution of the distribution function in phase space where kinetic effects play an important role. It has been extensively incorporated to modern plasma simulations in order to study various linear and nonlinear plasma dynamics. Contrary to the particle approach such as Particle-In-Cell (PIC) method, the Vlasov approach needs a large amount of computer resource due to the discretization of the phase space, but is superior in reducing numerical noise. Furthermore, it is easier to introduce dissipations such as collision and also source/sink terms which are important in the study of long time scale plasma dynamics as an open system. Here, we have advanced a conservative form of the interpolated differential operator (IDO-CF) scheme to solve the Vlasov-Poisson equation system, which has been developed in CFD. The method is an extended counterpart of the IDO scheme which is improved in keeping the conservation properties more rigorously. We have first investigated the conservation properties of the scheme such as the L-1 norm, total energy and entropy through numerical tests of the nonlinear Landau damping and two-stream instability by solving 2-dimensional (2-D) Vlasov-Poisson equation. It is found that the IDO-CF scheme generally shows an excellent numerical stability with a high accuracy in keeping the L-1 norm and total energy over many bounce periods of trapped particles. On the other hand, a certain amount of errors in the entropy are observed in all schemes, which is inevitable in the original Vlasov simulation. Then, we have developed a 4-D gyrokinetic full-f Vlasov code (3-D in configuration space and 1-D in velocity one) based on the IDO-CF scheme and tested it in the simulation of slab Ion Temperature Gradient (ITG) driven turbulence. It is found that the scheme keeps the good conservation properties of the L-1 norm and the energy without serious numerical instability. The present scheme can be
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)
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)
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.
Validation of a Numerical Method for Determining Liner Impedance
Watson, Willie R.; Jones, Michael G.; Tanner, Sharon E.; Parrott, Tony L.
1996-01-01
This paper reports the initial results of a test series to evaluate a method for determining the normal incidence impedance of a locally reacting acoustically absorbing liner, located on the lower wall of a duct in a grazing incidence, multi-modal, non-progressive acoustic wave environment without flow. This initial evaluation is accomplished by testing the methods' ability to converge to the known normal incidence impedance of a solid steel plate, and to the normal incidence impedance of an absorbing test specimen whose impedance was measured in a conventional normal incidence tube. The method is shown to converge to the normal incident impedance values and thus to be an adequate tool for determining the impedance of specimens in a grazing incidence, multi-modal, nonprogressive acoustic wave environment for a broad range of source frequencies.
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 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.
B-spline collocation methods for numerical solutions of the Burgers' equation
İdris Dağ; Dursun Irk; Ali Şahin
2005-01-01
Both time- and space-splitted Burgers' equations are solved numerically. Cubic B-spline collocation method is applied to the time-splitted Burgers' equation. Quadratic B-spline collocation method is used to get numerical solution of the space-splitted Burgers' equation. The results of both schemes are compared for some test problems.
Numerical solution of 2D-vector tomography problem using the method of approximate inverse
Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna
2016-08-01
We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.
Cox, T.J.; Runkel, R.L.
2008-01-01
Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.
Numerical methods for the sign problem in Lattice Field Theory
Bongiovanni, Lorenzo
2016-01-01
The great majority of algorithms employed in the study of lattice field theory are based on Monte Carlo's importance sampling method, i.e. on probability interpretation of the Boltzmann weight. Unfortunately in many theories of interest one cannot associated a real and positive weight to every configuration, that is because their action is explicitly complex or because the weight is multiplied by some non positive term. In this cases one says that the theory on the lattice is affected by the sign problem. An outstanding example of sign problem preventing a quantum field theory to be studied, is QCD at finite chemical potential. Whenever the sign problem is present, standard Monte Carlo methods are problematic to apply and, in general, new approaches are needed to explore the phase diagram of the complex theory. Here we will review three of the main candidate methods to deal with the sign problem, namely complex Langevin dynamics, Lefschetz thimbles and density of states method. We will first study complex Lan...
A finite volume method for numerical grid generation
Beale, S. B.
1999-07-01
A novel method to generate body-fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables , and is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re-zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid-correction procedure. The scalar variables are re-mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet-Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local-boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point-by-point and whole-field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright
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 co...
Evaluating numerical ODE/DAE methods, algorithms and software
Soderlind, Gustaf; Wang, Lina
2006-01-01
Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one method is better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris paribus conditions. Moreover, testing is an empirical science and as such requires a formal test protocol; without it conclusions are questionable, invalid or even false.We argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. The goals are computational stability, reproducibility, and improved software quality. We also focus on different error criteria and norms, and discuss modifications to DASPK and RADAU5. Finally, some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems.
Numerical evaluation of stability methods for rubble mound breakwater toes
Verpoorten, S.P.K.; Ockeloen, W.J.; Verhagen, H.J.
2015-01-01
Since 1977 dedicated studies are made to the stability of rubble mound break-water toes under wave attack. A large number of stability methods is available, but prediction accuracy is low and validity ranges are too small for use in prac-tice. In this research the decoupled model approach is used to
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.
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.
Advanced non-destructive methods for an efficient service performance
International Nuclear Information System (INIS)
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)
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...... 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)
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.
Piche, Steffanie
Understanding the impact of coastal forests on the propagation of rapidly advancing onshore tsunami bores is difficult due to complexity of this phenomenon and the large amount of parameters which must be considered. The research presented in the thesis focuses on understanding the protective effect of the coastal forest on the forces generated by the tsunami and its ability to reduce the propagation and velocity of the incoming tsunami bore. Concern for this method of protecting the coast from tsunamis is based on the effectiveness of the forest and its ability to withstand the impact forces caused by both the bore and the debris carried along by it. The devastation caused by the tsunami has been investigated in recent examples such as the 2011 Tohoku Tsunami in Japan and the Indian Ocean Tsunami which occurred in 2004. This research examines the reduction of the spatial extent of the tsunami bore inundation and runup due to the presence of the coastal forest, and attempts to quantify the impact forces induced by the tsunami bores and debris impact on the structures. This research work was performed using a numerical model based on the Smoothed Particle Hydrodynamics (SPH) method which is a single-phase three-dimensional model. The simulations performed in this study were separated into three sections. The first section focused on the reduction of the extent of the tsunami inundation and the magnitude of the bore velocity by the coastal forest. This section included the analysis of the hydrodynamic forces acting on the individual trees. The second section involved the numerical modeling of some of the physical laboratory experiments performed by researchers at the University of Ottawa, in cooperation with colleagues from the Ocean, Coastal and River Engineering Lab at the National Research Council, Ottawa, in an attempt to validate the movement and impact forces of floating driftwood on a column. The final section modeled the movement and impact of floating debris
M. Mosleh E. Abu Samak; Bakar, A. Ashrif A.; Muhammad Kashif; Mohd Saiful Dzulkifly Zan
2016-01-01
This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be...
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....
DEFF Research Database (Denmark)
Taghizadeh, Alireza; Mørk, Jesper; Chung, Il-Sug
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....
Numerical methods of safety analysis with weak source
International Nuclear Information System (INIS)
Behaviour of neutron flux in the reactor with the weak source is determined by differential equations of stochastic reactor kinetics, which are the generalization of well known dot kinetics equations. By solving these equations or Pontryagin equation, which is derived from Kolmogorov equation known in Markov processes theory, it is possible to calculate the probabilities of emergency system failure. Two methods are considered: first is finite differential technique (of two modifications) and another one is Monte Carlo. It occurred possible to separate the spatial and temporal coordinates on Pontryagin equation and drive the boundary task to Sturm-Liouville problem. It was found that Monte Carlo technique seems to be much more perspective
Numerical comparison of methods for solving linear differential equations of fractional order
Energy Technology Data Exchange (ETDEWEB)
Momani, Shaher [Department of Mathematics, Mutah University, P.O. Box 7, Al-Karak (Jordan)]. E-mail: shahermm@yahoo.com; Odibat, Zaid [Prince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa' Applied University, Salt (Jordan)]. E-mail: odibat@bau.edu.jo
2007-03-15
In this article, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear differential equations of fractional order. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. This paper will present a numerical comparison between the two methods and a conventional method such as the fractional difference method for solving linear differential equations of fractional order. The numerical results demonstrates that the new methods are quite accurate and readily implemented.
