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.
Numerical Simulation of Independent Advance of Ore Breaking in the Non-pillar Sublevel Caving Method
Institute of Scientific and Technical Information of China (English)
ZHOU Chuan-bo; YAO Ying-kang; GUO Liao-wu; YIN Xiao-peng; FAN Xiao-feng; SHANG Ying
2007-01-01
The mechanism of stress generation and propagation by detonation loading in five separate independent advance of ore breaking patterns is discussed in the paper. An elastic numerical model was developed using ANSYS/LS-DYNA 3D Nonlinear Dynamic Finite Element Software. In this package ANSYS is the preprocessor and LS-DYNA is the postprocessor. Numerical models in the paper to actual were 1:10 and the element mesh was dissected in scanning mode utilizing the symmetry characteristics of the numerical model. Five different advance rates were studied. Parameters, such as the time required to maximum stress, the action time of the available stress, the maximum velocity of the nodes, the stress penetration time, the magnitude of the stress peak and the time duration for high stress were numerically simulated. The 2.2 m advance appeared optimum from an analysis of the simulation results. The results from numerical simulation have been validated by tests with physical models.
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.
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.
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.
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.
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.
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...
Bayesian analysis of general failure data from an ageing distribution: advances in numerical methods
Energy Technology Data Exchange (ETDEWEB)
Procaccia, H.; Villain, B. [Electricite de France (EDF), 93 - Saint-Denis (France); Clarotti, C.A. [ENEA, Casaccia (Italy)
1996-12-31
EDF and ENEA carried out a joint research program for developing the numerical methods and computer codes needed for Bayesian analysis of component-lives in the case of ageing. Early results of this study were presented at ESREL`94. Since then the following further steps have been gone: input data have been generalized to the case that observed lives are censored both on the right and on the left; allowable life distributions are Weibull and gamma - their parameters are both unknown and can be statistically dependent; allowable priors are histograms relative to different parametrizations of the life distribution of concern; first-and-second-order-moments of the posterior distributions can be computed. In particular the covariance will give some important information about the degree of the statistical dependence between the parameters of interest. An application of the code to the appearance of a stress corrosion cracking in a tube of the PWR Steam Generator system is presented. (authors). 10 refs.
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 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
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
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...
Energy Technology Data Exchange (ETDEWEB)
Kollias, Pavlos [McGill Univ., Montreal, QC (Canada
2016-09-06
This the final report for the DE-SC0007096 - Advancing Clouds Lifecycle Representation in Numerical Models Using Innovative Analysis Methods that Bridge ARM Observations and Models Over a Breadth of Scales - PI: Pavlos Kollias. The final report outline the main findings of the research conducted using the aforementioned award in the area of cloud research from the cloud scale (10-100 m) to the mesoscale (20-50 km).
NATO Advanced Study Institute on Advanced Physical Oceanographic Numerical Modelling
1986-01-01
This book is a direct result of the NATO Advanced Study Institute held in Banyuls-sur-mer, France, June 1985. The Institute had the same title as this book. It was held at Laboratoire Arago. Eighty lecturers and students from almost all NATO countries attended. The purpose was to review the state of the art of physical oceanographic numerical modelling including the parameterization of physical processes. This book represents a cross-section of the lectures presented at the ASI. It covers elementary mathematical aspects through large scale practical aspects of ocean circulation calculations. It does not encompass every facet of the science of oceanographic modelling. We have, however, captured most of the essence of mesoscale and large-scale ocean modelling for blue water and shallow seas. There have been considerable advances in modelling coastal circulation which are not included. The methods section does not include important material on phase and group velocity errors, selection of grid structures, advanc...
Advanced 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.
Numerical methods in matrix computations
Björck, Åke
2015-01-01
Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work. Åke Björck is a professor emeritus at the Department of Mathematics, Linköping University. He is a Fellow of the Society of Industrial and Applied Mathematics.
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.
Wang, Ying; Krafczyk, Manfred; Geier, Martin; Schönherr, Martin
2014-05-01
The quantification of soil evaporation and of soil water content dynamics near the soil surface are critical in the physics of land-surface processes on many scales and are dominated by multi-component and multi-phase mass and energy fluxes between the ground and the atmosphere. Although it is widely recognized that both liquid and gaseous water movement are fundamental factors in the quantification of soil heat flux and surface evaporation, their computation has only started to be taken into account using simplified macroscopic models. As the flow field over the soil can be safely considered as turbulent, it would be natural to study the detailed transient flow dynamics by means of Large Eddy Simulation (LES [1]) where the three-dimensional flow field is resolved down to the laminar sub-layer. Yet this requires very fine resolved meshes allowing a grid resolution of at least one order of magnitude below the typical grain diameter of the soil under consideration. In order to gain reliable turbulence statistics, up to several hundred eddy turnover times have to be simulated which adds up to several seconds of real time. Yet, the time scale of the receding saturated water front dynamics in the soil is on the order of hours. Thus we are faced with the task of solving a transient turbulent flow problem including the advection-diffusion of water vapour over the soil-atmospheric interface represented by a realistic tomographic reconstruction of a real porous medium taken from laboratory probes. Our flow solver is based on the Lattice Boltzmann method (LBM) [2] which has been extended by a Cumulant approach similar to the one described in [3,4] to minimize the spurious coupling between the degrees of freedom in previous LBM approaches and can be used as an implicit LES turbulence model due to its low numerical dissipation and increased stability at high Reynolds numbers. The kernel has been integrated into the research code Virtualfluids [5] and delivers up to 30% of the
Directory of Open Access Journals (Sweden)
F. Álvarez-Velarde
2012-01-01
Full Text Available A fast numerical method for the calculation in a zero-dimensional approach of the equilibrium isotopic composition of an iteratively used transmutation system in an advanced fuel cycle, based on the Banach fixed point theorem, is described in this paper. The method divides the fuel cycle in successive stages: fuel fabrication, storage, irradiation inside the transmutation system, cooling, reprocessing, and incorporation of the external material into the new fresh fuel. The change of the fuel isotopic composition, represented by an isotope vector, is described in a matrix formulation. The resulting matrix equations are solved using direct methods with arbitrary precision arithmetic. The method has been successfully applied to a double-strata fuel cycle with light water reactors and accelerator-driven subcritical systems. After comparison to the results of the EVOLCODE 2.0 burn-up code, the observed differences are about a few percents in the mass estimations of the main actinides.
Introduction to precise numerical methods
Aberth, Oliver
2007-01-01
Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. All disc-based content for this title is now available on the Web. · Clearer, simpler descriptions and explanations ofthe various numerical methods· Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane.
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
Advanced numerical simulation of collapsible earth dams
Energy Technology Data Exchange (ETDEWEB)
De Farias, M.M.; Cordao Neto, M.P. [Brasilia Univ., Federal District (Brazil). Dept. of Civil and Environmental Engineering
2010-12-15
This paper discussed a systematic methodology for the hydromechanical coupled numerical analysis of earth dams constructed with unsaturated collapsible soil. Every design stage was considered, including construction, reservoir filling, and advance of saturation front until the steady-state flow condition is attained. A transient analysis of safety factors applicable to 3-dimensional conditions was presented, giving consideration to unsaturated materials and the interrelation between hydraulic and mechanical phenomena by solving equilibrium and continuity conditions at the same time. The finite element method was used to formulate equilibrium and continuity conditions for both soil skeleton and pore water, which necessitated a realistic mechanical model for the stress-strain-suction relation in unsaturated porous material and adequate constitutive models related to water flow and storage, giving special consideration to imposing appropriate boundary conditions for each simulation stage. The methodology was applied to the analysis of earth dams composed of soils at optimum, dry of optimum, and mixed compaction conditions. The dry section simulated dams constructed using poorly compacted, dry material, which are prone to collapse. By strategically placing the optimum materials in the areas of the earth fill that are most stressed, the mixed section could be designed less expensively with the same or better performance as the homogenous section at optimum conditions. The coupled analysis provides a higher safety factor than uncoupled analysis and a realistic picture of end-of-construction pore pressure distribution. The simulation of reservoir filling and saturation front advance permitted clear identification of the initialization, development, and evolution of internal failure mechanisms. 21 refs., 6 tabs., 19 figs.
7th European Conference on Numerical Mathematics and Advanced Applications
Of, Günther; Steinbach, Olaf
2008-01-01
The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of meetings held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. These proceedings contain a selection of invited plenary lectures, papers presented in minisymposia and contributed papers. Topics include theoretical aspects of new numerical techniques and algorithms as well as of applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scientific computing and their applications.
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
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...
Numerical methods in multibody dynamics
Eich-Soellner, Edda
1998-01-01
Today computers play an important role in the development of complex mechanical systems, such as cars, railway vehicles or machines. Efficient simulation of these systems is only possible when based on methods that explore the strong link between numerics and computational mechanics. This book gives insight into modern techniques of numerical mathematics in the light of an interesting field of applications: multibody dynamics. The important interaction between modeling and solution techniques is demonstrated by using a simplified multibody model of a truck. Different versions of this mechanical model illustrate all key concepts in static and dynamic analysis as well as in parameter identification. The book focuses in particular on constrained mechanical systems. Their formulation in terms of differential-algebraic equations is the backbone of nearly all chapters. The book is written for students and teachers in numerical analysis and mechanical engineering as well as for engineers in industrial research labor...
Operator theory and numerical methods
Fujita, H; Suzuki, T
2001-01-01
In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method.
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...
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.
Some recent advances in the numerical solution of differential equations
D'Ambrosio, Raffaele
2016-06-01
The purpose of the talk is the presentation of some recent advances in the numerical solution of differential equations, with special emphasis to reaction-diffusion problems, Hamiltonian problems and ordinary differential equations with discontinuous right-hand side. As a special case, in this short paper we focus on the solution of reaction-diffusion problems by means of special purpose numerical methods particularly adapted to the problem: indeed, following a problem oriented approach, we propose a modified method of lines based on the employ of finite differences shaped on the qualitative behavior of the solutions. Constructive issues and a brief analysis are presented, together with some numerical experiments showing the effectiveness of the approach and a comparison with existing solvers.
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...
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.
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.
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)
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.
Numerical methods for CVD simulation
Van Veldhuizen, S.; Vuik, C.; Kleijn, C.R.
2006-01-01
In this study various numerical schemes for simulating 2D laminar reacting gas flows, as typically found in Chemical Vapor Deposition (CVD) reactors, are proposed and compared. These systems are generally modeled by means of many stiffly coupled elementary gas phase reactions between a large number
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 Equations and its Applications
Argyros, Ioannis K
2012-01-01
This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter contains several new theoretical results and important applications in engineering, in dynamic economics systems, in input-output system, in the solution of nonlinear and linear differential equations, and optimization problem.
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.
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...
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.
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.``
Advances in energy harvesting methods
Elvin, Niell
2012-01-01
Advances in Energy Harvesting Methods presents a state-of-the-art understanding of diverse aspects of energy harvesting with a focus on: broadband energy conversion, new concepts in electronic circuits, and novel materials. This book covers recent advances in energy harvesting using different transduction mechanisms; these include methods of performance enhancement using nonlinear effects, non-harmonic forms of excitation and non-resonant energy harvesting, fluidic energy harvesting, and advances in both low-power electronics as well as material science. The contributors include a brief liter
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
Institute of Scientific and Technical Information of China (English)
王琪; 庄方方; 郭易圆; 章杰; 房杰
2013-01-01
The numerical method for the non-smooth dynamics of multibody systems is one of the hot topics of researches on the dynamics of multibody systems. In this paper, recent advances in the research on numerical methods are presented for the non-smooth dynamics of multibody systems with impact and friction. First, the Coulomb friction model, modified Coulomb friction model and the characteristics of the normal forces of multibody systems with unilateral and bilateral constraints are discussed. Second, recently developed numerical methods for the non-smooth dynamics of multibody systems based on continuous and discontinuous models are reviewed. The Event-driven scheme and time-stepping method for the non-smooth dynamics of multibody systems are described in detail based on the complementarity concept. These numerical methods are then analysed and compared. Finally, the problems in need of further studies are pointed out.%非光滑多体系统动力学数值计算方法是多体系统动力学研究的重要内容之一.本文介绍了近年来含摩擦与碰撞的非光滑多体系统动力学数值算法方面的研究进展.首先,讨论了库仑摩擦模型和修正的库仑摩擦模型,以及具有单边和双边约束的多体系统中法向约束力的特点.其次,回顾了基于连续模型和非连续模型的多体系统动力学方程的数值计算方法,详细介绍了基于互补概念的非光滑多体系统动力学的事件驱动法和时间步进法,分析比较了相关的数值算法.最后,指出了一些需要进一步研究的问题.
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.
A new numerical method on unstructured grids
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A new numerical method-basic function method is proposed. This method can directly discrete differential operators on unstructured grids. By using the expansion of basic function to approach the exact function,the central and upwind schemes of derivative are constructed. By using the polynomial as basic function,applying the technique of flux splitting method and the combination of central and upwind schemes,the non-physical fluctuation near the shock wave is suppressed. The first-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical results of many typical examples for one-,two-and three-dimensional inviscid compressible steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave. Especially,combining with the adaptive remeshing technique,the satisfactory results can be obtained by these schemes.
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.
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.
Preface to advances in numerical simulation of plasmas
Parker, Scott E.; Chacon, Luis
2016-10-01
This Journal of Computational Physics Special Issue, titled "Advances in Numerical Simulation of Plasmas," presents a snapshot of the international state of the art in the field of computational plasma physics. The articles herein are a subset of the topics presented as invited talks at the 24th International Conference on the Numerical Simulation of Plasmas (ICNSP), August 12-14, 2015 in Golden, Colorado. The choice of papers was highly selective. The ICNSP is held every other year and is the premier scientific meeting in the field of computational plasma physics.
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 in electron magnetic resonance
Energy Technology Data Exchange (ETDEWEB)
Soernes, A.R
1998-07-01
The focal point of the thesis is the development and use of numerical methods in the analysis, simulation and interpretation of Electron Magnetic Resonance experiments on free radicals in solids to uncover the structure, the dynamics and the environment of the system.
Numerical methods in nuclear engineering. Part 1
International Nuclear Information System (INIS)
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 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.
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
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.
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
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 Methods for Nonlinear PDEs in Finance
DEFF Research Database (Denmark)
Mashayekhi, Sima
Nonlinear Black-Scholes equations arise from considering parameters such as feedback and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some nite dierence schemes have been...... investigated to solve numerically such nonlinear equations. However the analytical solution of the linear Black-Scholes equation is known, dierent numerical methods have been considered for solving the equation to make a general numerical scheme for solving other more complicated models with no analytical...... solutions such as nonlinear Black-Scholes models. Therefore at rst some investigations for the standard linear Black-Scholes equation have been considered for instance choosing a suitable right boundary condition and applying some remedies for dealing with nonsmooth conditions of the equation. After...
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.
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
Institute of Scientific and Technical Information of China (English)
邓小康; 柳建新; 刘海飞; 童孝忠; 柳卓
2013-01-01
Within the roadway advanced detection methods, DC resistivity method has an extensive application because of its simple principle and operation. Numerical simulation of the effect of focusing current on advanced detection was carried out using a three-dimensional finite element method (FEM), meanwhile the electric-field distribution of the point source and nine-point power source were calculated and analyzed with the same electric charges. The results show that the nine-point power source array has a very good ability to focus, and the DC focus method can be used to predict the aquifer abnormality body precisely. By comparing the FEM modelling results with physical simulation results from soil sink, it is shown that the accuracy of forward simulation meets the requirement and the artificial disturbance from roadway has no impact on the DC focus method.% 在巷道超前探测的方法中，电阻率法由于原理简单、操作方便，有着很好的应用前景。运用三维有限元法对聚焦电流法的超前预报效果进行数值模拟，计算和分析点电源和九点式电源在供相同电流的情况下电场的分布情况。结果表明：九点式布极方式有很好的聚焦能力，聚焦电流法能准确地发现掘进面前方含水异常体。将数值模拟和物理土槽试验进行对比，正演模拟精度符合要求，巷道中的人为干扰对聚焦电流法超前探测没有影响。
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.
