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Author : Willem Hundsdorfer,Jan G. Verwer
Publisher : Springer Science & Business Media
Page : 479 pages
File Size : 54,7 Mb
Release : 2013-04-17
Category : Technology & Engineering
ISBN : 9783662090176
Unique book on Reaction-Advection-Diffusion problems
Author : Jianping Zhu
Publisher : BoD – Books on Demand
Page : 576 pages
File Size : 44,9 Mb
Release : 2011-10-26
Category : Computers
ISBN : 9789533074306
The purpose of this book is to introduce researchers and graduate students to a broad range of applications of computational simulations, with a particular emphasis on those involving computational fluid dynamics (CFD) simulations. The book is divided into three parts: Part I covers some basic research topics and development in numerical algorithms for CFD simulations, including Reynolds stress transport modeling, central difference schemes for convection-diffusion equations, and flow simulations involving simple geometries such as a flat plate or a vertical channel. Part II covers a variety of important applications in which CFD simulations play a crucial role, including combustion process and automobile engine design, fluid heat exchange, airborne contaminant dispersion over buildings and atmospheric flow around a re-entry capsule, gas-solid two phase flow in long pipes, free surface flow around a ship hull, and hydrodynamic analysis of electrochemical cells. Part III covers applications of non-CFD based computational simulations, including atmospheric optical communications, climate system simulations, porous media flow, combustion, solidification, and sound field simulations for optimal acoustic effects.
Author : Ivan Dimov,Lirkov Ivan Dimov,Stefka Dimova,Natalia Kolkovska
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 54,8 Mb
Release : 2011-01-14
Category : Computers
ISBN : 9783642184659
This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Numerical Methods and Applications, NMA 2010, held in Borovets, Bulgaria, in August 2010. The 60 revised full papers presented together with 3 invited papers were carefully reviewed and selected from numerous submissions for inclusion in this book. The papers are organized in topical sections on Monte Carlo and quasi-Monte Carlo methods, environmental modeling, grid computing and applications, metaheuristics for optimization problems, and modeling and simulation of electrochemical processes.
Author : Tim Jax,Andreas Bartel,Matthias Ehrhardt,Michael Günther,Gerd Steinebach
Publisher : Springer Nature
Page : 125 pages
File Size : 45,9 Mb
Release : 2021-07-24
Category : Mathematics
ISBN : 9783030768102
This book discusses the development of the Rosenbrock—Wanner methods from the origins of the idea to current research with the stable and efficient numerical solution and differential-algebraic systems of equations, still in focus. The reader gets a comprehensive insight into the classical methods as well as into the development and properties of novel W-methods, two-step and exponential Rosenbrock methods. In addition, descriptive applications from the fields of water and hydrogen network simulation and visual computing are presented.
Author : Daniel J. Duffy
Publisher : John Wiley & Sons
Page : 452 pages
File Size : 47,7 Mb
Release : 2013-10-28
Category : Business & Economics
ISBN : 9781118856482
The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.
Author : Maria do Carmo Coimbra,Alirio Egidio Rodrigues,Jaime Duarte Rodrigues,Rui Jorge Mendes Robalo,Rui Manuel Pires Almeida
Publisher : CRC Press
Page : 176 pages
File Size : 52,5 Mb
Release : 2016-11-30
Category : Mathematics
ISBN : 9781498723893
This book focuses on process simulation in chemical engineering with a numerical algorithm based on the moving finite element method (MFEM). It offers new tools and approaches for modeling and simulating time-dependent problems with moving fronts and with moving boundaries described by time-dependent convection-reaction-diffusion partial differential equations in one or two-dimensional space domains. It provides a comprehensive account of the development of the moving finite element method, describing and analyzing the theoretical and practical aspects of the MFEM for models in 1D, 1D+1d, and 2D space domains. Mathematical models are universal, and the book reviews successful applications of MFEM to solve engineering problems. It covers a broad range of application algorithm to engineering problems, namely on separation and reaction processes presenting and discussing relevant numerical applications of the moving finite element method derived from real-world process simulations.
Author : Adolf Ebel,Teimuraz Davitashvili
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 55,9 Mb
Release : 2007-05-02
Category : Science
ISBN : 9781402058752
This book contains the proceedings of the NATO Advanced Research Workshop on Air, Water and Soil Quality Modelling for Risk and Impact Assessment. The aim of the workshop was to further joint environmental compartment modelling and applications of control theory to environmental management. It provides an overview of ongoing research in this field regarding assessment of environmental risks and impacts.
