Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations PDF Download

Author: Willem Hundsdorfer
Publisher: Springer Science & Business Media
ISBN: 3662090171
Category : Technology & Engineering
Languages : en
Pages : 479

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Book Description
Unique book on Reaction-Advection-Diffusion problems

Author: Christopher Alan Kennedy
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 56

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Book Description
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.

Author: Hans Petter Langtangen
Publisher: Springer
ISBN: 3319554565
Category : Computers
Languages : en
Pages : 522

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Book Description
This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Author: Martin Stynes
Publisher:
ISBN: 9781470450212
Category : MATHEMATICS
Languages : en
Pages :

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Book Description
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: John Crank
Publisher: Oxford University Press
ISBN: 9780198534112
Category : Mathematics
Languages : en
Pages : 428

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Book Description
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: Jianping Zhu
Publisher: BoD – Books on Demand
ISBN: 9533074302
Category : Computers
Languages : en
Pages : 576

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Book Description
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
Publisher: Springer Science & Business Media
ISBN: 3642184650
Category : Computers
Languages : en
Pages : 524

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Book Description
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
Publisher: Springer Nature
ISBN: 3030768104
Category : Mathematics
Languages : en
Pages : 125

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Book Description
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: Maria do Carmo Coimbra
Publisher: CRC Press
ISBN: 1498723896
Category : Mathematics
Languages : en
Pages : 176

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Book Description
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: Ronald E Mickens
Publisher: World Scientific
ISBN: 981122255X
Category : Mathematics
Languages : en
Pages : 332

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Book Description
This second edition of Nonstandard Finite Difference Models of Differential Equations provides an update on the progress made in both the theory and application of the NSFD methodology during the past two and a half decades. In addition to discussing details related to the determination of the denominator functions and the nonlocal discrete representations of functions of dependent variables, we include many examples illustrating just how this should be done.Of real value to the reader is the inclusion of a chapter listing many exact difference schemes, and a chapter giving NSFD schemes from the research literature. The book emphasizes the critical roles played by the 'principle of dynamic consistency' and the use of sub-equations for the construction of valid NSFD discretizations of differential equations.