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 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
Numerical methods of microirrigation lateral design
Directory of Open Access Journals (Sweden)
Kettab A.
2002-01-01
Full Text Available The present work contributes to the hydraulic analysis of the lateral microirrigation by using the numerical methods: the control volumes method “CVM” and the Runge-Kutta method “RK4”. These methods are relatively simple to manipulate and agree to the use of the partial differential equations of the first order. The CVM method warrants to follow the hydraulic phenomenon step by step and facilitates iterative development; whereas, the RK4 method is used in the integration and the solution of the differential equations system. The risk of divergence, as the slowness of the computation is avoided by the recourse to the interpolation using the polynomial of Lagrange in order to accelerate the convergence toward the solution. The models of calculation used have the advantage to be simple, fast, precise, and allow their extension to large microirrigation network.
Institute of Scientific and Technical Information of China (English)
王琪; 陆启韶
2001-01-01
The Lagrange's method is one of the general methods to derive thedynamic equations for multibody systems, which are in the form ofordinary differential equations or differential-algebraic equations.Numerical analysisis an important way to investigate the behaviors of the dynamicsof multibody systems. In this paper, the firstkind and the second kind of Lagrange's equations and the modifiedLagrange's equations for multibody systems with their canonical formsare introduced, together with the characteristics of their numericalsolutions. The advances are reviewed in the followingnumerical methods, symplectic algorithms and the implicit algorithms forthe dynamic equations of multibody systems, as well as other algorithmsfor dynamic behaviors of multibody systems, such asPoincar'e maps and Lyapunov exponents.%Lagrange方法是建立多体系统动力学方程的普遍方法之一,其方程的形式为常微分方程组或微分 - 代数方程组,数值计算与数值分析是研究多体系统动力学特性的重要方法.本文简要介绍了多体系统动力学方程的第一、二类Lagrange方程和修正的Lagrange方程的基本形式及这些方程的正则形式,着重介绍了正则方程在数值计算中的特点,就多体系统Lagrange方程的隐式算法、辛算法和多体系统动力学特性的数值分析方法(包括数值仿真、Poincar'e映射和Lyapunov指数的计算方法)的研究现状进行了综述.
Fundamental numerical methods for electrical engineering
Energy Technology Data Exchange (ETDEWEB)
Rosloniec, Stanislaw [Warsaw Univ. of Technology (Poland). Inst. of Radioelectronics
2008-07-01
The book presents fundamental numerical methods which are most frequently applied in the electrical (electronic) engineering. A scope of this book is rather wide and includes solving the sets of linear and nonlinear equations, interpolation and approximation of the functions of one variable, integration and differentation of the functions of one and two variables, integration of the ordinary differential equations, and integration the partial differential equations of two variables. All methods discussed are illustrated with real-world examples of applications. It is shown how real engineering questions can be transformed into the corresponding mathematical problems and next effectively solved by using appropriate numerical methods. Usually, for teaching reasons, mathematical problems are solved step by step, and illustrated by numerous intermediate results. Thus, it is not only explained how the problem can be solved, but the details of the solution are also demonstrated. In Chapter 7 for instance three electrical rectifying devices and a transmission-line non- homogeneous impedance transformer are analyzed in this manner. Similarly, in Chapter 8 different aspects of Laplace boundary value problem formulated for various kinds of single and coupled TEM transmission lines are presented. In other words, six standard TEM transmission lines are investigated by means of the finite difference method. It is shown how a partial differential equation of the second order can be approximated by the corresponding difference equation defined on interior and boundary nodes of the introduced grid. At the next stage, the set of linear equations, formulated in this way, is recurrently solved by using the effective SOR technique. Additionally, ideas of '' fictitious nodes '' and the '' even and odd mode excitations '' methods are explained and illustrated. All methods and computational results, presented in the book, are of significant
A numerical method based on probability theory
Institute of Scientific and Technical Information of China (English)
唐立; 邹捷中; 杨文胜
2003-01-01
By using the connections between Brownian family with drift and elliptic differential equations, an efficient probabilistic computing method is given. This method is applied to a wide-range Diriehlet problem. Detail analysis and deduction of solving the problem are offered. The stochastic representation of the solution to the problem makes a 3-dimensional problem turned into a 2-dimensional problem. And an auxiliary ball is constructed. The strong Markov property and the joint distributions of the time and place of hitting spheres for Brownian family with drift are employed. Finally, good convergence of the numerical solution to the problem over domain with arbitrary boundary is obtained.
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)
Discrete mathematics, discrete physics and numerical methods
Directory of Open Access Journals (Sweden)
Felice Iavernaro
2007-12-01
Full Text Available Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences of Fichera about discrete and continuous world, we shall present some considerations about discrete phenomena which arise when designing numerical methods or discrete models for some classical physical problems.
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.
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.
Novel Numerical Method for Acquiring a Geometrical Description of Nanodielectrics
Energy Technology Data Exchange (ETDEWEB)
Tuncer, Enis [ORNL; Drummy, Lawrence F [ORNL
2010-01-01
Nanodielectric electrical insulation has shown promising characteristics in recent years. Potential applications are numerous, ranging from advanced capacitors to optical sensors. To be able to tailor novel materials and determine their full potential, one needs to establish the structure-property-performance relationship in these materials. One such approach is laid out in this study. We have employed a widely used numerical method (the finite element method) to estimate the effective permittivity of an actual binary mixture (a clay-filled nanodielectric) from a two-dimensional transmission electron microscopy image. The obtained effective permittivity was then used to determine the spectral densities for various depolarization factors. We show explicitly that the spectral density resolves the geometrical description in the nanodielectric. As a result, low frequency impedance data can be used as a microscopy technique. We believe that the approach employed here has potential in several fields of science and engineering.
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.
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).
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 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
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 numerical modelling of a fire. Final report
Energy Technology Data Exchange (ETDEWEB)
Heikkilae, L.; Keski-Rahkonen, O. [VTT Building Technology, Espoo (Finland)
1996-03-01
Experience and probabilistic risk assessments show that fires present a major hazard in a nuclear power plant (NPP). The PALOME project (1988-92) improved the quality of numerical simulation of fires to make it a useful tool for fire safety analysis. Some of the most advanced zone model fire simulation codes were acquired. The performance of the codes was studied through literature and personal interviews in earlier studies and BRI2 code from the Japanese Building Research Institute was selected for further use. In PALOME 2 project this work was continued. Information obtained from large-scale fire tests at the German HDR facility allowed reliable prediction of the rate of heat release and was used for code validation. BRI2 code was validated particularly by participation in the CEC standard problem `Prediction of effects caused by a cable fire experiment within the HDR-facility`. Participation in the development of a new field model code SOFIE specifically for fire applications as British-Swedish-Finnish cooperation was one of the goals of the project. SOFIE code was implemented at VTT and the first results of validation simulations were obtained. Well instrumented fire tests on electronic cabinets were carried out to determine source terms for simulation of room fires and to estimate fire spread to adjacent cabinets. The particular aim of this study was to measure the rate of heat release from a fire in an electronic cabinet. From the three tests, differing mainly in the amount of the fire load, data was obtained for source terms in numerical modelling of fires in rooms containing electronic cabinets. On the basis of these tests also a simple natural ventilation model was derived. (19 refs.).
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)
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.
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.
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.
Recent advances in radial basis function collocation methods
Chen, Wen; Chen, C S
2014-01-01
This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems. Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world’s ...
NUMERICAL INVERSION OF MULTIDIMENSIONAL LAPLACE TRANSFORMS USING MOMENT METHODS
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
This paper develops a numerical method to invert multi-dimensional Laplace transforms. By a variable transform, Laplace transforms are converted to multi-dimensional Hausdorff moment problems so that the numerical solution can be achieved. Stability estimation is also obtained. Numerical simulations show the efficiency and practicality of the method.
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.
Numerical Methods for Structured Matrices and Applications
Bini, Dario A; Olshevsky, Vadim; Tyrtsyhnikov, Eugene; van Barel, Marc
2010-01-01
This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to the topics where Georg Heinig had made outstanding achievements. In particular, this includes contributions from the fields of structured matrices, fast algorithms, operator theory, and applications to system theory and signal processing.
Numerical methods in simulation of resistance welding
DEFF Research Database (Denmark)
Nielsen, Chris Valentin; Martins, Paulo A.F.; Zhang, Wenqi;
2015-01-01
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...
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.
NOVEL METHOD SOLVING NUMERICAL INSTABILITIES IN TOPOLOGY OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Numerical instabilities are often encountered in FE solution of continuum topology optimization. The essence of the numerical instabilities is given from the inverse partial differential equation (PDE) point of view. On the basis of the strict mathematical theory, a novel method, named as window filter and multi-grid method, which solves the numerical instabilities, is proposed. Convergent analyses and a numerical example are presented.
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
Discrete mathematics, discrete physics and numerical methods
Felice Iavernaro; Donato Trigiante
2007-01-01
Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences o...
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.
NUMERICAL MANIFOLD METHOD AND ITS APPLICATION IN UNDERGROUND POENINGS
Institute of Scientific and Technical Information of China (English)
王芝银; 李云鹏
1998-01-01
A brief introduction is made for the Numerical Manifold Method and its analysingprocess in rock mechanics. Some aspects of the manifold method are improved in implementingprocess according to the practice of excavating underground openings. Corresponding formulasare given and a computer program of the Numerical Manifold Method has been completed in thispaper.
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.
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...
Okawa, Hirotada
2013-01-01
Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to evolve such systems, a proper understanding of the methods involved is quite important. Here we focus on the numerical solution of elliptic partial differential equations. Such equations arise when preparing initial data for numerical relativity, but also for monitoring the evolution of black holes. Because such elliptic equations play an important role in many branches of physics, we give an overview of the topic, and show how to numerically solve them with simple examples and sample codes written in C++ and Fortran90 for beginners in numerical relativity or other fields requiring numerical expertise.
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
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.
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.
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 method improvement for a subchannel code
Energy Technology Data Exchange (ETDEWEB)
Ding, W.J.; Gou, J.L.; Shan, J.Q. [Xi' an Jiaotong Univ., Shaanxi (China). School of Nuclear Science and Technology
2016-07-15
Previous studies showed that the subchannel codes need most CPU time to solve the matrix formed by the conservation equations. Traditional matrix solving method such as Gaussian elimination method and Gaussian-Seidel iteration method cannot meet the requirement of the computational efficiency. Therefore, a new algorithm for solving the block penta-diagonal matrix is designed based on Stone's incomplete LU (ILU) decomposition method. In the new algorithm, the original block penta-diagonal matrix will be decomposed into a block upper triangular matrix and a lower block triangular matrix as well as a nonzero small matrix. After that, the LU algorithm is applied to solve the matrix until the convergence. In order to compare the computational efficiency, the new designed algorithm is applied to the ATHAS code in this paper. The calculation results show that more than 80 % of the total CPU time can be saved with the new designed ILU algorithm for a 324-channel PWR assembly problem, compared with the original ATHAS code.
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 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.
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.
A Numerical Embedding Method for Solving the Nonlinear Optimization Problem
Institute of Scientific and Technical Information of China (English)
田保锋; 戴云仙; 孟泽红; 张建军
2003-01-01
A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.
Advanced computational electromagnetic methods and applications
Li, Wenxing; Elsherbeni, Atef; Rahmat-Samii, Yahya
2015-01-01
This new resource covers the latest developments in computational electromagnetic methods, with emphasis on cutting-edge applications. This book is designed to extend existing literature to the latest development in computational electromagnetic methods, which are of interest to readers in both academic and industrial areas. The topics include advanced techniques in MoM, FEM and FDTD, spectral domain method, GPU and Phi hardware acceleration, metamaterials, frequency and time domain integral equations, and statistics methods in bio-electromagnetics.
An improved numerical method for nonlinear terms of spectral model and its applications
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
At present, the spectral model is one of the most widely applied numerical models in the research of numerical prediction and climatic variation. To improve the precision and efficiency of spectral method can greatly contribute to the development of numerical prediction. As the core part of spectral method, the calculating method of nonlinear terms always concentrates on numerical solution of atmospheric dynamical processes in the spectral space. However, there was little study in this field in the late thirty years. According to the principle of nonlinear term calculation with the dimensionality degradation and latitudinal perfect spectral method, we designed a new nonlinear term calculating method and made it compatible well with the common numerical algorithms of the spectral model used internationally. With an own-designed spectral dynamical framework suiting for the numerical application in common uses, theoretical analyses and numerical experiments have also been deeply conducted to compare our new method with the widely-used transform method in an attempt to advance the development of numerical algorithms of spectral model.
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
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...
Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi
2016-09-01
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record PMID:26913930
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
Stochastic Analysis Method of Sea Environment Simulated by Numerical Models
Institute of Scientific and Technical Information of China (English)
刘德辅; 焦桂英; 张明霞; 温书勤
2003-01-01
This paper proposes the stochastic analysis method of sea environment simulated by numerical models, such as wave height, current field, design sea levels and longshore sediment transport. Uncertainty and sensitivity analysis of input and output factors of numerical models, their long-term distribution and confidence intervals are described in this paper.
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.
NUMERICALLY SOLVING PERIODICALLY PERTURBED CONSERVATIVE SYSTEMS BY PARAMETER EMBEDDING METHODS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The parameter embedding method is applied for numerically solving the perturbed conservative systems. By means of Newtonian iteration, a simple algorithm has been constructed. Finally, the convergence of the iteration is proved.
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.
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 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
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
Numerical Methods for the Lévy LIBOR Model
DEFF Research Database (Denmark)
Papapantoleon, Antonis; Skovmand, David
are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure. This enables...... simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets....
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.
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.
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...
Numerical methods for checking the regularity of subdivision schemes
Charina, Maria
2012-01-01
In this paper, motivated by applications in computer graphics and animation, we study the numerical methods for checking $C^k-$regularity of vector multivariate subdivision schemes with dilation 2I. These numerical methods arise from the joint spectral radius and restricted spectral radius approaches, which were shown in Charina (Charina, 2011) to characterize $W^k_p-$regularity of subdivision in terms of the same quantity. Namely, the $(k,p)-$joint spectral radius and the $(k,p)-$restricted spectral radius are equal. We show that the corresponding numerical methods in the univariate scalar and vector cases even yield the same upper estimate for the $(k,\\infty)-$joint spectral radius for a certain choice of a matrix norm. The difference between the two approaches becomes apparent in the multivariate case and we confirm that they indeed offer different numerical schemes for estimating the regularity of subdivision. We illustrate our results with several examples.
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.
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.)
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.
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.
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.
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...
EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY
Energy Technology Data Exchange (ETDEWEB)
FRANCOIS, MARIANNE M. [Los Alamos National Laboratory; DENDY, EDWARD D. [Los Alamos National Laboratory; LOWRIE, ROBERT B. [Los Alamos National Laboratory; LIVESCU, DANIEL [Los Alamos National Laboratory; STEINKAMP, MICHAEL J. [Los Alamos National Laboratory
2007-01-11
The authors compare the effects of different numerical schemes for the advection and material interface treatments on the single-mode Rayleigh-Taylor instability, using the RAGE hydro-code. The interface growth and its surface density (interfacial area) versus time are investigated. The surface density metric shows to be better suited to characterize the difference in the flow, than the conventional interface growth metric. They have found that Van Leer's limiter combined to no interface treatment leads to the largest surface area. Finally, to quantify the difference between the numerical methods they have estimated the numerical viscosity in the linear-regime at different scales.
Numerical 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.
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...
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.
Parallel processing numerical method for confined vortex dynamics and applications
Bistrian, Diana Alina
2013-10-01
This paper explores a combined analytical and numerical technique to investigate the hydrodynamic instability of confined swirling flows, with application to vortex rope dynamics in a Francis turbine diffuser, in condition of sophisticated boundary constraints. We present a new approach based on the method of orthogonal decomposition in the Hilbert space, implemented with a spectral descriptor scheme in discrete space. A parallel implementation of the numerical scheme is conducted reducing the computational time compared to other techniques.