Energy Technology Data Exchange (ETDEWEB)
X. Frank Xu
2010-03-30
Multiscale modeling of stochastic systems, or uncertainty quantization of multiscale modeling is becoming an emerging research frontier, with rapidly growing engineering applications in nanotechnology, biotechnology, advanced materials, and geo-systems, etc. While tremendous efforts have been devoted to either stochastic methods or multiscale methods, little combined work had been done on integration of multiscale and stochastic methods, and there was no method formally available to tackle multiscale problems involving uncertainties. By developing an innovative Multiscale Stochastic Finite Element Method (MSFEM), this research has made a ground-breaking contribution to the emerging field of Multiscale Stochastic Modeling (MSM) (Fig 1). The theory of MSFEM basically decomposes a boundary value problem of random microstructure into a slow scale deterministic problem and a fast scale stochastic one. The slow scale problem corresponds to common engineering modeling practices where fine-scale microstructure is approximated by certain effective constitutive constants, which can be solved by using standard numerical solvers. The fast scale problem evaluates fluctuations of local quantities due to random microstructure, which is important for scale-coupling systems and particularly those involving failure mechanisms. The Green-function-based fast-scale solver developed in this research overcomes the curse-of-dimensionality commonly met in conventional approaches, by proposing a random field-based orthogonal expansion approach. The MSFEM formulated in this project paves the way to deliver the first computational tool/software on uncertainty quantification of multiscale systems. The applications of MSFEM on engineering problems will directly enhance our modeling capability on materials science (composite materials, nanostructures), geophysics (porous media, earthquake), biological systems (biological tissues, bones, protein folding). Continuous development of MSFEM will
Directory of Open Access Journals (Sweden)
Zahra Masouri
2014-04-01
Full Text Available The focus of this paper is on the numerical solution of linear systems of Fredhlom integral equations of the second kind. For this purpose, the Chebyshev cardinal functions with Gauss-Lobatto points are used. By combination of properties of these functions and the effective Clenshaw-Curtis quadrature rule, an applicable numerical method for solving the mentioned systems is formulated. Some error bounds for the method are computed and its convergence rate is estimated. The method is numerically evaluated by solving some test problems caught from the literature by which the accuracy and computational efficiency of the method will be demonstrated.
High-performance and high-order numerical methods for 2D Navier-Stokes equations
Aurichio, Vinicius Henrique; Cucchieri, Attilio; Oliveira, Maria Luisa Bambozzi De
2015-11-01
Since numerical simulation of a flow is a computationally-intensive problem, our main goal is to develop numerical methods - to solve the fluid equations of motion (compressible Navier-Stokes) in 2D - that are also suitable for the high-performance computing framework. We study known methods, such as flux-splitting, MacCormack, and compact schemes, to guide our search. In particular, we consider some high-order versions of these methods, since they allow for high-resolution with less grid points, possibly reducing the computation times. Our effort is focused on obtaining shock-capturing, multiscale, low-numerical dissipation methods. CNPq-Brazil.
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...
Transforming Mean and Osculating Elements Using Numerical Methods
Ely, Todd A.
2015-03-01
Mean element propagation of perturbed two body orbits has as its mathematical basis the averaging theory of nonlinear dynamical systems. Mean elements define an orbit's long-term evolution characteristics consisting of both secular and long-period effects. Using averaging theory, a near-identity transformation can be found that transforms between the mean elements and their osculating counterparts that augment the mean elements with short period effects. The ability to perform the conversion is necessary so that orbit design conducted in either mean elements or osculating can be effectively converted between each element type. In the present work, the near-identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the mean or osculating elements to first-order.
Finite Element Method (Chapter from "Gratings: Theory and Numeric Applications")
Demésy, Guillaume; Nicolet, André; Vial, Benjamin
2013-01-01
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack lightened by a plane wave of arbitrary incidence and polarization angle. It relies on a rigorous treatment of the plane wave sources problem through an equivalent radiation problem with localized sources. Bloch conditions and a new Adaptative Perfectly Matched Layer have been implemented in order to truncate the computational domain. We derive this formulation for both mono-dimensional gratings in TE/TM polarization cases (2D or scalar case) and for the most general bidimensional or crossed gratings (3D or vector case). The main advantage of this formulation is its complete generality with respect to the studied geometries and the material properties. Its principle remains independent of both the number of diffractive elements by period and number of stack layers. The flexi...
Mathematical and Numerical Methods for Non-linear Beam Dynamics
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 ...
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.
Optimization Method for Indoor Thermal Comfort Based on Interactive Numerical Calculation
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In order to implement the optimal design of the indoor thermal comfort based on the numerical modeling method, the numerical calculation platform is combined seamlessly with the data-processing platform, and an interactive numerical calculation platform which includes the functions of numerical simulation and optimization is established. The artificial neural network (ANN) and the greedy strategy are introduced into the hill-climbing pattern heuristic search process, and the optimizing search direction can be predicted by using small samples; when searching along the direction using the greedy strategy, the optimal values can be quickly approached. Therefore, excessive external calling of the numerical modeling process can be avoided,and the optimization time is decreased obviously. The experimental results indicate that the satisfied output parameters of air conditioning can be quickly given out based on the interactive numerical calculation platform and the improved search method, and the optimization for indoor thermal comfort can be completed.
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
International Nuclear Information System (INIS)
Highlights: • An artificial accelerogram of the specified SSE is generated. • A dynamic FE model of the RCP in AP1000 (with gyroscopic and FSI effects) is developed. • The displacement, force, moment and stress in the RCP during the earthquake are summarized. - Abstract: The reactor coolant pump in the Advanced Passive Pressurized Water Reactor is a kind of nuclear canned-motor pump. The pump is classified as Seismic Category I, which must function normally during the Safe Shutdown Earthquake. When the nuclear power plant is located in seismically active region, the seismic response of the reactor coolant pump may become very important for the safety assessment of the whole nuclear power plant. In this article, an artificial accelerogram is generated. The response spectrum of the artificial accelerogram fits well with the design acceleration spectrum of the Safe Shutdown Earthquake. By applying the finite element modeling method, the dynamic finite element models of the rotor and stator in the reactor coolant pump are created separately. The rotor and stator are coupled by the journal bearings and the annular flow between the rotor and stator. Then the whole dynamic model of the reactor coolant pump is developed. Time domain analysis which uses the improved state-space Newmark method of a direct time integration scheme is carried out to investigate the response of the reactor coolant pump under the horizontal seismic load. The results show that the reactor coolant pump responds differently in the direction of the seismic load and in the perpendicular direction. During the Safe Shutdown Earthquake, the displacement response, the shear force, the moment and the journal bearing reaction forces in the reactor coolant pump are analyzed
Energy Technology Data Exchange (ETDEWEB)
De, Cheng, E-mail: 0100209064@sjtu.edu.cn; Zhen-Qiang, Yao, E-mail: zqyaosjtu@gmail.com; Ya-bo, Xue; Hong, Shen
2014-10-15
Highlights: • An artificial accelerogram of the specified SSE is generated. • A dynamic FE model of the RCP in AP1000 (with gyroscopic and FSI effects) is developed. • The displacement, force, moment and stress in the RCP during the earthquake are summarized. - Abstract: The reactor coolant pump in the Advanced Passive Pressurized Water Reactor is a kind of nuclear canned-motor pump. The pump is classified as Seismic Category I, which must function normally during the Safe Shutdown Earthquake. When the nuclear power plant is located in seismically active region, the seismic response of the reactor coolant pump may become very important for the safety assessment of the whole nuclear power plant. In this article, an artificial accelerogram is generated. The response spectrum of the artificial accelerogram fits well with the design acceleration spectrum of the Safe Shutdown Earthquake. By applying the finite element modeling method, the dynamic finite element models of the rotor and stator in the reactor coolant pump are created separately. The rotor and stator are coupled by the journal bearings and the annular flow between the rotor and stator. Then the whole dynamic model of the reactor coolant pump is developed. Time domain analysis which uses the improved state-space Newmark method of a direct time integration scheme is carried out to investigate the response of the reactor coolant pump under the horizontal seismic load. The results show that the reactor coolant pump responds differently in the direction of the seismic load and in the perpendicular direction. During the Safe Shutdown Earthquake, the displacement response, the shear force, the moment and the journal bearing reaction forces in the reactor coolant pump are analyzed.
Numerical methods of estimating the dispersion of radionuclides in atmosphere
International Nuclear Information System (INIS)
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
IMPROVED NUMERICAL METHODS FOR MODELING RIVER-AQUIFER INTERACTION.
