Initial-Boundary Value Problems and the Navier-Stokes Equation

Author: Heinz-Otto Kreiss,Jens Lorenz

Publisher: SIAM

ISBN: 0898715652

Category: Science

Page: 420

View: 3884


Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.

An Invitation to Applied Mathematics

Differential Equations, Modeling, and Computation

Author: Carmen Chicone

Publisher: Academic Press

ISBN: 0128041544

Category: Mathematics

Page: 878

View: 2875


An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics. Presents an integrated wealth of modeling, analysis, and numerical methods in one volume Provides practical and comprehensible introductions to complex subjects, for example, conservation laws, CFD, SPH, BEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested

Mathematics of Large Eddy Simulation of Turbulent Flows

Author: Luigi Carlo Berselli,Traian Iliescu,William J. Layton

Publisher: Springer Science & Business Media

ISBN: 9783540263166

Category: Computers

Page: 348

View: 3342


This volume focuses on the mathematical foundations of LES and its models and provides a connection between the tools of applied mathematics, partial differential equations and LES. A useful entry point into the field for PhD students in applied mathematics, computational mathematics and partial differential equations is offered.

Analytical and Numerical Approaches to Mathematical Relativity

Author: Jörg Frauendiener,Domenico J. W. Giulini,Volker Perlick

Publisher: Springer

ISBN: 354033484X

Category: Science

Page: 281

View: 3665


General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.

Partial Differential Equations for Scientists and Engineers

Author: Stanley J. Farlow

Publisher: Courier Corporation

ISBN: 0486134733

Category: Mathematics

Page: 414

View: 2825


Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, numerical and approximate methods. Solution guide available upon request. 1982 edition.

Boundary Value Problems, Integral Equations and Related Problems

Proceedings of the Third International Conference, Beijing and Baoding, China, 20-25 August 2010

Author: Guo Chun Wen

Publisher: World Scientific

ISBN: 9814327867

Category: Mathematics

Page: 436

View: 9803


In this volume, we report new results about various boundary value problems for partial differential equations and functional equations, theory and methods of integral equations and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theory and methods for inverse problems of mathematical physics, Clifford analysis and related problems. Contributors include: L Baratchart, B L Chen, D C Chen, S S Ding, K Q Lan, A Farajzadeh, M G Fei, T Kosztolowicz, A Makin, T Qian, J M Rassias, J Ryan, C-Q Ru, P Schiavone, P Wang, Q S Zhang, X Y Zhang, S Y Du, H Y Gao, X Li, Y Y Qiao, G C Wen, Z T Zhang, and others.

Numerical Simulation in Fluid Dynamics

A Practical Introduction

Author: Michael Griebel,Thomas Dornsheifer,Tilman Neunhoeffer

Publisher: SIAM

ISBN: 0898713986

Category: Mathematics

Page: 217

View: 4267


In this translation of the German edition, the authors provide insight into the numerical simulation of fluid flow. Using a simple numerical method as an expository example, the individual steps of scientific computing are presented: the derivation of the mathematical model; the discretization of the model equations; the development of algorithms; parallelization; and visualization of the computed data. In addition to the treatment of the basic equations for modeling laminar, transient flow of viscous, incompressible fluids - the Navier-Stokes equations - the authors look at the simulation of free surface flows; energy and chemical transport; and turbulence. Readers are enabled to write their own flow simulation program from scratch. The variety of applications is shown in several simulation results, including 92 black-and-white and 18 color illustrations. After reading this book, readers should be able to understand more enhanced algorithms of computational fluid dynamics and apply their new knowledge to other scientific fields.

A Mathematical Introduction to Fluid Mechanics

Author: Alexandre J. Chorin,J.E. Marsden

Publisher: Springer Science & Business Media

ISBN: 1461208831

Category: Science

Page: 172

View: 8491


A presentation of some of the basic ideas of fluid mechanics in a mathematically attractive manner. The text illustrates the physical background and motivation for some constructions used in recent mathematical and numerical work on the Navier- Stokes equations and on hyperbolic systems, so as to interest students in this at once beautiful and difficult subject. This third edition incorporates a number of updates and revisions, while retaining the spirit and scope of the original book.

Computational Fluid Dynamics for Engineers

Author: Bengt Andersson,Ronnie Andersson,Love Håkansson,Mikael Mortensen,Rahman Sudiyo,Berend van Wachem

Publisher: Cambridge University Press

ISBN: 1139505564

Category: Technology & Engineering

Page: N.A

View: 2966


Computational fluid dynamics, CFD, has become an indispensable tool for many engineers. This book gives an introduction to CFD simulations of turbulence, mixing, reaction, combustion and multiphase flows. The emphasis on understanding the physics of these flows helps the engineer to select appropriate models to obtain reliable simulations. Besides presenting the equations involved, the basics and limitations of the models are explained and discussed. The book combined with tutorials, project and power-point lecture notes (all available for download) forms a complete course. The reader is given hands-on experience of drawing, meshing and simulation. The tutorials cover flow and reactions inside a porous catalyst, combustion in turbulent non-premixed flow, and multiphase simulation of evaporation spray respectively. The project deals with design of an industrial-scale selective catalytic reduction process and allows the reader to explore various design improvements and apply best practice guidelines in the CFD simulations.

Partial Differential Equations

Modeling, Analysis, Computation

Author: R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp

Publisher: SIAM

ISBN: 0898715946

Category: Mathematics

Page: 665

View: 3059


Textbook with a unique approach that integrates analysis and numerical methods and includes modelling to address real-life problems.

Mathematical Foundations of Elasticity

Author: Jerrold E. Marsden,Thomas J. R. Hughes

Publisher: Courier Corporation

ISBN: 0486142272

Category: Technology & Engineering

Page: 576

View: 3062


Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.