Numeric Modified Adomian Decomposition Method for Power System Simulations
Energy Technology Data Exchange (ETDEWEB)
Dimitrovski, Aleksandar D [ORNL; Simunovic, Srdjan [ORNL; Pannala, Sreekanth [ORNL
2016-01-01
This paper investigates the applicability of numeric Wazwaz El Sayed modified Adomian Decomposition Method (WES-ADM) for time domain simulation of power systems. WESADM is a numerical method based on a modified Adomian decomposition (ADM) technique. WES-ADM is a numerical approximation method for the solution of nonlinear ordinary differential equations. The non-linear terms in the differential equations are approximated using Adomian polynomials. In this paper WES-ADM is applied to time domain simulations of multimachine power systems. WECC 3-generator, 9-bus system and IEEE 10-generator, 39-bus system have been used to test the applicability of the approach. Several fault scenarios have been tested. It has been found that the proposed approach is faster than the trapezoidal method with comparable accuracy.
Evolving excised black holes with TVD numerical methods
Neilsen, David
2003-04-01
Total Variation Diminishing (TVD) numerical methods have improved stability properties for nonlinear differential equations, and are widely used in computational fluid dynamics. While Einstein's equations are not genuinely nonlinear, these methods may be advantageous for solving the Einstein equations in specific instances, such as evolving fluid spacetimes and black holes with excision. Using a Frittelli-Reula formulation of the Einstein equations, I will present results of 1-D and 3-D black hole evolutions, and compare the performance of TVD methods with other numerical approaches.
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
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.
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
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.
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
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…
Advanced electromagnetic methods for aerospace vehicles
Balanis, Constantine A.; El-Sharawy, El-Budawy; Hashemi-Yeganeh, Shahrokh; Aberle, James T.; Birtcher, Craig R.
1991-01-01
The Advanced Helicopter Electromagnetics is centered on issues that advance technology related to helicopter electromagnetics. Progress was made on three major topics: composite materials; precipitation static corona discharge; and antenna technology. In composite materials, the research has focused on the measurements of their electrical properties, and the modeling of material discontinuities and their effect on the radiation pattern of antennas mounted on or near material surfaces. The electrical properties were used to model antenna performance when mounted on composite materials. Since helicopter platforms include several antenna systems at VHF and UHF bands, measuring techniques are being explored that can be used to measure the properties at these bands. The effort on corona discharge and precipitation static was directed toward the development of a new two dimensional Voltage Finite Difference Time Domain computer program. Results indicate the feasibility of using potentials for simulating electromagnetic problems in the cases where potentials become primary sources. In antenna technology the focus was on Polarization Diverse Conformal Microstrip Antennas, Cavity Backed Slot Antennas, and Varactor Tuned Circular Patch Antennas. Numerical codes were developed for the analysis of two probe fed rectangular and circular microstrip patch antennas fed by resistive and reactive power divider networks.
Methods and advances in the study of aeroelasticity with uncertainties
Institute of Scientific and Technical Information of China (English)
Dai Yuting; Yang Chao
2014-01-01
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 uncer-tainty, 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 l method. It covers the numerical calculation algo-rithm 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.
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)
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.
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
Advanced Methods in Black-Hole Perturbation Theory
Pani, Paolo
2013-01-01
Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved spacetime. Current state-of-the-art techniques are pedagogically explained and exciting open problems 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
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.
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.
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 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.
A general numerical method to solve for dislocation configurations
Xin, X. J.; Wagoner, R. H.; Daehn, G. S.
1999-08-01
The shape of a mechanically equilibrated dislocation line is of considerable interest in the study of plastic deformation of metals and alloys. A general numerical method for finding such configurations in arbitrary stress fields has been developed. Analogous to the finite-element method (FEM), a general dislocation line is approximated by a series of straight segments (elements) bounded by nodes. The equilibrium configuration is found by minimizing the system energy with respect to nodal positions using a Newton-Raphson procedure. This approach, termed the finite-segment method (FSM), confers several advantages relative to segment-based, explicit formulations. The utility, generality, and robustness of the FSM is demonstrated by analyzing the Orowan bypass mechanism and a model of dislocation generation and equilibration at misfitting particles. Energy differences from previous analytical methods based on simple loop shapes are significant, up to 80 pct. Explicit expressions for the coordinate transformations, energies, and forces required for numerical implementation are presented.
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 Broyden numerical Kutta condition for an unsteady panel method
Energy Technology Data Exchange (ETDEWEB)
Liu, P. [National Research Council Canada, Inst. for Marine Dynamics, Ottawa, Ontario (Canada)]. E-mail: Pengfei.Liu@nrc.ca; Bose, N. [Memorial Univ. of Newfoundland, Faculty of Engineering and Applied Science, Ocean and Naval Architectural Engineering, St. John' s, Newfoundland (Canada)]. E-mail: Nbose@engr.mun.ca; Colbourne, B. [National Research Council Canada, Inst. for Marine Dynamics, Ottawa, Ontario (Canada)]. E-mail: Bruce.Colbourne@nrc.ca
2003-07-01
In panel methods, numerical Kutta conditions are applied in order to ensure that pressure differences between the surfaces at the trailing edges of lifting surface elements are close to zero. Previous numerical Kutta conditions for 3-D panel methods have focused on use of the Newton-Raphson iterative procedure. For extreme unsteady motions, such as for oscillating hydrofoils or for a propeller behind a blockage, the Newton-Raphson procedure can have severe convergence difficulties. The Broyden iteration, a modified Newton-Raphson iteration procedure, is applied here to obtain improved convergence behavior. Using the Broyden iteration increases the reliability, robustness and in many cases computing efficiency for unsteady, multi-body interactive flows. This method was tested in a time domain code for an ice class propeller in both open water flow and during interaction with a nearby ice blockage. Predictions showed that the method was effective in these extreme flows. (author)
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.
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...
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 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...
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.
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 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.
Directory of Open Access Journals (Sweden)
Qian Zhang
2013-07-01
Full Text Available Analysis of advanced displacement in construction progress of tunnel excavation with weak surrounding rock is carried out by numerical method and comparison of model test result. In allusion to the problems of regional landslides and extruded large-deformation seriously impacting the stability of rock mass in construction process of large-section tunnel with weak surrounding rock, the elastic-plastic numerical simulation relying on Liangshui tunnel of Lan-Yu railroad is conducted on mechanical behaviors and deformation steric effect of tunnel construction and the calculation results are compared with the modeling data. The research results show that: the steric effect of excavation face is the dominant factor in the incidence of working face and the stress of surrounding rocks gradually releases from excavation face; the range of 0.5~1 times the cave diameter around rock mass in front of working face is the disturbance range and the key area of stabilization and reinforcement for wake surrounding rock. According to the analysis and construction practice, the supporting structure of large-section tunnel with weak surrounding rock should be established as soon as possible to control the displacement change of surrounding rock in the range of load-bearing ring, reduce disturbance and improve the self-bearing capability of surrounding rock. Because of the distinct excavation steric effect of weak surrounding rock, the secondary lining structure must be established in time to bear the later pressure and restrict the large displacement of surrounding rock. The research results can provide reliable basis for engineering stability control of analogous tunnels.
Numerical Methods for the Lévy LIBOR model
DEFF Research Database (Denmark)
Papapantoleon, Antonis; Skovmand, David
The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the Lévy LIBOR model of Eberlein and Özkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods ...... reduce this growth from exponential to quadratic in an approximation using truncated expansions of the product terms. We include numerical illustrations of the accuracy and speed of our method pricing caplets, swaptions and forward rate agreements....
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.
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.
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.
Numerical analysis of Weyl's method for integrating boundary layer equations
Najfeld, I.
1982-01-01
A fast method for accurate numerical integration of Blasius equation is proposed. It is based on the limit interchange in Weyl's fixed point method formulated as an iterated limit process. Each inner limit represents convergence to a discrete solution. It is shown that the error in a discrete solution admits asymptotic expansion in even powers of step size. An extrapolation process is set up to operate on a sequence of discrete solutions to reach the outer limit. Finally, this method is extended to related boundary layer equations.
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)
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.
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...
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.
Numerical Methods for Safeguarding the Performance of the Quenching Process
Institute of Scientific and Technical Information of China (English)
I. FELDE; T. RETI; S. Segerberg; J. Bodin; G. S. Sarmiento; G. E. Totten; J. GU
2004-01-01
A new numerical technique for testing and evaluation of quenching media and quenching systems is outlined. The measured time-temperature samples as a result of cooling curve test are analyzed by the new software developed, in order to characterize quantitatively the quenchants. The method applied is based on Fourier analysis. Examples for evaluation and comparison of cooling performance of quenchants are presented the applicability of the computational technique.
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...
Directory of Open Access Journals (Sweden)
Md. Asikur Rahman
2012-10-01
Full Text Available Clustering analysis is an important function of data mining. There are various clustering methods in DataMining. Based on these methods various clustering algorithms are developed. Ant-clustering algorithm isone of such approaches that perform cluster analysis based on “Swarm Intelligence’. Existing antclusteringalgorithm uses two user defined parameters to calculate the picking-up probability and droppingprobability those are used to form the cluster. But, use of user defined parameters may lead to form aninaccurate cluster. It is difficult to anticipate about the value of the user defined parameters in advance toform the cluster because of the diversified characteristics of the dataset. In this paper, we have analyzedthe existing ant-clustering algorithm and then numerical analysis method of linear equation is proposedbased on the characteristics of the dataset that does not need any user defined parameters to form theclusters. Results of numerical experiments on synthetic datasets demonstrate the effectiveness of theproposed method.
Directory of Open Access Journals (Sweden)
Md. Asikur Rahman
2012-09-01
Full Text Available Clustering analysis is an important function of data mining. There are various clustering methods in DataMining. Based on these methods various clustering algorithms are developed. Ant-clustering algorithm isone of such approaches that perform cluster analysis based on “Swarm Intelligence’. Existing antclusteringalgorithm uses two user defined parameters to calculate the picking-up probability and droppingprobability those are used to form the cluster. But, use of user defined parameters may lead to form aninaccurate cluster. It is difficult to anticipate about the value of the user defined parameters in advance toform the cluster because of the diversified characteristics of the dataset. In this paper, we have analyzedthe existing ant-clustering algorithm and then numerical analysis method of linear equation is proposedbased on the characteristics of the dataset that does not need any user defined parameters to form theclusters. Results of numerical experiments on synthetic datasets demonstrate the effectiveness of theproposed method.
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 Continuation Methods for Intrusive Uncertainty Quantification Studies
Energy Technology Data Exchange (ETDEWEB)
Safta, Cosmin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Najm, Habib N. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Phipps, Eric Todd [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2014-09-01
Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.
Numerical 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 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.
Rational Construction of Stochastic Numerical Methods for Molecular Sampling
Leimkuhler, Benedict
2012-01-01
In this article, we focus on the sampling of the configurational Gibbs-Boltzmann distribution, that is, the calculation of averages of functions of the position coordinates of a molecular $N$-body system modelled at constant temperature. We show how a formal series expansion of the invariant measure of a Langevin dynamics numerical method can be obtained in a straightforward way using the Baker-Campbell-Hausdorff lemma. We then compare Langevin dynamics integrators in terms of their invariant distributions and demonstrate a superconvergence property (4th order accuracy where only 2nd order would be expected) of one method in the high friction limit; this method, moreover, can be reduced to a simple modification of the Euler-Maruyama method for Brownian dynamics involving a non-Markovian (coloured noise) random process. In the Brownian dynamics case, 2nd order accuracy of the invariant density is achieved. All methods considered are efficient for molecular applications (requiring one force evaluation per times...
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 Simulation of Thermal Discharge Based on FVM Method
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A two-dimensional numerical model is proposed to simulate the thermal discharge from a power plant in Jiangsu Province. The equations in the model consist of two-dimensional non-steady shallow water equations and thermal waste transport equations. Finite volume method (FVM) is used to discretize the shallow water equations, and flux difference splitting (FDS) scheme is applied. The calculated area with the same temperature increment shows the effect of thermal discharge on sea water. A comparison between simulated results and the experimental data shows good agreement. It indicates that this method can give high precision in the heat transfer simulation in coastal areas.
Numerical methods for modeling photonic-crystal VCSELs
DEFF Research Database (Denmark)
Dems, Maciej; Chung, Il-Sug; Nyakas, Peter;
2010-01-01
We show comparison of four different numerical methods for simulating Photonic-Crystal (PC) VCSELs. We present the theoretical basis behind each method and analyze the differences by studying a benchmark VCSEL structure, where the PC structure penetrates all VCSEL layers, the entire top-mirror DBR......, a fraction of the top-mirror DBR or just the VCSEL cavity. The different models are evaluated by comparing the predicted resonance wavelengths and threshold gains for different hole diameters and pitches of the PC. The agreement between the models is relatively good, except for one model, which corresponds...
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 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.
Ductile damage prediction in metal forming processes: Advanced modeling and numerical simulation
Saanouni, K.
2013-05-01
This paper describes the needs required in modern virtual metal forming including both sheet and bulk metal forming of mechanical components. These concern the advanced modeling of thermo-mechanical behavior including the multiphysical phenomena and their interaction or strong coupling, as well as the associated numerical aspects using fully adaptive simulation strategies. First a survey of advanced constitutive equations accounting for the main thermomechanical phenomena as the thermo-elasto-plastic finite strains with isotropic and kinematic hardenings fully coupled with ductile damage will be presented. Only the macroscopic phenomenological approach with state variables (monoscale approach) will be discussed in the general framework of the rational thermodynamics for generalized micromorphic continua. The micro-macro (multi-scales approach) in the framework of polycrystalline inelasticity is not presented here for the sake of shortness but will be presented during the oral presentation. The main numerical aspects related to the resolution of the associated initial and boundary value problem will be outlined. A fully adaptive numerical methodology will be briefly described and some numerical examples will be given in order to show the high predictive capabilities of this adaptive methodology for virtual metal forming simulations.
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 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.
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.
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
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...
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.
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 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 ...
Calculation of free-fall trajectories using numerical optimization methods.
Hull, D. G.; Fowler, W. T.; Gottlieb, R. G.
1972-01-01
An important problem in space flight is the calculation of trajectories for nonthrusting vehicles between fixed points in a given time. A new procedure based on Hamilton's principle for solving such two-point boundary-value problems is presented. It employs numerical optimization methods to perform the extremization required by Hamilton's principle. This procedure is applied to the calculation of an Earth-Moon trajectory. The results show that the initial guesses required to obtain an iteration procedure which converges are not critical and that convergence can be obtained to any predetermined degree of accuracy.
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.
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.
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
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
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)
A Collocation Method for Numerical Solutions of Coupled Burgers' Equations
Mittal, R. C.; Tripathi, A.
2014-09-01
In this paper, we propose a collocation-based numerical scheme to obtain approximate solutions of coupled Burgers' equations. The scheme employs collocation of modified cubic B-spline functions. We have used modified cubic B-spline functions for unknown dependent variables u, v, and their derivatives w.r.t. space variable x. Collocation forms of the partial differential equations result in systems of first-order ordinary differential equations (ODEs). In this scheme, we did not use any transformation or linearization method to handle nonlinearity. The obtained system of ODEs has been solved by strong stability preserving the Runge-Kutta method. The proposed scheme needs less storage space and execution time. The test problems considered in the literature have been discussed to demonstrate the strength and utility of the proposed scheme. The computed numerical solutions are in good agreement with the exact solutions and competent with those available in earlier studies. The scheme is simple as well as easy to implement. The scheme provides approximate solutions not only at the grid points, but also at any point in the solution range.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
Energy Technology Data Exchange (ETDEWEB)
D. S. Lucas
2004-10-01
A graduate level course for Thermal Hydraulics (T/H) was taught through Idaho State University in the spring of 2004. A numerical approach was taken for the content of this course since the students were employed at the Idaho National Laboratory and had been users of T/H codes. The majority of the students had expressed an interest in learning about the Courant Limit, mass error, semi-implicit and implicit numerical integration schemes in the context of a computer code. Since no introductory text was found the author developed notes taught from his own research and courses taught for Westinghouse on the subject. The course started with a primer on control volume methods and the construction of a Homogeneous Equilibrium Model (HEM) (T/H) code. The primer was valuable for giving the students the basics behind such codes and their evolution to more complex codes for Thermal Hydraulics and Computational Fluid Dynamics (CFD). The course covered additional material including the Finite Element Method and non-equilibrium (T/H). The control volume primer and the construction of a three-equation (mass, momentum and energy) HEM code are the subject of this paper . The Fortran version of the code covered in this paper is elementary compared to its descendants. The steam tables used are less accurate than the available commercial version written in C Coupled to a Graphical User Interface (GUI). The Fortran version and input files can be downloaded at www.microfusionlab.com.