Energy Technology Data Exchange (ETDEWEB)
Tidwell, Vincent C.; Sue Tillery; Phillip King
2008-09-01
A new option for Local Time-Stepping (LTS) was developed to use in conjunction with the multiple-refined-area grid capability of the U.S. Geological Survey's (USGS) groundwater modeling program, MODFLOW-LGR (MF-LGR). The LTS option allows each local, refined-area grid to simulate multiple stress periods within each stress period of a coarser, regional grid. This option is an alternative to the current method of MF-LGR whereby the refined grids are required to have the same stress period and time-step structure as the coarse grid. The MF-LGR method for simulating multiple-refined grids essentially defines each grid as a complete model, then for each coarse grid time-step, iteratively runs each model until the head and flux changes at the interfacing boundaries of the models are less than some specified tolerances. Use of the LTS option is illustrated in two hypothetical test cases consisting of a dual well pumping system and a hydraulically connected stream-aquifer system, and one field application. Each of the hypothetical test cases was simulated with multiple scenarios including an LTS scenario, which combined a monthly stress period for a coarse grid model with a daily stress period for a refined grid model. The other scenarios simulated various combinations of grid spacing and temporal refinement using standard MODFLOW model constructs. The field application simulated an irrigated corridor along the Lower Rio Grande River in New Mexico, with refinement of a small agricultural area in the irrigated corridor.The results from the LTS scenarios for the hypothetical test cases closely replicated the results from the true scenarios in the refined areas of interest. The head errors of the LTS scenarios were much smaller than from the other scenarios in relation to the true solution, and the run times for the LTS models were three to six times faster than the true models for the dual well and stream-aquifer test cases, respectively. The results of the field
Advanced adaptive computational methods for Navier-Stokes simulations in rotorcraft aerodynamics
Stowers, S. T.; Bass, J. M.; Oden, J. T.
1993-01-01
A phase 2 research and development effort was conducted in area transonic, compressible, inviscid flows with an ultimate goal of numerically modeling complex flows inherent in advanced helicopter blade designs. The algorithms and methodologies therefore are classified as adaptive methods, which are error estimation techniques for approximating the local numerical error, and automatically refine or unrefine the mesh so as to deliver a given level of accuracy. The result is a scheme which attempts to produce the best possible results with the least number of grid points, degrees of freedom, and operations. These types of schemes automatically locate and resolve shocks, shear layers, and other flow details to an accuracy level specified by the user of the code. The phase 1 work involved a feasibility study of h-adaptive methods for steady viscous flows, with emphasis on accurate simulation of vortex initiation, migration, and interaction. Phase 2 effort focused on extending these algorithms and methodologies to a three-dimensional topology.
Numerical Methods and Comparisons for 1D and Quasi 2D Streamer Propagation Models
Huang, Mengmin; Guan, Huizhe; Zeng, Rong
2016-01-01
In this work, we propose four different strategies to simulate the one-dimensional (1D) and quasi two-dimensional (2D) model for streamer propagation. Each strategy involves of one numerical method for solving Poisson's equation and another method for solving continuity equations in the models, and a total variation diminishing three-stage Runge-Kutta method in temporal discretization. The numerical methods for Poisson's equation include finite volume method, discontinuous Galerkin methods, mixed finite element method and least-squared finite element method. The numerical method for continuity equations is chosen from the family of discontinuous Galerkin methods. The accuracy tests and comparisons show that all of these four strategies are suitable and competitive in streamer simulations from the aspects of accuracy and efficiency. By applying any strategy in real simulations, we can study the dynamics of streamer propagations and influences due to the change of parameters in both of 1D and quasi 2D models. T...
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...
Numerical simulation of liquefaction behaviour of granular materials using Discrete Element Method
Indian Academy of Sciences (India)
T G Sitharam; S V Dinesh
2003-09-01
In this paper, numerical simulation of 3-dimensional assemblies of 1000 polydisperse sphere particles using Discrete Element Method (DEM) is used to study the liquefaction behaviour of granular materials. Numerical simulations of cyclic triaxial shear tests under undrained conditions are performed at different confining pressures under constant strain amplitude. Results obtained in these numerical simulations indicate that with increase in confining pressure there is an increase in liquefaction resistance.
International Nuclear Information System (INIS)
In this paper we describe two analytical numerical methods applied to one-speed slab-geometry deep penetration transport problems. The linear discontinuous (LDN) equations are used to approximate the monoenergetic Boltzmann equation in slab geometry; they are obtained by considering a linear expansion of the angular flux inside each of the N elements of a uniform angular grid. The two analytical numerical methods are referred to as the spectral Green's function (SGF) nodal method and the Laplace transform (LTLDN) method. The SGF nodal method and the LTLDN method generate numerical solutions to the LDN equations that are completely free of spatial approximations, apart from finite arithmetic considerations. Numerical results to typical model problems and suggestions for future work are also presented. (orig.)
Advanced Discrete-Time Control Methods for Industrial Applications
Khatamianfar, Arash
2015-01-01
This thesis focuses on developing advanced control methods for two industrial systems in discrete-time aiming to enhance their performance in delivering the control objectives as well as considering the practical aspects. The first part addresses wind power dispatch into the electricity network using a battery energy storage system (BESS). To manage the amount of energy sold to the electricity market, a novel control scheme is developed based on discrete-time model predictive control (MPC) to...
Advances in nucleic acid-based detection methods.
Wolcott, M J
1992-01-01
Laboratory techniques based on nucleic acid methods have increased in popularity over the last decade with clinical microbiologists and other laboratory scientists who are concerned with the diagnosis of infectious agents. This increase in popularity is a result primarily of advances made in nucleic acid amplification and detection techniques. Polymerase chain reaction, the original nucleic acid amplification technique, changed the way many people viewed and used nucleic acid techniques in cl...
Underwater Photosynthesis of Submerged Plants – Recent Advances and Methods
PEDERSEN, OLE; Colmer, Timothy D.; Sand-Jensen, Kaj
2013-01-01
We describe the general background and the recent advances in research on underwater photosynthesis of leaf segments, whole communities, and plant dominated aquatic ecosystems and present contemporary methods tailor made to quantify photosynthesis and carbon fixation under water. The majority of studies of aquatic photosynthesis have been carried out with detached leaves or thalli and this selectiveness influences the perception of the regulation of aquatic photosynthesis. We thus recommend a...
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 in...... frames are implemented. The developed procedures allow for the exploration of new territories in optimization of architectural structures, and offer new methodological strategies for bridging conceptual gaps between optimization and architectural practice....
Advancing Comparative Climate Change Politics: Theory and Method
Mark Purdon
2015-01-01
Central to this special issue is the notion that the methods and conceptual tools of comparative politics can improve our understanding of global climate change politics. Building on recent advancements in the field of comparative environmental politics, the special issues offers a more comprehensive treatment of climate change politics in developed countries, emerging economies and least developed countries. In this introduction, I distil the key features of comparative politics, advocate fo...
Advanced Regression Methods in Finance and Economics: Three Essays
Hofmarcher, Paul
2012-01-01
In this thesis advanced regression methods are applied to discuss and investigate highly relevant research questions in the areas of finance and economics. In the field of credit risk the thesis investigates a hierarchical model which allows to obtain a consensus score, if several ratings are available for each firm. Autoregressive processes and random effects are used to model both a correlation structure between and within the obligors in the sample. The model also allows to validate ...
A Study on the Increase of Numerical Stability and Accuracy of the Transfer Matrix Method
Ioannis S. Zotos; Theodore N. Costopoulos
2008-01-01
Problem Statement: The transfer matrix method is a very useful tool for the static and dynamic analysis of structures. There are a number of issues though that worsens the numerical stability and the accuracy of this method. Approach: This study proposed a simple technique that can be used to handle these numerical difficulties and overcome the problems they give. Its main idea was to apply the method twice starting from two far ends of the structure. Results: An example from the calculation ...
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.
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.
A study of numerical methods for hyperbolic conservation laws with stiff source terms
Leveque, R. J.; Yee, H. C.
1988-01-01
The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.
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
THEORETICAL AND NUMERICAL COMPARISON ON DOUBLE-PROJECTION METHODS FOR VARIATIONAL INEQUALITIES
Institute of Scientific and Technical Information of China (English)
WANG Yiju; SUN Wenyu
2003-01-01
Recently, double projection methods for solving variational inequalities have received much attention due to their fewer projection times at each iteration. In this paper, we unify these double projection methods within two unified frameworks, which contain the existing double projection methods as special cases. On the basis of this unification, theoretical and numerical comparison between these double projection methods is presented.
Annual progress report FY 1976. [Numerical methods for time-dependent reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Hansen, K.F.; Henry, A.F.
1976-03-01
This project is directed toward development of numerical methods suitable for the computer solution of problems in reactor dynamics and safety. Specific areas of research include methods of integration of the time-dependent diffusion equations by finite difference and finite element methods; representation of reactor properties by various homogenization procedures; application of synthesis methods; and development of response matrix techniques.
On the numerical solution of the point reactor kinetics equations by generalized Runge-Kutta methods
International Nuclear Information System (INIS)
Generalized Runge-Kutta methods specifically devised for the numerical solution of stiff systems of ordinary differential equations are described. An A-stable method is employed to solve several sample point reactor kinetics problems, explicitly showing the quantities required by the method. The accuracy and speed of calculation as obtained by implementing the method in a microcomputer are found to be acceptable
Second order numerical method of two-fluid model of air-water flow
International Nuclear Information System (INIS)
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)
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...