Author : Dmitri Kuzmin,Rainald Löhner,Stefan Turek
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 44,9 Mb
Release : 2012-04-02
Category : Science
ISBN : 9789400740372
Addressing students and researchers as well as Computational Fluid Dynamics practitioners, this book is the most comprehensive review of high-resolution schemes based on the principle of Flux-Corrected Transport (FCT). The foreword by J.P. Boris and historical note by D.L. Book describe the development of the classical FCT methodology for convection-dominated transport problems, while the design philosophy behind modern FCT schemes is explained by S.T. Zalesak. The subsequent chapters present various improvements and generalizations proposed over the past three decades. In this new edition, recent results are integrated into existing chapters in order to describe significant advances since the publication of the first edition. Also, 3 new chapters were added in order to cover the following topics: algebraic flux correction for finite elements, iterative and linearized FCT schemes, TVD-like flux limiters, acceleration of explicit and implicit solvers, mesh adaptation, failsafe limiting for systems of conservation laws, flux-corrected interpolation (remapping), positivity preservation in RANS turbulence models, and the use of FCT as an implicit subgrid scale model for large eddy simulations.
Author : Karline Soetaert,Jeff Cash,Francesca Mazzia
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 41,5 Mb
Release : 2012-06-06
Category : Computers
ISBN : 9783642280702
Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.
Author : Ivan Lirkov,Svetozar Margenov
Publisher : Springer Science & Business Media
Page : 754 pages
File Size : 40,7 Mb
Release : 2008-03-28
Category : Computers
ISBN : 9783540788256
This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Large-Scale Scientific Computations, LSSC 2007, held in Sozopol, Bulgaria, in June 2007. The 81 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on robust multilevel and hierarchical preconditioning methods; monte carlo: tools, applications, distributed computing; operator splittings, their application and realization; recent advances in methods and applications for large scale computations and optimization of coupled engineering problems; control systems; environmental modelling; computational grid and large-scale problems; application of metaheuristics to large-scale problems; and contributed talks.
Author : Ashwani Kumar,S. C. Srivastava,S. N. Singh
Publisher : Springer Nature
Page : 455 pages
File Size : 49,8 Mb
Release : 2022-02-28
Category : Technology & Engineering
ISBN : 9789811674723
The book contains select proceedings of the International Conference on Smart Grid Energy Systems and Control (SGESC 2021). The proceedings is divided into 03 volumes, and this volume focuses on renewable energy towards the smart grid. It includes papers related to smart grid, renewable energy, its integration, and DERs in the network for better energy management and ancillary services. The book presents cutting-edge research in the emerging fields of micro, nano, and smart devices and systems from experts. Most of the contributors have built devices or systems or developed processes or algorithms in these areas. This book is a unique collection of chapters from different areas with a common theme and will be immensely useful to academic researchers and practitioners in the industry.
Author : Martin Stynes,David Stynes
Publisher : Unknown
Page : 128 pages
File Size : 50,9 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 1470450216
Many physical problems involve diffusive and convective (transport) processes. When diffusion dominates convection, standard numerical methods work satisfactorily. But when convection dominates diffusion, the standard methods become unstable, and special techniques are needed to compute accurate numerical approximations of the unknown solution. This convection-dominated regime is the focus of the book. After discussing at length the nature of solutions to convection-dominated convection-diffusion problems, the authors motivate and design numerical methods that are particularly suited to this c.
Author : Dmitri Kuzmin,Hennes Hajduk
Publisher : World Scientific
Page : 491 pages
File Size : 54,6 Mb
Release : 2023-08-28
Category : Mathematics
ISBN : 9789811278204
High-order numerical methods for hyperbolic conservation laws do not guarantee the validity of constraints that physically meaningful approximations are supposed to satisfy. The finite volume and finite element schemes summarized in this book use limiting techniques to enforce discrete maximum principles and entropy inequalities. Spurious oscillations are prevented using artificial viscosity operators and/or essentially nonoscillatory reconstructions.An introduction to classical nonlinear stabilization approaches is given in the simple context of one-dimensional finite volume discretizations. Subsequent chapters of Part I are focused on recent extensions to continuous and discontinuous Galerkin methods. Many of the algorithms presented in these chapters were developed by the authors and their collaborators. Part II gives a deeper insight into the mathematical theory of property-preserving numerical schemes. It begins with a review of the convergence theory for finite volume methods and ends with analysis of algebraic flux correction schemes for finite elements. In addition to providing ready-to-use algorithms, this text explains the design principles behind such algorithms and shows how to put theory into practice. Although the book is based on lecture notes written for an advanced graduate-level course, it is also aimed at senior researchers who develop and analyze numerical methods for hyperbolic problems.
Author : John Crank
Publisher : Oxford University Press
Page : 428 pages
File Size : 44,5 Mb
Release : 1979
Category : Mathematics
ISBN : 0198534116
Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Author : Christopher Alan Kennedy
Publisher : Unknown
Page : 56 pages
File Size : 55,8 Mb
Release : 2001
Category : Differential equations
ISBN : NASA:31769000643307
Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations. First, accuracy, stability, conservation, and dense output are considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, N=2, additive Runge-Kutta ARK methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms are of equal order to those of the elemental methods. Derived ARK methods have vanishing stability functions for very large values of the stiff scaled eigenvalue and retain high stability efficiency in the absence of stiffness.