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.
Numerical methods for assessment of the ship's pollutant emissions
Jenaru, A.; Acomi, N.
2016-08-01
The maritime transportation sector constitutes a source of atmospheric pollution. To avoid or minimize ships pollutant emissions the first step is to assess them. Two methods of estimation of the ships’ emissions are proposed in this paper. These methods prove their utility for shipboard and shore based management personnel from the practical perspective. The methods were demonstrated for a product tanker vessel where a permanent monitoring system for the pollutant emissions has previously been fitted. The values of the polluting agents from the exhaust gas were determined for the ship from the shipyard delivery and were used as starting point. Based on these values, the paper aimed at numerical assessing of ship's emissions in order to determine the ways for avoiding environmental pollution: the analytical method of determining the concentrations of the exhaust gas components, by using computation program MathCAD, and the graphical method of determining the concentrations of the exhaust gas components, using variation diagrams of the parameters, where the results of the on board measurements were introduced, following the application of pertinent correction factors. The results should be regarded as a supporting tool during the decision making process linked to the reduction of ship's pollutant emissions.
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.
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...
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....
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.
Mathematical analysis and numerical methods for science and technology
Dautray, Robert
These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which ...
Numerical optimization method for packing regular convex polygons
Galiev, Sh. I.; Lisafina, M. S.
2016-08-01
An algorithm is presented for the approximate solution of the problem of packing regular convex polygons in a given closed bounded domain G so as to maximize the total area of the packed figures. On G a grid is constructed whose nodes generate a finite set W on G, and the centers of the figures to be packed can be placed only at some points of W. The problem of packing these figures with centers in W is reduced to a 0-1 linear programming problem. A two-stage algorithm for solving the resulting problems is proposed. The algorithm finds packings of the indicated figures in an arbitrary closed bounded domain on the plane. Numerical results are presented that demonstrate the effectiveness of the method.
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
Method of Numerical Modeling for Constitutive Relations of Clay
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In order to study the method of numerical modeling for constitutive relations of clay, on the basis of the principle of interaction between plastic volumetric strain and plastic generalized shear strain, the two constitutive functionals that include the function of stress path were used as the basic framework of the constitutive model, which are able to demonstrate the dependence of stress path.The two partial differential cross terms appear in the expression of stress-strain increment relation, which are used to demonstrate the interaction between plastic volumetric strain and plastic generalized shear strain.The elasoplastic constitutive models of clay under two kinds of stress paths, CTC and TC, have been constructed using the triaxial test results.The three basic characteristics of deformation of soils, pressure sensitivity, dilatancy, and dependence of stress path, are well explained using these two models.Using visualization, the three-dimensional surfaces of shear and volume strains in the whole stress field under stress paths of CTC and TC are given.In addition, the two families of shear and volumetric yield loci under CTC and TC paths are plotted respectively.By comparing the results of deformation under these two stress paths, it has been found that, there are obvious differences in the strain peaks, the shapes of strain surfaces, and the trends of variation of volumetric yield loci, however both families of shear yield loci are similar.These results demonstrate that the influences of stress path on the constitutive relations of clay are considerably large and not negligible.The numerical modeling method that can sufficiently reflect the dependence of stress path is superior to the traditional one.
Why Video? How Technology Advances Method
Downing, Martin J., Jr.
2008-01-01
This paper reports on the use of video to enhance qualitative research. Advances in technology have improved our ability to capture lived experiences through visual means. I reflect on my previous work with individuals living with HIV/AIDS, the results of which are described in another paper, to evaluate the effectiveness of video as a medium that…
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].
Numerical Analysis of Multilayer Waveguides Using Effective Refractive Index Method
Institute of Scientific and Technical Information of China (English)
GAO Shao-Wen; CAO Jun-Cheng; FENG Song-Lin
2003-01-01
With the help of the effective refractive index method we have numerically analyzed a multilayer planar waveguide structure and calculated the propagation constants, confinement factors, and transverse electric (TE) modes. A five-layer waveguide model has been provided to analyze the electro-magne tic wave propagation process. The analysis method has been applied to the 980 nm laser with active layer of GaInAs/GaInAsP strained quantum wells, GaInAsP confinement layers and GaInP cap layers. By changing the thickness of confinement layers, we obtained confinement factor as high as 95% with higher TE modes TE1 and TE2. The results are in good agreement with the experiment by A. Al-Muhanna et al. and give the new idea to enhance output power of semiconductor lasers. The analysis method can also be extended to any other slab multilayer waveguide structures, and the results are useful to the fabrication of optic-electronic devices.
Hinderer, Tanja; Mroué, Abdul H; Hemberger, Daniel A; Lovelace, Geoffrey; Pfeiffer, Harald P
2013-01-01
We compute the periastron advance using the effective-one-body formalism for binary black holes moving on quasi-circular orbits and having spins collinear with the orbital angular momentum. We compare the predictions with the periastron advance recently computed in accurate numerical-relativity simulations and find remarkable agreement for a wide range of spins and mass ratios. These results do not use any numerical-relativity calibration of the effective-one-body model, and stem from two key ingredients in the effective-one-body Hamiltonian: (i) the mapping of the two-body dynamics of spinning particles onto the dynamics of an effective spinning particle in a (deformed) Kerr spacetime, fully symmetrized with respect to the two-body masses and spins, and (ii) the resummation, in the test-particle limit, of all post-Newtonian (PN) corrections linear in the spin of the particle. In fact, even when only the leading spin PN corrections are included in the effective-one-body spinning Hamiltonian but all the test-p...
Numerical Improvement of The Three-dimensional Boundary Element Method
Ortiz-Aleman, C.; Gil-Zepeda, A.; SÃ¡nchez-Sesma, F. J.; Luzon-Martinez, F.
2001-12-01
Boundary element methods have been applied to calculate the seismic response of various types of geological structures. Dimensionality reduction and a relatively easy fulfillment of radiation conditions at infinity are recognized advantages over domain approaches. Indirect Boundary Element Method (IBEM) formulations give rise to large systems of equations, and the considerable amount of operations required for solving them suggest the possibility of getting some benefit from exploitation of sparsity patterns. In this article, a brief study on the structure of the linear systems derived from the IBEM method is carried out. Applicability of a matrix static condensation algorithm to the inversion of the IBEM coefficient matrix is explored, in order to optimize the numerical burden of such method. Seismic response of a 3-D alluvial valley of irregular shape, as originally proposed by Sánchez-Sesma and Luzon (1995), was computed and comparisons on time consumption and memory allocation are established. An alternative way to deal with those linear systems is the use of threshold criteria for the truncation of the coefficient matrix, which implies the solution of sparse approximations instead of the original full IBEM systems (Ortiz-Aleman et al., 1998). Performance of this optimized approach is evaluated on its application to the case of a three-dimensional alluvial basin with irregular shape. Transfer functions were calculated for the frequency range from 0 to 1.25 Hz. Inversion of linear systems by using this algorithm lead to significant saving on computer time and memory allocation relative to the original IBEM formulation. Results represent an extension in the range of application of the IBEM method.
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
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).
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
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.
Numerical methods for portfolio selection with bounded constraints
Yin, G.; Jin, Hanqing; Jin, Zhuo
2009-11-01
This work develops an approximation procedure for portfolio selection with bounded constraints. Based on the Markov chain approximation techniques, numerical procedures are constructed for the utility optimization task. Under simple conditions, the convergence of the approximation sequences to the wealth process and the optimal utility function is established. Numerical examples are provided to illustrate the performance of the algorithms.
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)
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).
Numerical simulation of droplet dynamics using level set method
Energy Technology Data Exchange (ETDEWEB)
Tadashi Watanabe [Research and Development Group for Numerical Experiment, Japan Atomic Energy Research Institute Tokai-mura, Naka-gun, Ibaraki-ken, 319-1195 (Japan)
2005-07-01
Full text of publication follows: A levitated liquid droplet is used to measure the properties of molten metal at high temperature. Viscosity is, for instance, obtained from the damping of an oscillation of the droplet. The levitation of droplets is controlled by using electrostatic force or ultrasonic wave under the gravitational condition. The droplet is not in contact with a container, and the effect of the container wall is eliminated for a detailed measurement. Small disturbances such as an initial deformation or rotation, which can not be neglected completely in the measurement, however, still have a large effect on the measurement, since the relation between the properties and the oscillation parameters is given by the linear theory. In order to study the effect of initial disturbances and nonlinearity of the droplet dynamics on the measurement, numerical simulations of a liquid droplet are performed. Three-dimensional Navier- Stokes equations are solved using the level set method. The level set function, which is the distance from the droplet surface, is calculated by solving the transport equation to obtain the position of the surface. Mass conservation of the droplet is especially taken into account in the calculation of the level set function. The staggered mesh system is used and the second-order upwind differencing scheme is applied for convective terms. The second-order Adams-Bashforth method is used for time integration. Differences between two-dimensional and three-dimensional calculations are shown first, and it is found that the two-dimensional calculation is not suitable for simulating the droplet dynamics. The nonlinearity effect is studied next. The oscillation of the droplet is simulated by changing the amplitude of the initial deformation, which is given by the Legendre polynomial. The period and the damping of the oscillation are obtained, and the effect of the amplitude on the measurement of surface tension and viscosity is discussed. The
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.
Full Wave Simulation of Integrated Circuits Using Hybrid Numerical Methods
Tan, Jilin
Transmission lines play an important role in digital electronics, and in microwave and millimeter-wave circuits. Analysis, modeling, and design of transmission lines are critical to the development of the circuitry in the chip, subsystem, and system levels. In the past several decays, at the EM modeling level, the quasi-static approximation has been widely used due to its great simplicity. As the clock rates increase, the inter-connect effects such as signal delay, distortion, dispersion, reflection, and crosstalk, limit the performance of microwave systems. Meanwhile, the quasi-static approach loses its validity for some complex system structures. Since the successful system design of the PCB, MCM, and the chip packaging, rely very much on the computer aided EM level modeling and simulation, many new methods have been developed, such as the full wave approach, to guarantee the successful design. Many difficulties exist in the rigorous EM level analysis. Some of these include the difficulties in describing the behavior of the conductors with finite thickness and finite conductivity, the field singularity, and the arbitrary multilayered multi-transmission lines structures. This dissertation concentrates on the full wave study of the multi-conductor transmission lines with finite conductivity and finite thickness buried in an arbitrary lossy multilayered environment. Two general approaches have been developed. The first one is the integral equation method in which the dyadic Green's function for arbitrary layered media has been correctly formulated and has been tested both analytically and numerically. By applying this method, the double layered high dielectric permitivitty problem and the heavy dielectrical lossy problem in multilayered media in the CMOS circuit design have been solved. The second approach is the edge element method. In this study, the correct functional for the two dimensional propagation problem has been successfully constructed in a rigorous way
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
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
Advances in iterative methods for nonlinear equations
Busquier, Sonia
2016-01-01
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...
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 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.
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
SAMSAN- MODERN NUMERICAL METHODS FOR CLASSICAL SAMPLED SYSTEM ANALYSIS
Frisch, H. P.
1994-01-01
SAMSAN was developed to aid the control system analyst by providing a self consistent set of computer algorithms that support large order control system design and evaluation studies, with an emphasis placed on sampled system analysis. Control system analysts have access to a vast array of published algorithms to solve an equally large spectrum of controls related computational problems. The analyst usually spends considerable time and effort bringing these published algorithms to an integrated operational status and often finds them less general than desired. SAMSAN reduces the burden on the analyst by providing a set of algorithms that have been well tested and documented, and that can be readily integrated for solving control system problems. Algorithm selection for SAMSAN has been biased toward numerical accuracy for large order systems with computational speed and portability being considered important but not paramount. In addition to containing relevant subroutines from EISPAK for eigen-analysis and from LINPAK for the solution of linear systems and related problems, SAMSAN contains the following not so generally available capabilities: 1) Reduction of a real non-symmetric matrix to block diagonal form via a real similarity transformation matrix which is well conditioned with respect to inversion, 2) Solution of the generalized eigenvalue problem with balancing and grading, 3) Computation of all zeros of the determinant of a matrix of polynomials, 4) Matrix exponentiation and the evaluation of integrals involving the matrix exponential, with option to first block diagonalize, 5) Root locus and frequency response for single variable transfer functions in the S, Z, and W domains, 6) Several methods of computing zeros for linear systems, and 7) The ability to generate documentation "on demand". All matrix operations in the SAMSAN algorithms assume non-symmetric matrices with real double precision elements. There is no fixed size limit on any matrix in any
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
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...
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...
Numerical calculation of elastohydrodynamic lubrication methods and programs
Huang, Ping
2015-01-01
The book not only offers scientists and engineers a clear inter-disciplinary introduction and orientation to all major EHL problems and their solutions but, most importantly, it also provides numerical programs on specific application in engineering. A one-stop reference providing equations and their solutions to all major elastohydrodynamic lubrication (EHL) problems, plus numerical programs on specific applications in engineering offers engineers and scientists a clear inter-disciplinary introduction and a concise program for practical engineering applications to most important EHL problems
Numerical method for two-phase flow discontinuity propagation calculation
International Nuclear Information System (INIS)
In this paper, we present a class of numerical shock-capturing schemes for hyperbolic systems of conservation laws modelling two-phase flow. First, we solve the Riemann problem for a two-phase flow with unequal velocities. Then, we construct two approximate Riemann solvers: an one intermediate-state Riemann solver and a generalized Roe's approximate Riemann solver. We give some numerical results for one-dimensional shock-tube problems and for a standard two-phase flow heat addition problem involving two-phase flow instabilities
Advanced methods of 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...
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.
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 topolo......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...
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
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.
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,…
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 ...
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.
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 ...
Method and ethics in advancing jury research.
Robertshaw, P
1998-10-01
In this article the contemporary problems of the jury and jury research are considered. This is timely, in view of the current Home Office Consultation Paper on the future of, and alternatives to, the jury in serious fraud trials, to which the author has submitted representations on its jury aspects. The research position is dominated by the prohibitions in the Contempt of Court Act 1981. The types of indirect research on jury deliberation which have been achieved within this stricture are outlined. In the USA, direct research of the jury is possible but, for historical reasons, it has been in television documentaries that direct observation of the deliberation process has been achieved. The first issue is discussed and the problems of inauthenticity, 'the observer effect', and of existential invalidity in 'mock' or 'shadow' juries are noted. Finally, the kinds of issues that could be addressed if licensed jury deliberation research was legalized, are proposed. It is also suggested that there are methods available to transcend the problems associated with American direct research. PMID:9808945
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.
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 modeling of an advancing hydraulically-driven pile in sand
Institute of Scientific and Technical Information of China (English)
Meen-wah GUI
2011-01-01
The penetration of a model pile through sand was investigated via a numerical analysis. Data from nine triaxial compression tests on dense specimens at different stress levels was generalized and used to create an empirical non-linear plastic hardening stress-strain relation for use in the analysis. As the computer program used is capable of large displacement analyses in radial symmetry, we expected that the analysis would easily reproduce the tip resistance penetration profile of the model pile in sand of known density and stress. However, initial attempts led to over-prediction. Successful analyses required both successive reformations of the mesh and the complete elimination of the dilatant peak in soil strength, which is naturally eliminated under large confining stress directly beneath the advancing tip, and that soil in the far-field had strained insufficiently to reach peak strength. Thus, the soil around the shaft must have been sheared to a critical state as it flowed past the tip. The hypothesis that the resistance to displacement piles in sand is mainly a function of the deformability of the sand was again proven, and the use of peak strength in the traditional bearing capacity formulae was found to be inappropriate. Independent investigation in this direction is needed to quantify the hypothesis.
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.