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.
Advanced thermal hydraulic method using 3x3 pin modeling
International Nuclear Information System (INIS)
Advanced thermal hydraulic methods are being developed as part of the US DOE sponsored Nuclear Hub program called CASL (Consortium for Advanced Simulation of LWRs). One of the key objectives of the Hub program is to develop a multi-physics tool which evaluates neutronic, thermal hydraulic, structural mechanics and nuclear fuel rod performance in rod bundles to support power uprates, increased burnup/cycle length and life extension for US nuclear plants. Current design analysis tools are separate and applied in series using simplistic models and conservatisms in the analysis. In order to achieve key Nuclear Hub objectives a higher fidelity, multi-physics tool is needed to address the challenge problems that limit current reactor performance. This paper summarizes the preliminary development of a multi-physics tool by performing 3x3 pin modeling and making comparisons to available data. (author)
Tuncer, Enis; Lang, Sidney.B.
2004-01-01
The Fredholm integral equation of the laser intensity modulation method is solved with the application of the Monte Carlo technique and a least-squares solver. The numerical procedure is tested on simulated data.
The use of numerical methods in the solution of academic problems of classic mechanics
International Nuclear Information System (INIS)
In this work the use of numerical methods in the solution of physics academic problems is discussed, particularly those on classical mechanics. Frequently the solution of academic problems is limited to finding a differential equation which is left unsolved for having no analytical solution. However, by means of numerical methods we can solve these equations and enrich the physical analysis of the problem. This approach also makes the academic process a little closer to modern physical research, where numerical methods have increasingly been used in almost every field. In the present paper we discuss a classical mechanics problem using these methods. We start from both Newton's and Lagrange's formulations and apply different numerical algorithms in the solution of the obtained equations. During last academic semester, recently concluded, we tested the ideas of this work with students of Nuclear Physics career of the Higher Institute of Nuclear Sciences and technologies, at Havana, cuba. The results were encouraging. (Author) 7 refs
Directory of Open Access Journals (Sweden)
V. A. Golovin
1986-04-01
Full Text Available The algorithms of numerical and symbolic analysis methods of linear chains of derivatives and LU-decomposition. An example of the calculation circuit functions using programs that implement the proposed algorithms.
V. A. Golovin; I. S. Kashirskii; V. V. Taranenko
1986-01-01
The algorithms of numerical and symbolic analysis methods of linear chains of derivatives and LU-decomposition. An example of the calculation circuit functions using programs that implement the proposed algorithms.
A survey on C 1,1 fuctions: theory, numerical methods and applications
La Torre Davide; Rocca Matteo
2002-01-01
In this paper we survey some notions of generalized derivative for C 1,1 functions. Furthermore some optimality conditions and numerical methods for nonlinear minimization problems involving C1,1 data are studied.
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...
Springback Simulation: Impact of Some Advanced Constitutive Models and Numerical Parameters
Haddag, Badis; Balan, Tudor; Abed-Meraim, Farid
2005-08-01
The impact of material models on the numerical simulation of springback is investigated. The study is focused on the strain-path sensitivity of two hardening models. While both models predict the Bauschinger effect, their response in the transient zone after a strain-path change is fairly different. Their respective predictions are compared in terms of sequential test response and of strip-drawing springback. For this purpose, an accurate and general time integration algorithm has been developed and implemented in the Abaqus code. The impact of several numerical parameters is also studied in order to assess the overall accuracy of the finite element prediction. For some test geometries, both material and numerical parameters are shown to clearly influence the springback behavior at a large extent. Moreover, a general trend cannot always be extracted, thus justifying the need for the finite element simulation of the stamping process.
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
Briggs, Maxwell H.; Schifer, Nicholas A.
2012-01-01
The U.S. Department of Energy (DOE) and Lockheed Martin Space Systems Company (LMSSC) have been developing the Advanced Stirling Radioisotope Generator (ASRG) for use as a power system for space science missions. This generator would use two high-efficiency Advanced Stirling Convertors (ASCs), developed by Sunpower Inc. and NASA Glenn Research Center (GRC). The ASCs convert thermal energy from a radioisotope heat source into electricity. As part of ground testing of these ASCs, different operating conditions are used to simulate expected mission conditions. These conditions require achieving a particular operating frequency, hot end and cold end temperatures, and specified electrical power output for a given net heat input. In an effort to improve net heat input predictions, numerous tasks have been performed which provided a more accurate value for net heat input into the ASCs, including testing validation hardware, known as the Thermal Standard, to provide a direct comparison to numerical and empirical models used to predict convertor net heat input. This validation hardware provided a comparison for scrutinizing and improving empirical correlations and numerical models of ASC-E2 net heat input. This hardware simulated the characteristics of an ASC-E2 convertor in both an operating and non-operating mode. This paper describes the Thermal Standard testing and the conclusions of the validation effort applied to the empirical correlation methods used by the Radioisotope Power System (RPS) team at NASA Glenn.
Development of advanced nodal diffusion methods for modern computer architectures
International Nuclear Information System (INIS)
A family of highly efficient multidimensional multigroup advanced neutron-diffusion nodal methods, ILLICO, were implemented on sequential, vector, and vector-concurrent computers. Three-dimensional realistic benchmark problems can be solved in vectorized mode in less than 0.73 s (33.86 Mflops) on a Cray X-MP/48. Vector-concurrent implementations yield speedups as high as 9.19 on an Alliant FX/8. These results show that the ILLICO method preserves essentially all of its speed advantage over finite-difference methods. A self-consistent higher-order nodal diffusion method was developed and implemented. Nodal methods for global nuclear reactor multigroup diffusion calculations which account explicitly for heterogeneities in the assembly nuclear properties were developed and evaluated. A systematic analysis of the zero-order variable cross section nodal method was conducted. Analyzing the KWU PWR depletion benchmark problem, it is shown that when burnup heterogeneities arise, ordinary nodal methods, which do not explicitly treat the heterogeneities, suffer a significant systematic error that accumulates. A nodal method that treats explicitly the space dependence of diffusion coefficients was developed and implemented. A consistent burnup-correction method for nodal microscopic depletion analysis was developed
Class of modified parallel combined methods of real-time numerical simulation for a stiff system
Institute of Scientific and Technical Information of China (English)
朱珍民; 刘德贵; 陈丽容
2004-01-01
A class of modified parallel combined methods of real-time numerical simulation are presented for a stiff dynamic system. By combining the parallelism across the system with the parallelism across the method, and relaxing the dependence of stage value computation on sampling time of input function, a class of modified real-time parallel combined methods are constructed. Stiff and nonstiff subsystems are solved in parallel on a parallel computer by a parallel Rosenbrock method and a parallel RK method, respectively. Their order conditions and convergences are discussed. The numerical simulation experiments show that this class of modified algorithms can get high speed and efficiency.
Approximating Mathematical Semantic Web Services Using Approximation Formulas and Numerical Methods
Mogos, Andrei-Horia
2009-01-01
Mathematical semantic web services are very useful in practice, but only a small number of research results are reported in this area. In this paper we present a method of obtaining an approximation of a mathematical semantic web service, from its semantic description, using existing mathematical semantic web services, approximation formulas, and numerical methods techniques. We also give a method for automatic comparison of two complexity functions. In addition, we present a method for classifying the numerical methods mathematical semantic web services from a library.
Filtering material properties to improve FFT-based methods for numerical homogenization
Gélébart, Lionel; Ouaki, Franck
2014-01-01
FFT-based solvers introduced in the 1990s for the numerical homogenization of heterogeneous elastic materials have been extended to a wide range of physical properties. In parallel, alternative algorithms and modified discrete Green operators have been proposed to accelerate the method and/or improve the description of the local fields. In this short note, filtering material properties is proposed as a third complementary way to improve FFT-based methods. It is evidenced from numerical experi...
Numerical Methods for Parameter Estimation and Optimal Control of the Red River Network
Thai, Tran Hong
2005-01-01
In this thesis efficient numerical methods for the simulation, the parameter estimation, and the optimal control of the Red River system are presented. The model of the Red River system is based on the Saint-Venant equation system, which consists of two nonlinear first-order hyperbolic Partial Differential Equations (PDE) in space and in time. In general a system of equations of this type can not be solved analytically. Therefore I choose a numerical approach, namely the Method Of Lines (...
Saeed Hatamzadeh-Varmazyar; Zahra Masouri
2014-01-01
The focus of this article is on calculation of electrostatic charge distribution induced on conducting surfaces. For this purpose, the integral equation concept is used for mathematical modeling of the problem. A special set of exponential basis functions is introduced and defined to be used in formulation of a numerical method for solving the integral equation to obtain the charge distribution. The method is numerically evaluated via calculation of charge density for some structures by which...