Finite strip method combined with other numerical methods for the analysis of plates
Cheung, M. S.; Li, Wenchang
1992-09-01
Finite plate strips are combined with finite elements or boundary elements in the analysis of rectangular plates with some minor irregularities such as openings, skew edges, etc. The plate is divided into regular and irregular regions. The regular region is analyzed by the finite strip method while the irregular one is analyzed by the finite element or boundary element method. A special transition element and strip are developed in order to connect the both regions. Numerical examples will show the accuracy and efficiency of this combined analysis.
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 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
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…
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.
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)
A NUMERICAL EMBEDDING METHOD FOR SOLVING THE NONLINEAR COMPLEMENTARITY PROBLEM(Ⅰ)--THEORY
Institute of Scientific and Technical Information of China (English)
Jian-jun Zhang; De-ren Wang
2002-01-01
In this paper, we extend the numerical embedding method for solving the smooth equations to the nonlinear complementarity problem. By using the nonsmooth theory,we prove the existence and the continuation of the following path for the corresponding homotopy equations. Therefore the basic theory of the numerical embedding method for solving the nonlinear complementarity problem is established. In part Ⅱ of this paper, we will further study the implementation of the method and give some numerical exapmles.
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.
A parallel method for numerical solution of delay differential equations
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A parallel diagonally-iterated Runge-Kutta (PDIRK) method is constructed to solve stiff initial value problems for delay differential equations. The order and stability of this PDIRK method has been analyzed, and the iteration parameters of the method are tuned in such a way that fast convergence to the value of corrector is achieved.
Recent advances in theoretical and numerical studies of wire array Z-pinch in the IAPCM
Ding, Ning; Zhang, Yang; Xiao, Delong; Wu, Jiming; Huang, Jun; Yin, Li; Sun, Shunkai; Xue, Chuang; Dai, Zihuan; Ning, Cheng; Shu, Xiaojian; Wang, Jianguo; Li, Hua
2014-12-01
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
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.
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.
An introduction to nonlinear programming. IV - Numerical methods for constrained minimization
Sorenson, H. W.; Koble, H. M.
1976-01-01
An overview is presented of the numerical solution of constrained minimization problems. Attention is given to both primal and indirect (linear programs and unconstrained minimizations) methods of solution.
Numerical methods for simulating blood flow at macro, micro, and multi scales.
Imai, Yohsuke; Omori, Toshihiro; Shimogonya, Yuji; Yamaguchi, Takami; Ishikawa, Takuji
2016-07-26
In the past decade, numerical methods for the computational biomechanics of blood flow have progressed to overcome difficulties in diverse applications from cellular to organ scales. Such numerical methods may be classified by the type of computational mesh used for the fluid domain, into fixed mesh methods, moving mesh (boundary-fitted mesh) methods, and mesh-free methods. The type of computational mesh used is closely related to the characteristics of each method. We herein provide an overview of numerical methods recently used to simulate blood flow at macro and micro scales, with a focus on computational meshes. We also discuss recent progress in the multi-scale modeling of blood flow.
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 ...
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...
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 ANALYSIS ON BINOMIAL TREE METHODS FOR AMERICAN LOOKBACK OPTIONS
Institute of Scientific and Technical Information of China (English)
戴民
2001-01-01
Lookback options are path-dependent options. In general, the binomial tree methods,as the most popular approaches to pricing options, involve a path dependent variable as well as the underlying asset price for lookback options. However, for floating strike lookback options, a single-state variable binomial tree method can be constructed. This paper is devoted to the convergence analysis of the single-state binomial tree methods both for discretely and continuously monitored American floating strike lookback options. We also investigate some properties of such options, including effects of expiration date, interest rate and dividend yield on options prices,properties of optimal exercise boundaries and so on.
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.
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.)
A NUMERICAL METHOD FOR SIMULATING NONLINEAR FLUID-RIGID STRUCTURE INTERACTION PROBLEMS
Institute of Scientific and Technical Information of China (English)
XingJ.T; PriceW.G; ChenY.G
2005-01-01
A numerical method for simulating nonlinear fluid-rigid structure interaction problems is developed. The structure is assumed to undergo large rigid body motions and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and fluid-solid interaction interfaces. An Arbitrary-Lagrangian-Eulerian (ALE) mesh system is used to construct the numerical model. A multi-block numerical scheme of study is adopted allowing for the relative motion between moving overset grids, which are independent of one another. This provides a convenient method to overcome the difficulties in matching fluid meshes with large solid motions. Nonlinear numerical equations describing nonlinear fluid-solid interaction dynamics are derived through a numerical discretization scheme of study. A coupling iteration process is used to solve these numerical equations. Numerical examples are presented to demonstrate applications of the model developed.
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
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.
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.
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 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.
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 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.
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
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 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...
Neutrons and numerical methods. A new look at rotational tunneling
Energy Technology Data Exchange (ETDEWEB)
Johnson, M.R.; Kearley, G.J. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)
1997-04-01
Molecular modelling techniques are easily adapted to calculate rotational potentials in crystals of simple molecular compounds. A comparison with the potentials obtained from the tunnelling spectra provides a stringent means for validating current methods of calculating Van der Waals, Coulomb and covalent terms. (author). 5 refs.
Numerical 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
Directory of Open Access Journals (Sweden)
Chian-Yi Liu
2016-09-01
Full Text Available Satellite observations can either be assimilated as radiances or as retrieved physical parameters to reduce error in the initial conditions used by the Numerical Weather Prediction (NWP model. Assimilation of radiances requires a radiative transfer model to convert atmospheric state in model space to that in radiance space, thus requiring a lot of computational resources especially for hyperspectral instruments with thousands of channels. On the other hand, assimilating the retrieved physical parameters is computationally more efficient as they are already in thermodynamic states, which can be compared with NWP model outputs through the objective analysis scheme. A microwave (MW sounder and an infrared (IR sounder have their respective observational limitation due to the characteristics of adopted spectra. The MW sounder observes at much larger field-of-view (FOV compared to an IR sounder. On the other hand, MW has the capability to reveal the atmospheric sounding when the clouds are presented, but IR observations are highly sensitive to clouds, The advanced IR sounder is able to reduce uncertainties in the retrieved atmospheric temperature and moisture profiles due to its higher spectral-resolution than the MW sounder which has much broader spectra bands. This study tries to quantify the optimal use of soundings retrieved from the microwave sounder AMSU and infrared sounder AIRS onboard the AQUA satellite in the regional Weather and Research Forecasting (WRF model through three-dimensional variational (3D-var data assimilation scheme. Four experiments are conducted by assimilating soundings from: (1 clear AIRS single field-of-view (SFOV; (2 retrieved from using clear AMSU and AIRS observations at AMSU field-of-view (SUP; (3 all SFOV soundings within AMSU FOVs must be clear; and (4 SUP soundings which must have all clear SFOV soundings within the AMSU FOV. A baseline experiment assimilating only conventional data is generated for comparison
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....
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.
FULLY COUPLED SIMULATION OF COSMIC REIONIZATION. I. NUMERICAL METHODS AND TESTS
Energy Technology Data Exchange (ETDEWEB)
Norman, Michael L.; So, Geoffrey C. [CASS, University of California, San Diego, 9500 Gilman Drive La Jolla, CA 92093-0424 (United States); Reynolds, Daniel R. [Southern Methodist University, 6425 Boaz Lane, Dallas, TX 75205 (United States); Harkness, Robert P. [SDSC, University of California, San Diego, 9500 Gilman Drive La Jolla, CA 92093-0505 (United States); Wise, John H. [Center for Relativistic Astrophysics, Georgia Institute of Technology, 837 State Street, Atlanta, GA 30332 (United States)
2015-01-01
We describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large ∼(100 Mpc){sup 3} cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes 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. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray 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 hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200{sup 3} Eulerian grid cells and dark matter particles.
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....
Higher geometry an introduction to advanced methods in analytic geometry
Woods, Frederick S
2005-01-01
For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study
Numerical methods of computation of singular and hypersingular integrals
Directory of Open Access Journals (Sweden)
I. V. Boikov
2001-01-01
and technology one is faced with necessity of calculating different singular integrals. In analytical form calculation of singular integrals is possible only in unusual cases. Therefore approximate methods of singular integrals calculation are an active developing direction of computing in mathematics. This review is devoted to the optimal with respect to accuracy algorithms of the calculation of singular integrals with fixed singularity, Cauchy and Hilbert kernels, polysingular and many-dimensional singular integrals. The isolated section is devoted to the optimal with respect to accuracy algorithms of the calculation of the hypersingular integrals.
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.
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.
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...
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.
The numerical wind atlas - the KAMM/WAsP method
DEFF Research Database (Denmark)
Frank, H.P.; Rathmann, Ole; Mortensen, Niels Gylling;
2001-01-01
The method of combining the Karlsruhe Atmospheric Mesoscale Model, KAMM, with the Wind Atlas Analysis and Application Program, WAsP, to make local predictions of the wind resource is presented. It combines the advantages of mesoscale modeling - overviewover a big region and use of global data bases...... - with the local prediction capacity of the small-scale model WAsP. Results are presented for Denmark, Ireland, Northern Portugal and Galicia, and the Faroe Islands. Wind atlas files were calculated fromwind data simulated with the mesoscale model using model grids with a resolution of 2.5, 5, and 10 km. Using...... of wind atlas data on the size of WAsP-maps. It is recommended that a topographic maparound a site should extend 10 km out from it. If there is a major roughness change like a coast line further away in a frequent wind direction this should be included at even greater distances, perhaps up to 20 km away....
Numerical computation of sapphire crystal growth using heat exchanger method
Lu, Chung-Wei; Chen, Jyh-Chen
2001-05-01
The finite element software FIDAP is employed to study the temperature and velocity distribution and the interface shape during a large sapphire crystal growth process using a heat exchanger method (HEM). In the present study, the energy input to the crucible by the radiation and convection inside the furnace and the energy output through the heat exchanger is modeled by the convection boundary conditions. The effects of the various growth parameters are studied. It is found that the contact angle is obtuse before the solid-melt interface touches the sidewall of the crucible. Therefore, hot spots always appear in this process. The maximum convexity decreases significantly when the cooling-zone radius (RC) increases. The maximum convexity also decreases significantly as the combined convection coefficient inside the furnace (hI) decreases.
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 ...
Grenga, Temistocle
The aim of this research is to further develop a dynamically adaptive algorithm based on wavelets that is able to solve efficiently multi-dimensional compressible reactive flow problems. This work demonstrates the great potential for the method to perform direct numerical simulation (DNS) of combustion with detailed chemistry and multi-component diffusion. In particular, it addresses the performance obtained using a massive parallel implementation and demonstrates important savings in memory storage and computational time over conventional methods. In addition, fully-resolved simulations of challenging three dimensional problems involving mixing and combustion processes are performed. These problems are particularly challenging due to their strong multiscale characteristics. For these solutions, it is necessary to combine the advanced numerical techniques applied to modern computational resources.
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.
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)
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
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.
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
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.
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...
Directory of Open Access Journals (Sweden)
Xueshang eFeng
2016-03-01
Full Text Available This paper presents a comparative study of divergence cleaning methods of magnetic field in the solar coronal three-dimensional numerical simulation. For such purpose, the diffusive method, projection method, generalized Lagrange multiplier method and constrained-transport method are used. All these methods are combined with a finite-volume scheme based on a six-component grid system in spherical coordinates. In order to see the performance between the four divergence cleaning methods, solar coronal numerical simulation for Carrington rotation 2056 has been studied. Numerical results show that the average relative divergence error is around $10^{-4.5}$ for the constrained-transport method, while about $10^{-3.1}- 10^{-3.6}$ for the other three methods. Although there exist some differences in the average relative divergence errors for the four employed methods, our tests show they can all produce basic structured solar wind.
On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations
Directory of Open Access Journals (Sweden)
H. Montazeri
2012-01-01
Full Text Available We consider a system of nonlinear equations F(x=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.
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.
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.
Advanced Finite Element Method for Nano-Resonators
Zschiedrich, L; Kettner, B; Schmidt, F
2006-01-01
Miniaturized optical resonators with spatial dimensions of the order of the wavelength of the trapped light offer prospects for a variety of new applications like quantum processing or construction of meta-materials. Light propagation in these structures is modelled by Maxwell's equations. For a deeper numerical analysis one may compute the scattered field when the structure is illuminated or one may compute the resonances of the structure. We therefore address in this paper the electromagnetic scattering problem as well as the computation of resonances in an open system. For the simulation efficient and reliable numerical methods are required which cope with the infinite domain. We use transparent boundary conditions based on the Perfectly Matched Layer Method (PML) combined with a novel adaptive strategy to determine optimal discretization parameters like the thickness of the sponge layer or the mesh width. Further a novel iterative solver for time-harmonic Maxwell's equations is presented.
Application of nonlinear optimization method to sensitivity analysis of numerical model
Institute of Scientific and Technical Information of China (English)
XU Hui; MU Mu; LUO Dehai
2004-01-01
A nonlinear optimization method is applied to sensitivity analysis of a numerical model. Theoretical analysis and numerical experiments indicate that this method can give not only a quantitative assessment whether the numerical model is able to simulate the observations or not, but also the initial field that yields the optimal simulation. In particular, when the simulation results are apparently satisfactory, and sometimes both model error and initial error are considerably large, the nonlinear optimization method, under some conditions, can identify the error that plays a dominant role.
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.
Hybrid analytic-numeric calculation method for light through a bounded planar dielectric
Nicolau, J.B.; Groesen, van E.
2005-01-01
We present a hybrid analytic-numeric method to calculate the transmission and reflection of light that is fluxed into a bounded complicated optical structure surrounded by air. The solution is obtained by numerical calculations inside a square containing the structure and by analytical calculations
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...
Current advances in diagnostic methods of Acanthamoeba keratitis
Institute of Scientific and Technical Information of China (English)
Wang Yuehua; Feng Xianmin; Jiang Linzhe
2014-01-01
Objective The objective of this article was to review the current advances in diagnostic methods for Acanthamoeba keratitis (AK).Data sources Data used in this review were retrieved from PubMed (1970-2013).The terms "Acanthamoeba keratitis" and "diagnosis" were used for the literature search.Study selection Data from published articles regarding AK and diagnosis in clinical trials were identified and reviewed.Results The diagnostic methods for the eight species implicated in AK were reviewed.Among all diagnostic procedures,corneal scraping and smear examination was an essential diagnostic method.Polymerase chain reaction was the most sensitive and accurate detection method.Culturing of Acanthamoeba was a reliable method for final diagnosis of AK.Confocal microscopy to detect Acanthamoeba was also effective,without any invasive procedure,and was helpful in the early diagnosis of AK.Conclusion Clinically,conjunction of various diagnostic methods to diagnose AK was necessary.
Institute of Scientific and Technical Information of China (English)
YU Xin-yi; GAO Hai-bo; DENG Zong-quan
2009-01-01
Based on the study of passive articulated rover, a complete suspension kinematics model from wheel to inertial reference frame is presented, which uses D-H method of manipulator and presentation with Euler an-gle of pitch, roll and yaw. An improved contact model is adopted aimed at the loose and rough lunar terrain. U-sing this kinematics model and numerical continuous and discrete Newton' s method with iterative factor, the numerical method for estimation of kinematical parameters of articulated rovers on loose and rough terrain is con-strueted. To demonstrate this numerical method, an example of two torsion bar rocker-bogie lunar rover with eight wheels is presented. Simulation results show that the numerical method for estimation of kinematical pa-rameters of articulated rovers based on improved contact model can improve the precision of kinematical estima-tion on loose and rough terrain and decrease errors caused by contact models established based on general hy-pothesis.
New method for computer numerical control machine tool calibration: Relay method
Institute of Scientific and Technical Information of China (English)
LIU Huanlao; SHI Hanming; LI Bin; ZHOU Huichen
2007-01-01
Relay measurement method,which uses the kilogram-meter (KGM) measurement system to identify volumetric errors on the planes of computer numerical con trol (CNC) machine tools,is verified through experimental tests.During the process,all position errors on the entire plane table are measured by the equipment,which is limited to a small field.All errors are obtained first by measuring the error of the basic position near the original point.On the basis of that positional error,the positional errors far away from the original point are measured.Using this analogy,the error information on the positional points on the entire plane can be obtained.The process outlined above is called the relay meth od.Test results indicate that the accuracy and repeatability are high,and the method can be used to calibrate geometric errors on the plane of CNC machine tools after backlash errors have been well compensated.
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 ...
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.
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
Rosenbaum, J. S.
1976-01-01
If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.
Directory of Open Access Journals (Sweden)
Yingjun Jiang
2015-04-01
Full Text Available In order to better understand the mechanical properties of graded crushed rocks (GCRs and to optimize the relevant design, a numerical test method based on the particle flow modeling technique PFC2D is developed for the California bearing ratio (CBR test on GCRs. The effects of different testing conditions and micro-mechanical parameters used in the model on the CBR numerical results have been systematically studied. The reliability of the numerical technique is verified. The numerical results suggest that the influences of the loading rate and Poisson's ratio on the CBR numerical test results are not significant. As such, a loading rate of 1.0–3.0 mm/min, a piston diameter of 5 cm, a specimen height of 15 cm and a specimen diameter of 15 cm are adopted for the CBR numerical test. The numerical results reveal that the CBR values increase with the friction coefficient at the contact and shear modulus of the rocks, while the influence of Poisson's ratio on the CBR values is insignificant. The close agreement between the CBR numerical results and experimental results suggests that the numerical simulation of the CBR values is promising to help assess the mechanical properties of GCRs and to optimize the grading design. Besides, the numerical study can provide useful insights on the mesoscopic mechanism.
Grandinetti, Lucio; Purnama, Anton
2015-01-01
Presenting the latest findings in the field of numerical analysis and optimization, this volume balances pure research with practical applications of the subject. Accompanied by detailed tables, figures, and examinations of useful software tools, this volume will equip the reader to perform detailed and layered analysis of complex datasets. Many real-world complex problems can be formulated as optimization tasks. Such problems can be characterized as large scale, unconstrained, constrained, non-convex, non-differentiable, and discontinuous, and therefore require adequate computational methods, algorithms, and software tools. These same tools are often employed by researchers working in current IT hot topics such as big data, optimization and other complex numerical algorithms on the cloud, devising special techniques for supercomputing systems. The list of topics covered include, but are not limited to: numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, opt...
Institute of Scientific and Technical Information of China (English)
Jin-Ling Luo; Hong-Lin Kang; Jian Li; Wu-Ye Dai
2011-01-01
Numerical simulation methods of aerodynamic heating were compared by considering the influence of numerical schemes and turbulence models, and attempting to investigate the applicability of numerical simulation methods on predicting heat flux in engineering applications. For some typical cases provided with detailed experimental data, four spatial schemes and four turbulence models were adopted to calculate surface heat flux. By analyzing and comparing,some influencing regularities of numerical schemes and turbulence models on calculating heat flux had been acquired. It is clear that AUSM+-up scheme with rapid compressibilitymodified high Reynolds number k-ω model should be appropriate for calculating heat flux. The numerical methods selected as preference above were applied to calculate the heat flux of a 3-D complex geometry in high speed turbulent flows. The results indicated that numerical simulation can capture the complex flow phenomena and reveal the mechanism of aerodynamic heating. Especially, the numerical result of the heat flux at the stagnation point of the wedge was well in agreement with the prediction of Kemp-Riddel formula, and the surface heat flux distribution was consistent with experiment results, which implied that numerical simulation can be introduced to predict heat flux in engineering applications.
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.
Institute of Scientific and Technical Information of China (English)
WU Zhao-chun; WANG Dao-zeng
2009-01-01
e computational results agree with the measured data. By use of orthogonal curvilinear coordinate system, the methods can be easily extended to the numerical simulation of the tidal flow in a tortuous channel.
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
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.
Numerical simulation of laminar jet-forced flow using lattice Boltzmann method
Institute of Scientific and Technical Information of China (English)
Yuan LI; Ya-li DUAN; Yan GUO; Ru-xun LIU
2009-01-01
In the paper, a numerical study on symmetrical and asymmetrical laminar jet-forced flows is carried out by using a lattice Boltzmann method (LBM) with a special boundary treatment. The simulation results are in very good agreement with the available numerical prediction. It is shown that the LBM is a competitive method for the laminar jet-forced flow in terms of computational efficiency and stability.
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
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.
NUMERICAL SIMULATON OF IMPROVED BOUSSINESQ EQUATIONS BY A FINITE ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
Zhao Ming; Teng Bin; Liu Shu-xue
2003-01-01
The improved Boussinesq equations for varying depth derived by Beji and Nadaoka[1]significantly improved the linear dispersive properties of wave models in intermediate water depths. In this study, a finite element method was developed to solve the improved Boussinesq equations. A spongy layer was applied at the open boundary of the computational domain to absorb the wave energy. The fourth-order predictor-corrector method was employed in the time integration. Several test cases were illustrated. The numerical results of this model were compared with laboratory data and those from other numerical models. It turns out that the present numerical model is capable of giving satisactory prediction for wave propagation.
Wang, Yi
2016-07-21
Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.
A numerical method for multiple cracks in an infinite elastic plate
Institute of Scientific and Technical Information of China (English)
YAN Xiang-qiao; WU Hai-peng
2005-01-01
This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and Starfied and the crack tip displacement discontinuity elements proposed by the author. In the numerical method implementation, the left or the right crack tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The numerical method is called a hybrid displacement discontinuity method. The following test examples of crack problems in an infinite plate under tension are included: "center-inclined cracked plate", "interaction of two collinear cracks with equal length", "interaction of three collinear cracks with equal length", "interaction of two parallel cracks with equal length", and "interaction of one horizontal crack and one inclined crack". The present numerical results show that the numerical method is simple yet very accurate for analyzing the interaction of multiple cracks in an infinite plate.
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)
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.
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...
Numerical methods in vehicle system dynamics: state of the art and current developments
Arnold, M.; Burgermeister, B.; Führer, C.; Hippmann, G.; Rill, G.
2011-07-01
Robust and efficient numerical methods are an essential prerequisite for the computer-based dynamical analysis of engineering systems. In vehicle system dynamics, the methods and software tools from multibody system dynamics provide the integration platform for the analysis, simulation and optimisation of the complex dynamical behaviour of vehicles and vehicle components and their interaction with hydraulic components, electronical devices and control structures. Based on the principles of classical mechanics, the modelling of vehicles and their components results in nonlinear systems of ordinary differential equations (ODEs) or differential-algebraic equations (DAEs) of moderate dimension that describe the dynamical behaviour in the frequency range required and with a level of detail being characteristic of vehicle system dynamics. Most practical problems in this field may be transformed to generic problems of numerical mathematics like systems of nonlinear equations in the (quasi-)static analysis and explicit ODEs or DAEs with a typical semi-explicit structure in the dynamical analysis. This transformation to mathematical standard problems allows to use sophisticated, freely available numerical software that is based on well approved numerical methods like the Newton-Raphson iteration for nonlinear equations or Runge-Kutta and linear multistep methods for ODE/DAE time integration. Substantial speed-ups of these numerical standard methods may be achieved exploiting some specific structure of the mathematical models in vehicle system dynamics. In the present paper, we follow this framework and start with some modelling aspects being relevant from the numerical viewpoint. The focus of the paper is on numerical methods for static and dynamic problems, including software issues and a discussion which method fits best for which class of problems. Adaptive components in state-of-the-art numerical software like stepsize and order control in time integration are
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
An efficient numerical method for 3D viscous ship hydrodynamics with free-surface gravity waves
Lewis, M.R.; Koren, B.; Groth, C.; Zingg, D.W.
2006-01-01
A new numerical method for water flows with free-surface gravity waves is investigated. The method is first analyzed with respect to the existence of steady free-surface waves, and the dispersion properties of these waves. Next, the method is used to compute the free water surface generated by a sta
Numerical Modeling of 2-D and 3-D Flows using Artificial Compressibility Method and Collocated Mesh
Directory of Open Access Journals (Sweden)
Yasin Aghaee-Shalmani
2016-01-01
Full Text Available In this paper, applications of a numerical model on simulation of two and three-dimensional ﬂows are presented. This model solves Navier-Stokes equations using ﬁnite volume method and large eddy simulation (LES in a collocated mesh. Artiﬁcial compressibility method with dual t ime stepping is used to solve the time dependent equations. Also a modiﬁed m omentum i nterpolation method (MIM based on the unsteady ﬂows i s deployed t o overcome t he non-physical pressure oscillation. Capability of the presented numerical code for ﬂow s imulation, i s a ssessed by a pplication f or twodimensional square and three-dimensional lid-driven cavity ﬂows. Numerical r esults of cavity ﬂow presents very good agreement with the numerical and experimental data of other existent researches.
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...
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
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
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.
Numerical-Analytical Method for Magnetic Field Computation in Rotational Electric Machines
Institute of Scientific and Technical Information of China (English)
章跃进; 江建中; 屠关镇
2003-01-01
A numerical-analytical method is applied for the two-dimensional magnetic field computation in rotational electric machines in this paper. The analytical expressions for air gap magnetic field axe derived. The pole pairs in the expressions are taken into account so that the solution region can be reduced within one periodic range. The numerical and analytical magnetic field equations are linked with equal vector magnetic potential boundary conditions. The magnetic field of a brushless permanent magnet machine is computed by the proposed method. The result is compared to that obtained by finite element method so as to validate the correction of th method.
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
Brugnano, Luigi; Trigiante, Donato
2009-01-01
One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. For example, it is well known that standard (even symplectic) methods can only exactly preserve quadratic Hamiltonians. In this paper, a new family of methods, called Hamiltonian Boundary Value Methods (HBVMs), is introduced and analyzed. HBVMs are able to exactly preserve, in the discrete solution, Hamiltonian functions of polynomial type of arbitrarily high degree. These methods turn out to be symmetric, perfectly $A$-stable, and can have arbitrarily high order. A few numerical tests confirm the theoretical results.
Directory of Open Access Journals (Sweden)
Pengzhan Huang
2011-01-01
Full Text Available Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.
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.
Fine analysis on advanced detection of transient electromagnetic method
Institute of Scientific and Technical Information of China (English)
Wang Bo; Liu Shengdong; Yang Zhen; Wang Zhijun; Huang Lanying
2012-01-01
Fault fracture zones and water-bearing bodies in front of the driving head are the main disasters in mine laneways,thus it is important to perform their advanced detection and prediction in advance in order to provide reliable technical support for the excavation.Based on the electromagnetic induction theory,we analyzed the characteristics of primary and secondary fields with a positive and negative wave form of current,proposed the fine processing of the advanced detection with variation rate of apparent resistivity and introduced in detail the computational formulae and procedures.The result of physical simulation experiments illustrate that the tectonic interface of modules can be judged by first-order rate of apparent resistivity with a boundary error of 5％,and the position of water body determined by the fine analysis method agrees well with the result of borehole drilling.This shows that in terms of distinguishing structure and aqueous anomalies,the first-order rate of apparent resistivity is more sensitive than the secondorder rate of apparent resistivity.However,some remaining problems are suggested for future solutions.
Advanced numerical models for the thermo-mechanical-metallurgical analysis in hot forging processes
Ducato, Antonino; Fratini, Livan; Micari, Fabrizio
2013-05-01
In the paper a literature review of the numerical modeling of thermo-mechanical-metallurgical evolutions of a metal in hot forging operations is presented. In particular models of multiaxial loading tests are considered for carbon steels. The collected examples from literature regard phases transformations, also martensitic transformations, morphologies evolutions and transformation plasticity phenomena. The purpose of the tests is to show the correlation between the mechanical and the metallurgical behavior of a carbon steel during a combination of several types of loads. In particular a few mechanical tests with heat treatment are analyzed. Furthermore, Ti-6Al-4V titanium alloy is considered. Such material is a multi-phasic alloy, at room temperature made of two main different phases, namely Alpha and Beta, which evolve during both cooling and heating stages. Several numerical applications, conducted using a commercial implicit lagrangian FEM code are presented too. This code can conduct tri-coupled thermo-mechanical-metallurgical simulations of forming processes. The numerical model has been used to carry out a 3D simulation of a forging process of a complex shape part. The model is able to take into account the effects of all the phenomena resulting from the coupling of thermal, mechanical and metallurgical events. As simulation results strongly depend on the accuracy of input data, physical simulation experiments on real-material samples are carried out to characterize material behavior during phase transformation.
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.
Advances on methods for mapping QTL in plant
Institute of Scientific and Technical Information of China (English)
ZHANG Yuan-Ming
2006-01-01
Advances on methods for mapping quantitative trait loci (QTL) are firstly summarized.Then, some new methods, including mapping multiple QTL, fine mapping of QTL, and mapping QTL for dynamic traits, are mainly described. Finally, some future prospects are proposed, including how to dig novel genes in the germplasm resource, map expression QTL (eQTL) by the use of all markers,phenotypes and micro-array data, identify QTL using genetic mating designs and detect viability loci. The purpose is to direct plant geneticists to choose a suitable method in the inheritance analysis of quantitative trait and in search of novel genes in germplasm resource so that more potential genetic information can be uncovered.
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...
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.
Numerical Methods for the Stray-Field Calculation: A Comparison of recently developed Algorithms
Abert, Claas; Selke, Gunnar; Drews, André; Schrefl, Thomas
2012-01-01
Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor grid methods and the finite-element method with shell transformation in terms of computational complexity, storage requirements and accuracy tested on several benchmark problems. These methods can be subdivided into integral methods (fast Fourier transform methods, tensor-grid method) which solve the stray field directly and in differential equation methods (finite-element method), which compute the stray field as the solution of a partial differential equation. It turns out that for cuboid structures the integral methods, which work on cuboid grids (fast Fourier transform methods and tensor grid methods) outperform the finite-element method in terms of the ratio of computational effort to accuracy. Among these three methods the tensor grid method is the fastest. However, the use of the tensor grid method in the c...
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...
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)
Nielsen, Bjoern Fredrik
1997-12-31
The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.
Review of numerical methods for simulation of the aortic root: Present and future directions
Mohammadi, Hossein; Cartier, Raymond; Mongrain, Rosaire
2016-05-01
Heart valvular disease is still one of the main causes of mortality and morbidity in develop countries. Numerical modeling has gained considerable attention in studying hemodynamic conditions associated with valve abnormalities. Simulating the large displacement of the valve in the course of the cardiac cycle needs a well-suited numerical method to capture the natural biomechanical phenomena which happens in the valve. The paper aims to review the principal progress of the numerical approaches for studying the hemodynamic of the aortic valve. In addition, the future directions of the current approaches as well as their potential clinical applications are discussed.
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.
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.
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...
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.
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.
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.
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)
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.
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 Constrained-Gradient Method to Control Divergence Errors in Numerical MHD
Hopkins, Philip F
2015-01-01
In numerical magnetohydrodynamics (MHD), a major challenge is maintaining zero magnetic field-divergence (div-B). Constrained transport (CT) schemes can achieve this at high accuracy, but have generally been restricted to very specific methods. For more general (meshless, moving-mesh, or ALE) methods, 'divergence-cleaning' schemes reduce the div-B errors, however they can still be significant, especially at discontinuities, and can lead to systematic deviations from correct solutions which converge away very slowly. Here we propose a new constrained gradient (CG) scheme which augments these with a hybrid projection step, and can be applied to any numerical scheme with a reconstruction. This iteratively approximates the least-squares minimizing, globally divergence-free reconstruction of the fluid. We emphasize that, unlike 'locally divergence free' methods, this actually minimizes the numerically unstable div-B terms, without affecting the convergence order of the method. We implement this in the mesh-free co...
Decoupling Conditions for Elasto-plastic Consolidation Question Based onNumerical Modeling Method
Institute of Scientific and Technical Information of China (English)
Cheng Tao; Wang Jingtao; Dong Bichang
2005-01-01
Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applied to Biot's consolidation theory. Incremental governing partial differential equations are established using this method. According to the stress path, the decoupling condition of these equations is discussed. Based on these conditions, an incremental diffusion equation and uncoupling governing equations are presented. The method is then applied to numerical analyses of three examples. The results show that (1) the effect of the stress path should be taken into account in the simulation of the soil consolidation question; (2) this decoupling method can predict the evolvement of pore water pressure; (3) the settlement using cam-clay model is less than that using numerical model because of dilatancy.