Numerical method for solving linear Fredholm fuzzy integral equations of the second kind
International Nuclear Information System (INIS)
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
Institute of Scientific and Technical Information of China (English)
罗振东; 朱江; 谢正辉; 张桂芳
2003-01-01
The non-stationary natural convection problem is studied. A lowest order finite difference scheme based on mixed finite element method for non-stationary natural convection problem, by the spatial variations discreted with finite element method and time with finite difference scheme was derived, where the numerical solution of velocity, pressure, and temperature can be found together, and a numerical example to simulate the close square cavity is given, which is of practical importance.
A Path Integral Approach to Derivative Security Pricing: II. Numerical Methods
Marco Rosa-Clot; Stefano Taddei
1999-01-01
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic numerical method. Then, we apply the latter to some specific financial problems. In particular, we consider the pricing of a European option, a zero-coupon bond, a caplet, an American option, and a Bermudan swaption.
International Nuclear Information System (INIS)
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 method of identifying parameters of oil-water saturation by nuclear logging
International Nuclear Information System (INIS)
This paper considers the problem of identifying parameters of oil and water saturated quartzite-feldspar beds from neutron-neutron and neutron activation logs. These beds are similar to a wider class of polymictic ones. The unknown parameters are porosity, partial volumes of water and oil and the mineral constituents. Here, the mathematical model of the problem is presented, a system of equations for determining the parameters is formulated, and a method numerical solvation is suggested. The efficiency of the approach is supported by results of numerical experiments. In cases when the ill-conditioned nature is essential, the numerical method includes a special regularization procedure
Numerical method for estimating the size of chaotic regions of phase space
International Nuclear Information System (INIS)
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
Numerical simulation of single bubbles rising through subchannels with interface tracking method
International Nuclear Information System (INIS)
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
Advanced reactor physics methods for heterogeneous reactor cores
Thompson, Steven A.
To maintain the economic viability of nuclear power the industry has begun to emphasize maximizing the efficiency and output of existing nuclear power plants by using longer fuel cycles, stretch power uprates, shorter outage lengths, mixed-oxide (MOX) fuel and more aggressive operating strategies. In order to accommodate these changes, while still satisfying the peaking factor and power envelope requirements necessary to maintain safe operation, more complexity in commercial core designs have been implemented, such as an increase in the number of sub-batches and an increase in the use of both discrete and integral burnable poisons. A consequence of the increased complexity of core designs, as well as the use of MOX fuel, is an increase in the neutronic heterogeneity of the core. Such heterogeneous cores introduce challenges for the current methods that are used for reactor analysis. New methods must be developed to address these deficiencies while still maintaining the computational efficiency of existing reactor analysis methods. In this thesis, advanced core design methodologies are developed to be able to adequately analyze the highly heterogeneous core designs which are currently in use in commercial power reactors. These methodological improvements are being pursued with the goal of not sacrificing the computational efficiency which core designers require. More specifically, the PSU nodal code NEM is being updated to include an SP3 solution option, an advanced transverse leakage option, and a semi-analytical NEM solution option.
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...
Numerical Methods for Computing Effective Transport Properties of Flashing Brownian Motors
Latorre, Juan C; Pavliotis, Grigorios A
2013-01-01
We develop a numerical algorithm for computing the effective drift and diffusivity of the steady-state behavior of an overdamped particle driven by a periodic potential whose amplitude is modulated in time by multiplicative noise and forced by additive Gaussian noise (the mathematical structure of a flashing Brownian motor). The numerical algorithm is based on a spectral decomposition of the solution to the Fokker-Planck equation with periodic boundary conditions and the cell problem which result from homogenization theory. We also show that the numerical method of Wang, Peskin, Elston (WPE, 2003) for computing said quantities is equivalent to that resulting from homogenization theory. We show how to adapt the WPE numerical method to this problem by means of discretizing the multiplicative noise via a finite-volume method into a discrete-state Markov jump process which preserves many important properties of the original continuous-state process, such as its invariant distribution and detailed balance. Our num...
Tan, L B; Webb, D C; Kormi, K; Al-Hassani, S T
2001-03-01
The proliferation of stent designs poses difficult problems to clinicians, who have to learn the relative merits of all stents to ensure optimal selection for each lesion, and also to regulatory authorities who have the dilemma of preventing the inappropriate marketing of substandard stents while not denying patients the benefits of advanced technology. Of the major factors influencing long-term results, those of patency and restenosis are being actively studied whereas the mechanical characteristics of devices influencing the technical results of stenting remain under-investigated. Each different stent design has its own particular features. A robust method for the independent objective comparison of the mechanical performance of each design is required. To do this by experimental measurement alone may be prohibitively expensive. A less costly option is to combine computer analysis, employing the standard numerical technique of the finite element method (FEM), with targeted experimental measurements of the specific mechanical behaviour of stents. In this paper the FEM technique is used to investigate the structural behaviour of two different stent geometries: Freedom stent geometry and Palmaz-Schatz (P-S) stent geometry. The effects of altering the stent geometry, the stent wire diameter and contact with (and material properties of) a hard eccentric intravascular lesion (simulating a calcified plaque) on stent mechanical performance were investigated. Increasing the wire diameter and the arterial elastic modulus by 150% results in the need to increase the balloon pressure to expand the stent by 10-fold. Increasing the number of circumferential convolutions increases the pressure required to initiate radial expansion of mounted stents. An incompressible plaque impinging on the mid portion of a stent causes a gross distortion of the Freedom stent and an hour-glass deformity in the P-S stent. These findings are of relevance for future comparative studies of the
Towards numerical simulations of supersonic liquid jets using ghost fluid method
International Nuclear Information System (INIS)
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
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.
High order numerical methods for the space non-homogeneous Boltzmann equation
International Nuclear Information System (INIS)
In this paper we present accurate methods for the numerical solution of the Boltzmann equation of rarefied gas. The methods are based on a time splitting technique. The transport is solved by a third order accurate (in space) positive and flux conservative (PFC) method. The collision step is treated by a Fourier approximation of the collision integral, which guarantees spectral accuracy in velocity, coupled with several high order integrators in time. Strang splitting is used to achieve second order accuracy in space and time. Several numerical tests illustrate the properties of the methods
Energy Technology Data Exchange (ETDEWEB)
Holladay, Jamelyn D.; Wang, Yong
2015-05-01
Microscale (<5W) reformers for hydrogen production have been investigated for over a decade. These devices are intended to provide hydrogen for small fuel cells. Due to the reformer’s small size, numerical simulations are critical to understand heat and mass transfer phenomena occurring in the systems. This paper reviews the development of the numerical codes and details the reaction equations used. The majority of the devices utilized methanol as the fuel due to methanol’s low reforming temperature and high conversion, although, there are several methane fueled systems. As computational power has decreased in cost and increased in availability, the codes increased in complexity and accuracy. Initial models focused on the reformer, while more recently, the simulations began including other unit operations such as vaporizers, inlet manifolds, and combustors. These codes are critical for developing the next generation systems. The systems reviewed included, plate reactors, microchannel reactors, annulus reactors, wash-coated, packed bed systems.
A NEW NUMERICAL WAVE FLUME COMBINING THE 0-1 TYPE BEM AND THE VOF METHOD
Institute of Scientific and Technical Information of China (English)
GUO Li-dong; SUN Da-peng; WU Hao
2012-01-01
A new coupling numerical wave model,based on both the Boundary Element Method (BEM) and the Volume Of Fluid (VOF) method,is established by taking advantages of the both methods to solve the wave-structure interaction problems.In this model,the wave transformation in front of structures is calculated by the 0-1 type BEM,and the intense wave motions near the structures are calculated by the VOF method.In this paper,the characteristics of the BEM and the VOF method are discussed first,and then the coupling treatments are describcd in detail.In the end,the accuracy and the validity of the coupling model are examined by comparing the numerical results with experiment results and other numerical results available for the interactions between regular waves with a monolayer horizontal plate.