Numerical methods for the simulation of continuous sedimentation in ideal clarifier-thickener units
Energy Technology Data Exchange (ETDEWEB)
Buerger, R.; Karlsen, K.H.; Risebro, N.H.; Towers, J.D.
2001-10-01
We consider a model of continuous sedimentation. Under idealizing assumptions, the settling of the solid particles under the influence of gravity can be described by the initial value problem for a nonlinear hyperbolic partial differential equation with a flux function that depends discontinuously on height. The purpose of this contribution is to present and demonstrate two numerical methods for simulating continuous sedimentation: a front tracking method and a finite finite difference method. The basic building blocks in the front tracking method are the solutions of a finite number of certain Riemann problems and a procedure for tracking local collisions of shocks. The solutions of the Riemann problems are recalled herein and the front tracking algorithm is described. As an alternative to the front tracking method, a simple scalar finite difference algorithm is proposed. This method is based on discretizing the spatially varying flux parameters on a mesh that is staggered with respect to that of the conserved variable, resulting in a straightforward generalization of the well-known Engquist-Osher upwind finite difference method. The result is an easily implemented upwind shock capturing method. Numerical examples demonstrate that the front tracking and finite difference methods can be used as efficient and accurate simulation tools for continuous sedimentation. The numerical results for the finite difference method indicate that discontinuities in the local solids concentration are resolved sharply and agree with those produced by the front tracking method. The latter is free of numerical dissipation, which leads to sharply resolved concentration discontinuities, but is more complicated to implement than the former. Available mathematical results for the proposed numerical methods are also briefly reviewed. (author)
Solutions manual to accompany An introduction to numerical methods and analysis
Epperson, James F
2014-01-01
A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, sp
A 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.
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.
Numerical Simulation of Flow Field in Flow-guide Tank of China Advanced Research Reactor
Institute of Scientific and Technical Information of China (English)
2001-01-01
The flow-guide tank of China advanced research reactor (CARR) is located at the top of the reactor vessel and connected with the inlet coolant pipe. It acts as a reactor inlet coolant distributor and plays an important role in reducing the flow-induced vibration of the internal components of the reactor core. Several designs of the flow-guide tank have been proposed, however, the final design option has to be made after detailed investigation of the velocity profile within the flow-guide tank for each configuration.
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.
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.
A HIGHLY ACCURATE NUMERICAL METHOD FOR FLOWPROBLEMS WITH INTERACTIONS OF DISCONTINUITIES
Institute of Scientific and Technical Information of China (English)
Xiaonan Wu; Youlan Zhu
2002-01-01
A type of shock fitting method is used to solve some two and three dimensional flowproblems with interactions of various discontinuities. The numerical results show that highaccuracy is achieved for the flow field, especially at the discontinuities. Comparisons withthe Lax-Friedrichs scheme and the ENO scheme confirm the accuracy of the method.
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.
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.).
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.
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)
Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation
Institute of Scientific and Technical Information of China (English)
Zhihui Li; Hanxin Zhang
2007-01-01
A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuumflow regimes can be presented on the basis of the kinetic Boltzmann-Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integration method can be developed and adopted to attack complex flows with different Mach numbers. HPF parallel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarily with massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuillechannel flow and pressure-driven gas flows in twodimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of microscale gas flows occuring in the Micro-Electro-Mechanical System (MEMS).
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...
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.
Directory of Open Access Journals (Sweden)
M. Mosleh E. Abu Samak
2016-04-01
Full Text Available 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.
Institute of Scientific and Technical Information of China (English)
CHENMing; TANGTiantong; ZHANGXiaolin
2003-01-01
In this paper, an effective numerical method based on wavelet moment method is presented to enhance the analysis of interdigital transducer (IDT)for the excitation of surface acoustic waves (SAW) on the piezoelectric substrate of acoustic-optical devices. This problem is formulated in terms of an integral equa-tion, and its electric charge matrix equations obtained by the method of moment (MoM) are effectively solved by Daubechies discrete wavelet transform. One of the mosts triking advantage of this method is that it can greatly ac-celerate the computing with the help of conjugate gradient methods because the wavelet transform make the moment matrices sparse. As a result of the use of this method, the transducer input power coupling factors to both surface and bulk waves are computed. Analysis results show this method is a powerful numerical technique in analysis of IDT for acousto-optical devices.
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.
Bahrami, Saeed; Doulati Ardejani, Faramarz; Aslani, Soheyla; Baafi, Ernest
2014-12-01
The groundwater inflow into a mine during its life and after ceasing operations is one of the most important concerns of the mining industry. This paper presents a hydrogeological assessment of the Irankuh Zn-Pb mine at 20 km south of Esfahan and 1 km northeast of Abnil in west-Central Iran. During mine excavation, the upper impervious bed of a confined aquifer was broken and water at high-pressure flowed into an open pit mine associated with the Kolahdarvazeh deposit. The inflow rates were 6.7 and 1.4 m(3)/s at the maximum and minimum quantities, respectively. Permeability, storage coefficient, thickness and initial head of the fully saturated confined aquifer were 3.5 × 10(-4) m/s, 0.2, 30 m and 60 m, respectively. The hydraulic heads as a function of time were monitored at four observation wells in the vicinity of the pit over 19 weeks and at an observation well near a test well over 21 h. In addition, by measuring the rate of pumping out from the pit sump, at a constant head (usually equal to height of the pit floor), the real inflow rates to the pit were monitored. The main innovations of this work were to make comparison between numerical modelling using a finite element software called SEEP/W and actual data related to inflow and extend the applicability of the numerical model. This model was further used to estimate the hydraulic heads at the observation wells around the pit over 19 weeks during mining operations. Data from a pump-out test and observation wells were used for model calibration and verification. In order to evaluate the model efficiency, the modelling results of inflow quantity and hydraulic heads were compared to those from analytical solutions, as well as the field data. The mean percent error in relation to field data for the inflow quantity was 0.108. It varied between 1.16 and 1.46 for hydraulic head predictions, which are much lower values than the mean percent errors resulted from the analytical solutions (from 1.8 to 5
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
Hol, J.; Wiebenga, J. H.; Hörning, M.; Dietrich, F.; Dane, C.
2016-08-01
For the characterization of friction conditions under sheet metal forming process conditions, different friction test set-ups are being used in industry. However, different friction tests and test set-ups are known to result in scattering friction results. In this work, the TriboForm software is utilized to numerically model the frictional behavior. The simulated coefficients of friction are experimentally validated using friction results from a standardized strip drawing friction test set-up. The experimental and simulation results of the friction behavior show a good overall agreement. This demonstrates that the TriboForm software enables simulating friction conditions for varying tribology conditions, i.e. resulting in a generally applicable approach for friction characterization under industrial sheet metal forming process conditions.
Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.
1996-01-01
A numerical model of heat transfer using combined conduction, radiation and convection in AADSF was used to evaluate temperature gradients in the vicinity of the crystal/melt interface for variety of hot and cold zone set point temperatures specifically for the growth of mercury cadmium telluride (MCT). Reverse usage of hot and cold zones was simulated to aid the choice of proper orientation of crystal/melt interface regarding residual acceleration vector without actual change of furnace location on board the orbiter. It appears that an additional booster heater will be extremely helpful to ensure desired temperature gradient when hot and cold zones are reversed. Further efforts are required to investigate advantages/disadvantages of symmetrical furnace design (i.e. with similar length of hot and cold zones).
Numerical simulation of the reactive flow in advanced (HSR) combustors using KIVA-2
Winowich, Nicholas S.
1991-01-01
Recent work has been done with the goal of establishing ultralow emission aircraft gas turbine combustors. A significant portion of the effort is the development of three dimensional computational combustor models. The KIVA-II computer code which is based on the Implicit Continuous Eulerian Difference mesh Arbitrary Lagrangian Eulerian (ICED-ALE) numerical scheme is one of the codes selected by NASA to achieve these goals. This report involves a simulation of jet injection through slanted slots within the Rich burn/Quick quench/Lean burn (RQL) baseline experimental rig. The RQL combustor distinguishes three regions of combustion. This work specifically focuses on modeling the quick quench mixer region in which secondary injection air is introduced radially through 12 equally spaced slots around the mixer circumference. Steady state solutions are achieved with modifications to the KIVA-II program. Work currently underway will evaluate thermal mixing as a function of injection air velocity and angle of inclination of the slots.
A numerical study of the European option by the MLPG method with moving kriging interpolation.
Phaochoo, P; Luadsong, A; Aschariyaphotha, N
2016-01-01
In this paper, the meshless local Petrov-Galerkin (MLPG) method is applied for solving a generalized Black-Scholes equation in financial problems. This equation is a PDE governing the price evolution of a European call or a European put under the Black-Scholes model. The θ-weighted method and MLPG are used for discretizing the governing equation in time variable and option pricing, respectively. We show that the spectral radius of amplification matrix with the discrete operator is less than 1. This ensures that this numerical scheme is stable. Numerical experiments are performed with time varying volatility and the results are compared with the analytical and the numerical results of other methods. PMID:27064892
FINITE ELEMENT METHOD ON NUMERICAL SIMULATION OF STRATUM CORNEUM'S PENETRATION PROPERTY
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
How the outer substance could penetrate through the skin lies in the stratum corneum, because it is the main barrier in the multi-layers of the skin. Supposing the keratin cell with a special geometry as tetrakaidecahedron, the penetration property of stratum corneum was the key problem which was numerically simulated with finite element method. At first the discretization of the stratum corneum region was given in two steps: first, the discretization of the keratin cell; second, the discretization of fattiness that surrounds the keratin. Then there was the work of numerical simulation. In this procedure, the finite element method and the multi-grid method were used. The former was to obtain the discretization of basic elements; the latter was to decrease the high frequency error. At last the visualization of the numerical simulation was shown.
Development of CAD implementing the algorithm of boundary elements’ numerical analytical method
Directory of Open Access Journals (Sweden)
Yulia V. Korniyenko
2015-03-01
Full Text Available Up to recent days the algorithms for numerical-analytical boundary elements method had been implemented with programs written in MATLAB environment language. Each program had a local character, i.e. used to solve a particular problem: calculation of beam, frame, arch, etc. Constructing matrices in these programs was carried out “manually” therefore being time-consuming. The research was purposed onto a reasoned choice of programming language for new CAD development, allows to implement algorithm of numerical analytical boundary elements method and to create visualization tools for initial objects and calculation results. Research conducted shows that among wide variety of programming languages the most efficient one for CAD development, employing the numerical analytical boundary elements method algorithm, is the Java language. This language provides tools not only for development of calculating CAD part, but also to build the graphic interface for geometrical models construction and calculated results interpretation.
The numerical solution of differential-algebraic systems by Runge-Kutta methods
Hairer, Ernst; Lubich, Christian
1989-01-01
The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.
Numerical methods for 3D tokamak simulations using a flux-surface independent grid
Energy Technology Data Exchange (ETDEWEB)
Stegmeir, A.; Coster, D.; Maj, O.; Lackner, K. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, 85748 Garching (Germany)
2014-06-15
A numerical approach for 3D Tokamak simulations using a flux surface independent grid is presented. The grid consists of few poloidal planes with a Cartesian isotropic grid within each poloidal plane. Perpendicular operators can be discretised within a poloidal plane using standard second order finite difference methods. The discretisation of parallel operators is achieved with a field line following map and an interpolation. The application of the support operator method to the parallel diffusion operator conserves the self-adjointness of the operator on the discrete level and keeps the numerical decay rate at a low level. The developed numerical methods can be applied to geometries where an X-point is present. (copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
An adaptive numerical method for free surface flows passing rigidly mounted obstacles
Nikitin, Kirill D; Terekhov, Kirill M; Vassilevski, Yuri V; Yanbarisov, Ruslan
2016-01-01
The paper develops a method for the numerical simulation of a free-surface flow of incompressible viscous fluid around a streamlined body. The body is a rigid stationary construction partially submerged in the fluid. The application we are interested in the paper is a flow around a surface mounted offshore oil platform. The numerical method builds on a hybrid finite volume / finite difference discretization using adaptive octree cubic meshes. The mesh is dynamically refined towards the free surface and the construction. Special care is taken to devise a discretization for the case of curvilinear boundaries and interfaces immersed in the octree Cartesian background computational mesh. To demonstrate the accuracy of the method, we show the results for two benchmark problems: the sloshing 3D container and the channel laminar flow passing the 3D cylinder of circular cross-section. Further, we simulate numerically a flow with surface waves around an offshore oil platform for the realistic set of geophysical data.
A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.
Ling, Hong; Luo, Ercang; Dai, Wei
2006-12-22
Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy. PMID:16996099
Novel hybrid methods applied for the numerical simulation of three-phase biotechnological flows
Energy Technology Data Exchange (ETDEWEB)
Diez Robles, Lucia
2009-07-01
Granular Activated Sludge (GAS) is na novel biological secondary treatment of wastewater which presents multiple advantages with respect to Conventional Activated Sludge (CAS). For fluid mechanical analysis of the bioreactor in which GAS is cultivated, two strategies are adopted: numerical analysis which is carried out in the present thesis and optical in situ measurements which validate the numerical results. The Eulerian-Eulerian multi-fluid approach does not offer a satisfactory description of the three-phase flow as there is a lack of appropriate mathematical models and the solution of the equation systems is problematic. Hybrid methods are here developed in order to complement the classical numerical techniques. These improve the convergence of the numerical simulation, generate results more in accordance with the experimental results and reduce the CPU time required for the calculations. An additional momentum exchange between the dispersed phases is also proposed for the consideration of the four-way coupling case. (orig.)
Numerical weather prediction in two dimensions with topography, using a finite volume method
Bousquet, Arthur; Hong, Youngjoon; Temam, Roger; Tribbia, Joseph
2014-01-01
We aim to study a finite volume scheme to solve the two dimensional inviscid primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions to the system of equations. In that respect, a version of a projection method is introduced to enforce the compatibility condition on the horizontal velocity field, which comes from the boundary conditions. The resulting scheme allows for a significant reduction of the errors near the topography when compared to more standard finite volume schemes. In the numerical simulations, we first present the associated good convergence results that are satisfied by the solutions simulated by our scheme when compared to particular analytic solutions. We then report on numerical experiments using realistic parameters. Finally, the effects of a random small-scale forcing on the velocity equation is numerically investigated. The numerical results show that such a forcing is responsible for recurrent ...
Energy Technology Data Exchange (ETDEWEB)
Keski-Rahkonen, O.; Bjoerkman, J.; Heikkilae, L. [Technical Research Centre of Finland, Espoo (Finland). Fire Technology Lab.
1992-12-31
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).
Liu, Qing
2016-01-01
As a numerically accurate and computationally efficient mesoscopic numerical method, the lattice Boltzmann (LB) method has achieved great success in simulating microscale rarefied gas flows. In this paper, an LB method based on the cascaded collision operator is presented to simulate microchannel gas flows in the transition flow regime. The Bosanquet-type effective viscosity is incorporated into the cascaded lattice Boltzmann (CLB) method to account for the rarefaction effects. In order to gain accurate simulations and match the Bosanquet-type effective viscosity, the combined bounce-back/specular-reflection scheme with a modified second-order slip boundary condition is employed in the CLB method. The present method is applied to study gas flow in a microchannel with periodic boundary condition and gas flow in a long microchannel with pressure boundary condition over a wide range of Knudsen numbers. The predicted results, including the velocity profile, the mass flow rate, and the non-linear pressure deviatio...
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.
Directory of Open Access Journals (Sweden)
Petráš Ivo
2011-01-01
Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.
Tetsuo Inoue
1998-01-01
The charge simulation method has been applied to solve a lot of problems in electrical engineering. However, the principle of the method is not known enough even now. This paper is devoted to giving the theoretical and mathematical base for the charge simulation method of numerical conformal mappings in ring domains. Therefore for example, the uniform, convergence of approximations, the theoretical distribution of charge points, and the charges will be mathematically discussed. An...