Advanced methods for fabrication of PHWR and LMFBR fuels
International Nuclear Information System (INIS)
For self-reliance in nuclear power, the Department of Atomic Energy (DAE), India is pursuing two specific reactor systems, namely the pressurised heavy water reactors (PHWR) and the liquid metal cooled fast breeder reactors (LMFBR). The reference fuel for PHWR is zircaloy-4 clad high density (≤ 96 per cent T.D.) natural UO2 pellet-pins. The advanced PHWR fuels are UO2-PuO2 (≤ 2 per cent), ThO2-PuO2 (≤ 4 per cent) and ThO2-U233O2 (≤ 2 per cent). Similarly, low density (≤ 85 per cent T.D.) (UPu)O2 pellets clad in SS 316 or D9 is the reference fuel for the first generation of prototype and commercial LMFBRs all over the world. However, (UPu)C and (UPu)N are considered as advanced fuels for LMFBRs mainly because of their shorter doubling time. The conventional method of fabrication of both high and low density oxide, carbide and nitride fuel pellets starting from UO2, PuO2 and ThO2 powders is 'powder metallurgy (P/M)'. The P/M route has, however, the disadvantage of generation and handling of fine powder particles of the fuel and the associated problem of 'radiotoxic dust hazard'. The present paper summarises the state-of-the-art of advanced methods of fabrication of oxide, carbide and nitride fuels and highlights the author's experience on sol-gel-microsphere-pelletisation (SGMP) route for preparation of these materials. The SGMP process uses sol gel derived, dust-free and free-flowing microspheres of oxides, carbide or nitride for direct pelletisation and sintering. Fuel pellets of both low and high density, excellent microhomogeneity and controlled 'open' or 'closed' porosity could be fabricated via the SGMP route. (author). 5 tables, 14 figs., 15 refs
Advanced Burnup Method using Inductively Coupled Plasma Mass Spectrometry
Energy Technology Data Exchange (ETDEWEB)
Hilton, Bruce A. [Idaho Natonal Laboratory, P.O. Box 1625, Idaho Falls, ID 83415-6188 (United States); Glagolenko, Irina; Giglio, Jeffrey J.; Cummings, Daniel G
2009-06-15
Nuclear fuel burnup is a key parameter used to assess irradiated fuel performance, to characterize the dependence of property changes due to irradiation, and to perform nuclear materials accountability. For advanced transmutation fuels and high burnup LWR fuels that have multiple fission sources, the existing Nd-148 ASTM burnup determination practice requires input of calculated fission fractions (identifying the specific fission source isotope and neutron energy that yielded fission, e.g., U-235 from thermal neutron, U-238 from fast neutron) from computational neutronics analysis in addition to the measured concentration of a single fission product isotope. We report a novel methodology of nuclear fuel burnup determination, which is completely independent of model predictions and reactor types. The proposed method leverages the capability of Inductively Coupled Plasma Mass Spectrometry (ICP-MS) to quantify multiple fission products and actinides and uses these data to develop a system of burnup equations whose solution is the fission fractions. The fission fractions are substituted back in the equations to determine burnup. This technique requires high fidelity fission yield data, which is not uniformly available for all fission products. We discuss different means that can potentially assist in indirect determination, verification and improvement (refinement) of the ambiguously known fission yields. A variety of irradiated fuel samples are characterized by ICP-MS and the results used to test the advanced burnup method. The samples include metallic alloy fuel irradiated in fast spectrum reactor (EBRII) and metallic alloy in a tailored spectrum and dispersion fuel in the thermal spectrum of the Advanced Test Reactor (ATR). The derived fission fractions and measured burnups are compared with calculated values predicted by neutronics models. (authors)
Advanced Burnup Method using Inductively Coupled Plasma Mass Spectrometry
International Nuclear Information System (INIS)
Nuclear fuel burnup is a key parameter used to assess irradiated fuel performance, to characterize the dependence of property changes due to irradiation, and to perform nuclear materials accountability. For advanced transmutation fuels and high burnup LWR fuels that have multiple fission sources, the existing Nd-148 ASTM burnup determination practice requires input of calculated fission fractions (identifying the specific fission source isotope and neutron energy that yielded fission, e.g., U-235 from thermal neutron, U-238 from fast neutron) from computational neutronics analysis in addition to the measured concentration of a single fission product isotope. We report a novel methodology of nuclear fuel burnup determination, which is completely independent of model predictions and reactor types. The proposed method leverages the capability of Inductively Coupled Plasma Mass Spectrometry (ICP-MS) to quantify multiple fission products and actinides and uses these data to develop a system of burnup equations whose solution is the fission fractions. The fission fractions are substituted back in the equations to determine burnup. This technique requires high fidelity fission yield data, which is not uniformly available for all fission products. We discuss different means that can potentially assist in indirect determination, verification and improvement (refinement) of the ambiguously known fission yields. A variety of irradiated fuel samples are characterized by ICP-MS and the results used to test the advanced burnup method. The samples include metallic alloy fuel irradiated in fast spectrum reactor (EBRII) and metallic alloy in a tailored spectrum and dispersion fuel in the thermal spectrum of the Advanced Test Reactor (ATR). The derived fission fractions and measured burnups are compared with calculated values predicted by neutronics models. (authors)
Review: Advances in delta-subsidence research using satellite methods
Higgins, Stephanie A.
2016-05-01
Most of the world's major river deltas are sinking relative to local sea level. The effects of subsidence can include aquifer salinization, infrastructure damage, increased vulnerability to flooding and storm surges, and permanent inundation of low-lying land. Consequently, determining the relative importance of natural vs. anthropogenic pressures in driving delta subsidence is a topic of ongoing research. This article presents a review of knowledge with respect to delta surface-elevation loss. The field is rapidly advancing due to applications of space-based techniques: InSAR (interferometric synthetic aperture radar), GPS (global positioning system), and satellite ocean altimetry. These techniques have shed new light on a variety of subsidence processes, including tectonics, isostatic adjustment, and the spatial and temporal variability of sediment compaction. They also confirm that subsidence associated with fluid extraction can outpace sea-level rise by up to two orders of magnitude, resulting in effective sea-level rise that is one-hundred times faster than the global average rate. In coming years, space-based and airborne instruments will be critical in providing near-real-time monitoring to facilitate management decisions in sinking deltas. However, ground-based observations continue to be necessary for generating complete measurements of surface-elevation change. Numerical modeling should seek to simulate couplings between subsidence processes for greater predictive power.
Review: Advances in delta-subsidence research using satellite methods
Higgins, Stephanie A.
2015-11-01
Most of the world's major river deltas are sinking relative to local sea level. The effects of subsidence can include aquifer salinization, infrastructure damage, increased vulnerability to flooding and storm surges, and permanent inundation of low-lying land. Consequently, determining the relative importance of natural vs. anthropogenic pressures in driving delta subsidence is a topic of ongoing research. This article presents a review of knowledge with respect to delta surface-elevation loss. The field is rapidly advancing due to applications of space-based techniques: InSAR (interferometric synthetic aperture radar), GPS (global positioning system), and satellite ocean altimetry. These techniques have shed new light on a variety of subsidence processes, including tectonics, isostatic adjustment, and the spatial and temporal variability of sediment compaction. They also confirm that subsidence associated with fluid extraction can outpace sea-level rise by up to two orders of magnitude, resulting in effective sea-level rise that is one-hundred times faster than the global average rate. In coming years, space-based and airborne instruments will be critical in providing near-real-time monitoring to facilitate management decisions in sinking deltas. However, ground-based observations continue to be necessary for generating complete measurements of surface-elevation change. Numerical modeling should seek to simulate couplings between subsidence processes for greater predictive power.
The application of advanced rotor (performance) methods for design calculations
Energy Technology Data Exchange (ETDEWEB)
Bussel, G.J.W. van [Delft Univ. of Technology, Inst. for Wind Energy, Delft (Netherlands)
1997-08-01
The calculation of loads and performance of wind turbine rotors has been a topic for research over the last century. The principles for the calculation of loads on rotor blades with a given specific geometry, as well as the development of optimal shaped rotor blades have been published in the decades that significant aircraft development took place. Nowadays advanced computer codes are used for specific problems regarding modern aircraft, and application to wind turbine rotors has also been performed occasionally. The engineers designing rotor blades for wind turbines still use methods based upon global principles developed in the beginning of the century. The question what to expect in terms of the type of methods to be applied in a design environment for the near future is addressed here. (EG) 14 refs.
Methods and Systems for Advanced Spaceport Information Management
Fussell, Ronald M. (Inventor); Ely, Donald W. (Inventor); Meier, Gary M. (Inventor); Halpin, Paul C. (Inventor); Meade, Phillip T. (Inventor); Jacobson, Craig A. (Inventor); Blackwell-Thompson, Charlie (Inventor)
2007-01-01
Advanced spaceport information management methods and systems are disclosed. In one embodiment, a method includes coupling a test system to the payload and transmitting one or more test signals that emulate an anticipated condition from the test system to the payload. One or more responsive signals are received from the payload into the test system and are analyzed to determine whether one or more of the responsive signals comprises an anomalous signal. At least one of the steps of transmitting, receiving, analyzing and determining includes transmitting at least one of the test signals and the responsive signals via a communications link from a payload processing facility to a remotely located facility. In one particular embodiment, the communications link is an Internet link from a payload processing facility to a remotely located facility (e.g. a launch facility, university, etc.).
Hermand, Jean-Pierre; Berrada, Mohamed; Meyer, Matthias; Asch, Mark
2005-09-01
Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK '94 experimental conditions.
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.
Crouseilles, Nicolas; Lemou, Mohammed
2016-01-01
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\\em in both space and time}.Such PDE models arise in semiclassical modeling of quantum dynamics with band-crossings, and otherhighly oscillatory waves. Our first main idea is to use the nonlinear geometric optics ansatz, which builds theoscillatory phase into an independent variable. We then choose suitable initial data, based on the Chapman-Enskog expansion, for the new model. For a scalar model, we prove that so constructed model will have certain smoothness, and consequently, for a first order approximation scheme we prove uniform error estimates independent of the (possibly small) wave length. The method is extended to systems arising from a semiclassical model for surface hopping, a non-adiabatic quantum dynamic phenomenon. Numerous numerical examples demonstrate that the method has the desired properties...
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.
Viscous-Inviscid Coupling Methods for Advanced Marine Propeller Applications
Directory of Open Access Journals (Sweden)
Martin Greve
2012-01-01
Full Text Available The paper reports the development of coupling strategies between an inviscid direct panel method and a viscous RANS method and their application to complex propeller ows. The work is motivated by the prohibitive computational cost associated to unsteady viscous flow simulations using geometrically resolved propellers to analyse the dynamics of ships in seaways. The present effort aims to combine the advantages of the two baseline methods in order to reduce the numerical effort without compromising the predictive accuracy. Accordingly, the viscous method is used to calculate the global flow field, while the inviscid method predicts the forces acting on the propeller. The corresponding reaction forces are employed as body forces to mimic the propeller influence on the viscous flow field. Examples included refer to simple verification cases for an isolated propeller blade, open-water validation simulations for a complete propeller, and more challenging investigations of a manoeuvring vessel in seaways. Reported results reveal a fair predictive agreement between the coupled approach and fully viscous simulations and display the efficiency of the coupled approach.
Casimir Forces via Worldline Numerics: Method Improvements and Potential Engineering Applications
Aehlig, Klaus; Fischbacher, Thomas; Gerhard, Jochen
2011-01-01
The string theory inspired Worldline Numerics approach to Casimir force calculations has some favourable characteristics that might make it well suited for geometric optimization problems as they arise e.g. in NEMS device engineering. We explain this aspect in detail, developing some refinements of the method along the way. Also, we comment on the problem of generalizing Worldline Numerics from scalars to photons in the presence of conductors.
Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.
1992-01-01
The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.
Analysis of liquid steel flow in a multi-strand tundish using numerical methods
Directory of Open Access Journals (Sweden)
P. Warzecha
2015-07-01
Full Text Available The article presents the results of liquid steel flow and mixing in tundish when applying turbulence inhibitor to modernize the tundish working zone. The flow of six-strand continuous casting tundish of a trough-type was investigated with numerical modeling. For turbulence modeling, the Reynolds-Averaged Navier-Stokes (RANS equation and the Large Eddy Simulation (LES methods have been used. Numerical simulations are carried out with the finitevolume commercial code AnsysFluent.
A numerical method for the time coarsening of transport processes at the atomistic scale
Gonzalez-Ferreiro, B.; Romero, I.; Ortiz, M.
2016-05-01
We propose a novel numerical scheme for the simulation of slow transport processes at the atomistic scale. The scheme is based on a model for non-equilibrium statistical thermodynamics recently proposed by the authors, and extends it by formulating a variational integrator, i.e. a discrete functional whose optimality conditions provide all the governing equations of the problem. The method is employed to study surface segregation of AuAg alloys and its convergence is confirmed numerically.
Terrain Modelling with GIS for Tectonic Geomorphology : Numerical Methods and Applications
Jordan, Gyözö
2004-01-01
Analysis of digital elevation models (DEMs) by means of geomorphometry provides means of recognising fractures and characterising the morphotectonics of an area in a quantitative way. The objective of the thesis is to develop numerical methods and a consistent GIS methodology for tectonic geomorphology and apply it to test sites. Based on the study of landforms related to faults, geomorphological characteristics are translated into mathematical and numerical algorithms. The methodology is bas...
Study Notes on Numerical Solutions of the Wave Equation with the Finite Difference Method
Adib, A B
2000-01-01
In this introductory work I will present the Finite Difference method for hyperbolic equations, focusing on a method which has second order precision both in time and space (the so-called leap-frog method) and applying it to the case of the 1d and 2d wave equation. A brief derivation of the energy and equation of motion of a wave is done before the numerical part in order to make the transition from the continuum to the lattice clearer. To illustrate the extension of the method to more complex equations, I also add dissipative terms of the kind $-\\eta \\dot{u}$ into the equations. The von Neumann numerical stability analysis and the Courant criterion, two of the most popular in the literature, are briefly discussed. In the end I present some numerical results obtained with the leap-frog algorithm, illustrating the importance of the lattice resolution through energy plots.
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.
A Numerical Method for Cavity Identification in Beams on an Elastic Foundation
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
An analytical solution for the natural frequencies of a beam containing a cavity on an elastic foundation is presented. Based on the analytical solution, a numerical method for identifying cavities in the foundation is developed. The position and size of the cavities are identified by minimizing an objective function, which is formulated according to the difference between the computed and measured natural frequencies of the system. The conjugate gradient algorithm is adopted for minimizing the objective function. Some numerical examples are presented to demonstrate the applicability of the presented cavity determination method. The results show that the presented method can be used to identify the cavity position and size conveniently and efficiently.
A study of numerical methods for hyperbolic conservation laws with stiff source terms
Leveque, R. J.; Yee, H. C.
1990-01-01
In the present study of the behavior of typical numerical methods in the case of a model advection equation having a parameter-dependent source term, two approaches to the incorporation of the source terms are used: MacCormack-type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. The latter are found to perform slightly better. The model scalar equation is used to show that the incorrectness of the propagation speeds of discontinuities observed in the stiff case is due to the introduction of nonequilibrium values through numerical dissipation in the advection step.
Numerical modeling of concrete hydraulic fracturing with extended finite element method
Institute of Scientific and Technical Information of China (English)
REN QingWen; DONG YuWen; YU TianTang
2009-01-01
The extended finite element method (XFEM) is a new numerical method for modeling discontinuity.Research about numerical modeling for concrete hydraulic fracturing by XFEM is explored. By building the virtual work principle of the fracture problem considering water pressure on the crack surface, the governing equations of XFEM for hydraulic fracture modeling are derived. Implementation of the XFEM for hydraulic fracturing is presented. Finally, the method is verified by two examples and the advan-tages of the XFEM for hydraulic fracturing analysis are displayed.
Numerical modeling of concrete hydraulic fracturing with extended finite element method
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The extended finite element method (XFEM) is a new numerical method for modeling discontinuity. Research about numerical modeling for concrete hydraulic fracturing by XFEM is explored. By building the virtual work principle of the fracture problem considering water pressure on the crack surface, the governing equations of XFEM for hydraulic fracture modeling are derived. Implementation of the XFEM for hydraulic fracturing is presented. Finally, the method is verified by two examples and the advan- tages of the XFEM for hydraulic fracturing analysis are displayed.
Holladay, J. D.; Wang, Y.
2015-05-01
Microscale (methanol as the fuel due to methanol's low reforming temperature and high conversion, although, there are several methane fueled systems. The increased computational power and more complex codes have led to improved accuracy of numerical simulations. Initial models focused on the reformer, while more recently, the simulations began including other unit operations such as vaporizers, inlet manifolds, and combustors. These codes are critical for developing the next generation systems. The systems reviewed included plate reactors, microchannel reactors, and annulus reactors for both wash-coated and packed bed systems.
Numerical algorithm based on the PDE method for solution of the Fokker-Planck equation
International Nuclear Information System (INIS)
This paper discus a fast and accurate algorithm for numerical solution of Fokker-Planck equation (FPE) based on the PDE (Partial Differential Equation) method. The PDE concepts and methods largely are used in computer simulation of fluid-dynamical systems. This method can be used for studying of stochastic beam dynamics in one dimensional phase space in the storage ring. The performances of the PDE-method are calculated using the stochastic cooling process in the CR storage ring (FAIR, Germany).
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The numerical solution of functional differential equations with a proportional delay is considered. The stability of general linear methods for linear systems of neutral type is investigated. It is shown that a general linear method with strict stability at infinity can preserve the asymptotic stability of the underlying system if we employ an appropriate equi-stage interpolation to approximate the delay argument.