Numerical solution of Navier stokes equation using control volume and finite element method
Musa Adam Aigo
2016-01-01
The aim of this paper is twofold first we will provide a numerical solution of the Navier Stokes equation using the Projection technique and finite element method. The problem will be introduced in weak formulation and a Finite Element method will be developed, then solve in a fast way the sparse system derived. Second, the projection method with Control volume approach will be applied to get a fast solution, in iterations count.
İnan B.; Bahadir A. R.
2015-01-01
In this paper, numerical solutions of the generalized Burgers-Huxley equation are obtained using a new technique of forming improved exponential finite difference method. The technique is called implicit exponential finite difference method for the solution of the equation. Firstly, the implicit exponential finite difference method is applied to the generalized Burgers-Huxley equation. Since the generalized Burgers-Huxley equation is nonlinear the scheme leads to a system of nonlinear equatio...
Numerical Polynomial Homotopy Continuation Method to Locate All The Power Flow Solutions
Mehta, Dhagash; Nguyen, Hung; Turitsyn, Konstantin
2014-01-01
The manuscript addresses the problem of finding all solutions of power flow equations or other similar nonlinear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly in the context of direct methods for transient stability analysis and voltage stability assessment. We introduce a novel form of homotopy continuation method called the numerical polynomial homotopy continuation (NPHC) method that is mathematically guaranteed to find...
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.
International Nuclear Information System (INIS)
The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified PN approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)
Bisetti, Fabrizio; Attili, Antonio; Pitsch, Heinz
2014-08-13
Combustion of fossil fuels is likely to continue for the near future due to the growing trends in energy consumption worldwide. The increase in efficiency and the reduction of pollutant emissions from combustion devices are pivotal to achieving meaningful levels of carbon abatement as part of the ongoing climate change efforts. Computational fluid dynamics featuring adequate combustion models will play an increasingly important role in the design of more efficient and cleaner industrial burners, internal combustion engines, and combustors for stationary power generation and aircraft propulsion. Today, turbulent combustion modelling is hindered severely by the lack of data that are accurate and sufficiently complete to assess and remedy model deficiencies effectively. In particular, the formation of pollutants is a complex, nonlinear and multi-scale process characterized by the interaction of molecular and turbulent mixing with a multitude of chemical reactions with disparate time scales. The use of direct numerical simulation (DNS) featuring a state of the art description of the underlying chemistry and physical processes has contributed greatly to combustion model development in recent years. In this paper, the analysis of the intricate evolution of soot formation in turbulent flames demonstrates how DNS databases are used to illuminate relevant physico-chemical mechanisms and to identify modelling needs.
International Nuclear Information System (INIS)
A scheduling system has been developed by integrating symbolic processing functions for constraint handling and modification guidance, with numeric processing functions for schedule optimization and evaluation. The system is composed of an automatic schedule generation module, interactive schedule revision module and schedule evaluation module. The goal of the problem solving is the flattening of the daily resources requirement throughout the scheduling period. The automatic schedule generation module optimizes the initial schedule according to the formulatable portion of requirement description specified in a predicate-like language. A planning engineer refines the near-goal schedule through a knowledge-based interactive optimization process to obtain the goal schedule which fully covers the requirement description, with the interactive schedule revision module and schedule evaluation module. A scheduling system has been implemented on the basis of the proposed problem solving framework and experimentally applied to real-world sized scheduling problems for plant construction. With a result of the overall plant construction scheduling, a section schedule optimization process is described with the emphasis on the symbolic processing functions. (author)
Bisetti, Fabrizio
2014-07-14
Combustion of fossil fuels is likely to continue for the near future due to the growing trends in energy consumption worldwide. The increase in efficiency and the reduction of pollutant emissions from combustion devices are pivotal to achieving meaningful levels of carbon abatement as part of the ongoing climate change efforts. Computational fluid dynamics featuring adequate combustion models will play an increasingly important role in the design of more efficient and cleaner industrial burners, internal combustion engines, and combustors for stationary power generation and aircraft propulsion. Today, turbulent combustion modelling is hindered severely by the lack of data that are accurate and sufficiently complete to assess and remedy model deficiencies effectively. In particular, the formation of pollutants is a complex, nonlinear and multi-scale process characterized by the interaction of molecular and turbulent mixing with a multitude of chemical reactions with disparate time scales. The use of direct numerical simulation (DNS) featuring a state of the art description of the underlying chemistry and physical processes has contributed greatly to combustion model development in recent years. In this paper, the analysis of the intricate evolution of soot formation in turbulent flames demonstrates how DNS databases are used to illuminate relevant physico-chemical mechanisms and to identify modelling needs. © 2014 The Author(s) Published by the Royal Society.
Dongarra, Jack
2012-11-01
We propose to study the impact on the energy footprint of two advanced algorithmic strategies in the context of high performance dense linear algebra libraries: (1) mixed precision algorithms with iterative refinement allow to run at the peak performance of single precision floating-point arithmetic while achieving double precision accuracy and (2) tree reduction technique exposes more parallelism when factorizing tall and skinny matrices for solving over determined systems of linear equations or calculating the singular value decomposition. Integrated within the PLASMA library using tile algorithms, which will eventually supersede the block algorithms from LAPACK, both strategies further excel in performance in the presence of a dynamic task scheduler while targeting multicore architecture. Energy consumption measurements are reported along with parallel performance numbers on a dual-socket quad-core Intel Xeon as well as a quad-socket quad-core Intel Sandy Bridge chip, both providing component-based energy monitoring at all levels of the system, through the Power Pack framework and the Running Average Power Limit model, respectively. © 2012 IEEE.
Institute of Scientific and Technical Information of China (English)
Ou Jing; Yang Jin-Hong
2011-01-01
The B2-Eirene (SOLPS 4.0) code package is used to investigate the plasma parallel flow,i.e.,the scrape-off layer (SOL) flow,in the experimental advanced superconducting tokamak (EAST) divertor. Simulation results show that the SOL flow in the divertor region can exhibit complex behaviour,such as a high Mach flow and flow reversal in different plasma regimes. When the divertor plasma is in the detachment state,the high Mach flow with approaching or exceeding sonic speed is observed away from the target plate in our simulation. When the divertor plasma is in the high recycling The driving mechanisms for the high Mach flow and the reversed flow are analysed theoretically through momentum and continuity equations,respectively. The profile of the ionization sources is shown to be a possible formation condition causing the complex behaviour of the SOL flow. In addition,the effects of the high Mach flow and the flow reversal on the impurity transport are also discussed in this paper.
Xiao, Wenbin; Dong, Wencai
2016-06-01
In the framework of 3D potential flow theory, Bessho form translating-pulsating source Green's function in frequency domain is chosen as the integral kernel in this study and hybrid source-and-dipole distribution model of the boundary element method is applied to directly solve the velocity potential for advancing ship in regular waves. Numerical characteristics of the Green function show that the contribution of local-flow components to velocity potential is concentrated at the nearby source point area and the wave component dominates the magnitude of velocity potential in the far field. Two kinds of mathematical models, with or without local-flow components taken into account, are adopted to numerically calculate the longitudinal motions of Wigley hulls, which demonstrates the applicability of translating-pulsating source Green's function method for various ship forms. In addition, the mesh analysis of discrete surface is carried out from the perspective of ship-form characteristics. The study shows that the longitudinal motion results by the simplified model are somewhat greater than the experimental data in the resonant zone, and the model can be used as an effective tool to predict ship seakeeping properties. However, translating-pulsating source Green function method is only appropriate for the qualitative analysis of motion response in waves if the ship geometrical shape fails to satisfy the slender-body assumption.
Directory of Open Access Journals (Sweden)
István Bíró
2016-01-01
Full Text Available The aim of this article is to demonstrate the application of a simple numerical method which is suitable for motion analysis of different mechanical systems. For mechanical engineer students it is important task. Mechanical systems consisting of rigid bodies are linked to each other by different constraints. Kinematical and kinetical analysis of them leads to integration of second order differential equations. In this way the kinematical functions of parts of mechanical systems can be determined. Degrees of freedom of the mechanical system increase as a result of built-in elastic parts. Numerical methods can be applied to solve such problems. The simple numerical method will be demonstrated in MS Excel by author by the aid of two examples. MS Excel is a quite useful tool for mechanical engineers because easy to use it and details can be seen moreover failures can be noticed. Some parts of results obtained by using the numerical method were checked by analytical way. The published method can be used in higher education for mechanical engineer students.
The Second Development Method and Application Based on Ansys in Advanced Digital Manufacturing
Institute of Scientific and Technical Information of China (English)
SUN Yuantao; WANG Shaomei; ZHAO Zhangyan
2006-01-01
The computer aided engineering is aiming at the numerical simulation-the important link in the advanced digital manufacturing. Its second development based on Ansys platform can be carried out often. In common, the Visual Basic and APDL are important development tools and are applied in the product design at the same time. In the paper, the secondary development flow and method based on Ansys is described. The parameter design and analysis process of the bridge girder erecting equipment is carried on with Ansys software and its secondary development tools-APDL and Visual Basics, including the interact between the mode of Ansys batch solving and Visual Basic. The method speeds up design and enhances the product the quality and the performance.
New families of symplectic splitting methods for numerical integration in dynamical astronomy
Blanes, Sergio; Farres, Ariadna; Laskar, Jacques; Makazaga, Joseba; Murua, Ander
2012-01-01
We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a large time span. We derive in a systematic way an independent set of necessary and sufficient conditions to be satisfied by the coefficients of splitting methods to achieve a prescribed order of accuracy. Splitting methods satisfying such (generalized) order conditions are appropriate in particular for the numerical simulation of the Solar System described in Jacobi coordinates. We show that, when using Poincar\\'e Heliocentric coordinates, the same order of accuracy may be obtained by imposing an additional polynomial equation on the coefficients of the splitting method. We construct several splitting methods for each of the two sets of coordinates by solving the corresponding systems of polynomial equations and finding the optimal solutions. The experiments reported here indicate that the efficie...
Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model
Directory of Open Access Journals (Sweden)
Guang-an Zou
2013-01-01
Full Text Available A 1.5-layer reduced-gravity shallow-water ocean model in spherical coordinates is described and discretized in a staggered grid (standard Arakawa C-grid with the forward-time central-space (FTCS method and the Leap-frog finite difference scheme. The discrete Fourier analysis method combined with the Gershgorin circle theorem is used to study the stability of these two finite difference numerical models. A series of necessary conditions of selection criteria for the time-space step sizes and model parameters are obtained. It is showed that these stability conditions are more accurate than the Courant-Friedrichs-Lewy (CFL condition and other two criterions (Blumberg and Mellor, 1987; Casulli, 1990, 1992. Numerical experiments are proposed to test our stability results, and numerical model that is designed is also used to simulate the ocean current.
Rembiasz, T.; Obergaulinger, M.; Cerdá-Durán, P.; Aloy, M. Á.; Müller, E.
2016-05-01
We study the influence of numerical methods and grid resolution on the termination of the magnetorotational instability (MRI) by means of parasitic instabilities in threedimensional shearing-disc simulations reproducing typical conditions found in core-collapse supernovae. Whether or not the MRI is able to amplify weak magnetic fields in this context strongly depends, among other factors, on the amplitude at which its growth terminates. The qualitative results of our study do not depend on the numerical scheme. In all our models, MRI termination is caused by Kelvin-Helmholtz instabilities, consistent with theoretical predictions. Quantitatively, however, there are differences, but numerical convergence can be achieved even at relatively low grid resolutions if high-order reconstruction methods are used.
Taghizadeh, Alireza; Chung, Il-Sug
2016-01-01
We show the strength of the Fourier modal method (FMM) for numerically investigating the optical properties of vertical cavities including subwavelength gratings. Three different techniques for determining the resonance frequency and Q-factor of a cavity mode are compared. Based on that, the Fabry-Perot approach has been chosen due to its numerical efficiency. The computational uncertainty in determining the resonance frequency and Q-factor is investigated, showing that the uncertainty in the Q-factor calculation can be a few orders of magnitude larger than that in the resonance frequency calculation. Moreover, a method for reducing 3D simulations to lower-dimensional simulations is suggested, and is shown to enable approximate and fast simulations of certain device parameters. Numerical calculation of the cavity dispersion, which is an important characteristic of vertical cavities, is illustrated. By employing the implemented FMM, it is shown that adiabatic heterostructures designs are advantageous compared ...
Rembiasz, T; Cerdá-Durán, P; Aloy, M Á; Müller, E
2016-01-01
We study the influence of numerical methods and grid resolution on the termination of the magnetorotational instability (MRI) by means of parasitic instabilities in three-dimensional shearing-disc simulations reproducing typical conditions found in core-collapse supernovae. Whether or not the MRI is able to amplify weak magnetic fields in this context strongly depends, among other factors, on the amplitude at which its growth terminates. The qualitative results of our study do not depend on the numerical scheme. In all our models, MRI termination is caused by Kelvin-Helmholtz instabilities, consistent with theoretical predictions. Quantitatively, however, there are differences, but numerical convergence can be achieved even at relatively low grid resolutions if high-order reconstruction methods are used.
Advanced methods for the study of PWR cores
International Nuclear Information System (INIS)
This document gathers the transparencies presented at the 6. technical session of the French nuclear energy society (SFEN) in October 2003. The transparencies of the annual meeting are presented in the introductive part: 1 - status of the French nuclear park: nuclear energy results, management of an exceptional climatic situation: the heat wave of summer 2003 and the power generation (J.C. Barral); 2 - status of the research on controlled thermonuclear fusion (J. Johner). Then follows the technical session about the advanced methods for the study of PWR reactor cores: 1 - the evolution approach of study methodologies (M. Lambert, J. Pelet); 2 - the point of view of the nuclear safety authority (D. Brenot); 3 - the improved decoupled methodology for the steam pipe rupture (S. Salvatores, J.Y. Pouliquen); 4 - the MIR method for the pellet-clad interaction (renovated IPG methodology) (E. Baud, C. Royere); 5 - the improved fuel management (IFM) studies for Koeberg (C. Cohen); 6 - principle of the methods of accident study implemented for the European pressurized reactor (EPR) (F. Foret, A. Ferrier); 7 - accident studies with the EPR, steam pipe rupture (N. Nicaise, S. Salvatores); 8 - the co-development platform, a new generation of software tools for the new methodologies (C. Chauliac). (J.S.)
Numerical solution of the problem of selecting the optimum method of operating oil wells
Energy Technology Data Exchange (ETDEWEB)
Skryago, A.M.; Chirikov, L.I.; Fridman, G.Sh.; Kolokolov, A.A.; Panteleyev, G.V.; Terent' yev, S.A.; Zabudskiy, G.G.
1981-01-01
A mathematical model is studied for selecting the optimum method of operating the wells of an oil field, which is a linear Boolean programming problem. It is shown that this problem is equivalent to the generalized packet problem and a single product variant model of sectoral planning. Numerical calculations on the computer using as the initial problem the modified method of E. Balash, for the generalized packet problem the method of M.F. Kazakovaya, and the single product variant problem of sectoral planning the method of A. Ye. Bakhtin, show the greatest effectiveness for the problem studied of A. Ye. Bakhtin's method.
Institute of Scientific and Technical Information of China (English)
崔明; 梁栋
2002-01-01
The numerical methods for miscible displacment in aggregated or sorbing medium areconsidered. A mixed finite element method is adopted for the pressure equation. The concentra-tion in the mobile water is approximated by a combination of a Galerkin finite element method andthe method of characteristics and the concentration in immobile water is approximated by a stan-dard Galerkin method. The moving mesh technique which depends on time t is adopted here. Themoving meshes can vary in different spacial domains with different variable times. Optima errorestimates in energy norm and L2 norm are obtained under certain constraints.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Deals with the application of Kreiss resolvent condition in the error growth analysis of numerical methods, and studies the stability of Runge-Kutta method in respect of Kreiss resolvent condition with emphasis on the study on the subclass of collocation methods with abscissas in [ 0,1 ] by applying the methods to the test equation U＇(t) = λ U(t) + μU( t - τ)τ ＞ 0 with complex constraintsμ and λ, and proves under some assumptions on the R-K methods that the error growth is uniformly bounded in the stability region.