Using a finite horizon numerical optimisation method for a periodic optimal control problem
Azzato, Jeffrey D.; Krawczyk, Jacek
2007-01-01
Computing a numerical solution to a periodic optimal control problem is difficult. A method of approximating a solution to a given (stochastic) optimal control problem using Markov chains was developed in [3]. This paper describes an attempt at applying this method to a periodic optimal control problem introduced in [2].
Plakhov, Iu. V.; Mytsenko, A. V.; Shel'Pov, V. A.
A numerical integration method is developed that is more accurate than Everhart's (1974) implicit single-sequence approach for integrating orbits. This method can be used to solve problems of space geodesy based on the use of highly precise laser observations.
An efficient step-size control method in numerical integration for astrodynamical equations
Liu, C. Z.; Cui, D. X.
2002-11-01
Using the curvature of the integral curve, a step-size control method is introduced in this paper. This method will prove to be the efficient scheme in the sense that it saves computation time and improve accuracy of numerical integration.
Numerical Method for Determining Stiffness Characteristics of an Arbitrary Form Superelement
Directory of Open Access Journals (Sweden)
Tsybenko Alexander
2015-12-01
Full Text Available As part of the superelement approximation technology for fragments (subsystems of the analyzed structures, a numerical method of determining the characteristics of arbitrary type superelements was developed. The examples of simulation models with two-node superelements demonstrated the efficacy of the method in the structural analysis of elastic systems.
Numerical experiments on the performance of the RBF meshfree Galerkin Methods for solid mechanics
HAMRANI, Abderrachid; Monteiro, Eric; BELAIDI, Idir; Lorong, Philippe
2015-01-01
In this work the advances in meshfree methods, partic- ularly the Radial Basis Function based meshfree Galerkin Methods, are presented with the purpose of analyzing the performance of their meshless approximations and integration techniques. The Radial Point Interpolation Method (RPIM) is studied based on the global Galerkin weak form performed using classical Gaussian integration and the stabilized conforming nodal integration scheme. The numeri- cal performance of this category of methods i...
Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems
Energy Technology Data Exchange (ETDEWEB)
Hykes, J. M.; Ferrer, R. M. [Studsvik Scandpower, Inc., 504 Shoup Avenue, Idaho Falls, ID (United States)
2013-07-01
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 {sup 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)
Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems
International Nuclear Information System (INIS)
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 98Nb 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)
International Nuclear Information System (INIS)
The seismic protection of historical and monumental buildings, namely dating back from the ancient age up to the 20th Century, is being looked at with greater and greater interest, above all in the Euro-Mediterranean area, its cultural heritage being strongly susceptible to undergo severe damage or even collapse due to earthquake. The cultural importance of historical and monumental constructions limits, in many cases, the possibility to upgrade them from the seismic point of view, due to the fear of using intervention techniques which could have detrimental effects on their cultural value. Consequently, a great interest is growing in the development of sustainable methodologies for the use of Reversible Mixed Technologies (RMTs) in the seismic protection of the existing constructions. RMTs, in fact, are conceived for exploiting the peculiarities of innovative materials and special devices, and they allow ease of removal when necessary. This paper deals with the experimental and numerical studies, framed within the EC PROHITECH research project, on the application of RMTs to the historical and monumental constructions mainly belonging to the cultural heritage of the Euro-Mediterranean area. The experimental tests and the numerical analyses are carried out at five different levels, namely full scale models, large scale models, sub-systems, devices, materials and elements
Numerical Study on Crossflow Printed Circuit Heat Exchanger for Advanced Small Modular Reactors
International Nuclear Information System (INIS)
Various fluids such as water, gases (helium), molten salts (FLiNaK, FLiBe) and liquid metal (sodium) are used as a coolant of advanced small modular reactors (SMRs). The printed circuit heat exchanger (PCHE) has been adopted as the intermediate and/or secondary heat exchanger of SMR systems because this heat exchanger is compact and effective. The size and cost of PCHE can be changed by the coolant type of each SMR. In this study, the crossflow PCHE analysis code for advanced small modular reactor has been developed for the thermal design and cost estimation of the heat exchanger. The analytical solution of single pass, both unmixed fluids crossflow heat exchanger model was employed to calculate a two dimensional temperature profile of a crossflow PCHE. The analytical solution of crossflow heat exchanger was simply implemented by using built in function of the MATLAB program. The effect of fluid property uncertainty on the calculation results was evaluated. In addition, the effect of heat transfer correlations on the calculated temperature profile was analyzed by taking into account possible combinations of primary and secondary coolants in the SMR systems. Size and cost of heat exchanger were evaluated for the given temperature requirement of each SMR
Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly
2016-01-01
This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.
A Finite Volume Method with Unstructured Triangular Grids for Numerical Modeling of Tidal Current
Institute of Scientific and Technical Information of China (English)
SHI Hong-da; LIU zhen
2005-01-01
The finite volume method (FVM) has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker's problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.
Recent advances in computational structural reliability analysis methods
Thacker, Ben H.; Wu, Y.-T.; Millwater, Harry R.; Torng, Tony Y.; Riha, David S.
1993-01-01
The goal of structural reliability analysis is to determine the probability that the structure will adequately perform its intended function when operating under the given environmental conditions. Thus, the notion of reliability admits the possibility of failure. Given the fact that many different modes of failure are usually possible, achievement of this goal is a formidable task, especially for large, complex structural systems. The traditional (deterministic) design methodology attempts to assure reliability by the application of safety factors and conservative assumptions. However, the safety factor approach lacks a quantitative basis in that the level of reliability is never known and usually results in overly conservative designs because of compounding conservatisms. Furthermore, problem parameters that control the reliability are not identified, nor their importance evaluated. A summary of recent advances in computational structural reliability assessment is presented. A significant level of activity in the research and development community was seen recently, much of which was directed towards the prediction of failure probabilities for single mode failures. The focus is to present some early results and demonstrations of advanced reliability methods applied to structural system problems. This includes structures that can fail as a result of multiple component failures (e.g., a redundant truss), or structural components that may fail due to multiple interacting failure modes (e.g., excessive deflection, resonate vibration, or creep rupture). From these results, some observations and recommendations are made with regard to future research needs.
Exploration of Advanced Probabilistic and Stochastic Design Methods
Mavris, Dimitri N.
2003-01-01
The primary objective of the three year research effort was to explore advanced, non-deterministic aerospace system design methods that may have relevance to designers and analysts. The research pursued emerging areas in design methodology and leverage current fundamental research in the area of design decision-making, probabilistic modeling, and optimization. The specific focus of the three year investigation was oriented toward methods to identify and analyze emerging aircraft technologies in a consistent and complete manner, and to explore means to make optimal decisions based on this knowledge in a probabilistic environment. The research efforts were classified into two main areas. First, Task A of the grant has had the objective of conducting research into the relative merits of possible approaches that account for both multiple criteria and uncertainty in design decision-making. In particular, in the final year of research, the focus was on the comparison and contrasting between three methods researched. Specifically, these three are the Joint Probabilistic Decision-Making (JPDM) technique, Physical Programming, and Dempster-Shafer (D-S) theory. The next element of the research, as contained in Task B, was focused upon exploration of the Technology Identification, Evaluation, and Selection (TIES) methodology developed at ASDL, especially with regards to identification of research needs in the baseline method through implementation exercises. The end result of Task B was the documentation of the evolution of the method with time and a technology transfer to the sponsor regarding the method, such that an initial capability for execution could be obtained by the sponsor. Specifically, the results of year 3 efforts were the creation of a detailed tutorial for implementing the TIES method. Within the tutorial package, templates and detailed examples were created for learning and understanding the details of each step. For both research tasks, sample files and
An unconditionally stable method for numerically solving solar sail spacecraft equations of motion
Karwas, Alex
Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach
Comparative Assessment of Advanced Gay Hydrate Production Methods
Energy Technology Data Exchange (ETDEWEB)
M. D. White; B. P. McGrail; S. K. Wurstner
2009-06-30
Displacing natural gas and petroleum with carbon dioxide is a proven technology for producing conventional geologic hydrocarbon reservoirs, and producing additional yields from abandoned or partially produced petroleum reservoirs. Extending this concept to natural gas hydrate production offers the potential to enhance gas hydrate recovery with concomitant permanent geologic sequestration. Numerical simulation was used to assess a suite of carbon dioxide injection techniques for producing gas hydrates from a variety of geologic deposit types. Secondary hydrate formation was found to inhibit contact of the injected CO{sub 2} regardless of injectate phase state, thus diminishing the exchange rate due to pore clogging and hydrate zone bypass of the injected fluids. Additional work is needed to develop methods of artificially introducing high-permeability pathways in gas hydrate zones if injection of CO{sub 2} in either gas, liquid, or micro-emulsion form is to be more effective in enhancing gas hydrate production rates.