Numerical Methods For Hyperbolic Equations

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Numerical Methods for Hyperbolic Equations

Elena Vázquez-Cendón,Arturo Hidalgo,Pilar Garcia Navarro,Luis Cea
Numerical Methods for Hyperbolic Equations Book PDF

Author : Elena Vázquez-Cendón,Arturo Hidalgo,Pilar Garcia Navarro,Luis Cea
Publisher : CRC Press
Page : 436 pages
File Size : 52,6 Mb
Release : 2012-11-05
Category : Mathematics
ISBN : 9780415621502

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Numerical Methods for Hyperbolic Equations by Elena Vázquez-Cendón,Arturo Hidalgo,Pilar Garcia Navarro,Luis Cea Pdf

Numerical Methods for Hyperbolic Equations is a collection of 49 articles presented at the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications (Santiago de Compostela, Spain, 4-8 July 2011). The conference was organized to honour Professor Eleuterio Toro in the month of his 65th birthday. The topics covered include: • Recent advances in the numerical computation of environmental conservation laws with source terms • Multiphase flow and porous media • Numerical methods in astrophysics • Seismology and geophysics modelling • High order methods for hyperbolic conservation laws • Numerical methods for reactive flows • Finite volume and discontinous Galerkin schemes for stiff source term problems • Methods and models for biomedical problems • Numerical methods for reactive flows The research interest of Eleuterio Toro, born in Chile on 16th July 1946, is reflected in Numerical Methods for Hyperbolic Equations, and focuses on: numerical methods for partial differential equations, with particular emphasis on methods for hyperbolic equations; design and application of new algorithms; hyperbolic partial differential equations as mathematical models of various types of processes; mathematical modelling and simulation of physico/chemical processes that include wave propagation phenomena; modelling of multiphase flows; application of models and methods to real problems. Eleuterio Toro received several honours and distinctions, including the honorary title OBE from Queen Elizabeth II (Buckingham Palace, London 2000); Distinguished Citizen of the City of Carahue (Chile, 2001); Life Fellow, Claire Hall, University of Cambridge (UK, 2003); Fellow of the Indian Society for Shock Wave Research (Bangalore, 2005); Doctor Honoris Causa (Universidad de Santiago de Chile, 2008); William Penney Fellow, University of Cambridge (UK, 2010); Doctor Honoris Causa (Universidad de la Frontera, Chile, 2012). Professor Toro is author of two books, editor of two books and author of more than 260 research works. In the last ten years he has been invited and keynote speaker in more than 100 scientific events. Professor Toro has held many visiting appointments round the world, which include several European countries, Japan, China and USA.

Lecture Notes on Numerical Methods for Hyperbolic Equations

Elena Vázquez-Cendón
Lecture Notes on Numerical Methods for Hyperbolic Equations Book PDF

Author : Elena Vázquez-Cendón
Publisher : CRC Press
Page : 144 pages
File Size : 52,9 Mb
Release : 2011-05-23
Category : Mathematics
ISBN : 9780203590621

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Lecture Notes on Numerical Methods for Hyperbolic Equations by Elena Vázquez-Cendón Pdf

This volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, 2-4 July 2011). The course was organized in recognition of Prof. Eleuterio Toro‘s contribution to education and training on numerical methods for partial differential equation

Handbook of Numerical Methods for Hyperbolic Problems

Remi Abgrall,Chi-Wang Shu
Handbook of Numerical Methods for Hyperbolic Problems Book PDF

Author : Remi Abgrall,Chi-Wang Shu
Publisher : Elsevier
Page : 666 pages
File Size : 55,7 Mb
Release : 2016-11-17
Category : Mathematics
ISBN : 9780444637956

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Handbook of Numerical Methods for Hyperbolic Problems by Remi Abgrall,Chi-Wang Shu Pdf

Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications Written by leading subject experts in each field who provide breadth and depth of content coverage

Finite Volume Methods for Hyperbolic Problems

Randall J. LeVeque
Finite Volume Methods for Hyperbolic Problems Book PDF

Author : Randall J. LeVeque
Publisher : Cambridge University Press
Page : 582 pages
File Size : 49,7 Mb
Release : 2002-08-26
Category : Mathematics
ISBN : 9781139434188

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Finite Volume Methods for Hyperbolic Problems by Randall J. LeVeque Pdf

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.

Numerical Solution of Hyperbolic Differential Equations

M. Shoucri,Merit Mounir Shoucri
Numerical Solution of Hyperbolic Differential Equations Book PDF

Author : M. Shoucri,Merit Mounir Shoucri
Publisher : Unknown
Page : 148 pages
File Size : 46,7 Mb
Release : 2008
Category : Differential equations, Hyperbolic
ISBN : UOM:39076002793920

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Numerical Solution of Hyperbolic Differential Equations by M. Shoucri,Merit Mounir Shoucri Pdf

The application of the method of characteristics for the numerical solution of hyperbolic type partial differential equations will be presented. Especial attention will be given to the numerical solution of the Vlasov equation, which is of fundamental importance in the study of the kinetic theory of plasmas, and to other equations pertinent to plasma physics. Examples will be presented with possible combination with fractional step methods in the case of several dimensions. The methods are quite general and can be applied to different equations of hyperbolic type in the field of mathematical physics. Examples for the application of the method of characteristics to fluid equations will be presented, for the numerical solution of the shallow water equations and for the numerical solution of the equations of the incompressible ideal magnetohydrodynamic (MHD) flows in plasmas.

Mathematical Aspects of Numerical Solution of Hyperbolic Systems

A.G. Kulikovskii,N.V. Pogorelov,A. Yu. Semenov
Mathematical Aspects of Numerical Solution of Hyperbolic Systems Book PDF

Author : A.G. Kulikovskii,N.V. Pogorelov,A. Yu. Semenov
Publisher : CRC Press
Page : 560 pages
File Size : 46,5 Mb
Release : 2000-12-21
Category : Mathematics
ISBN : 9781482273991

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Mathematical Aspects of Numerical Solution of Hyperbolic Systems by A.G. Kulikovskii,N.V. Pogorelov,A. Yu. Semenov Pdf

This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics,

Handbook of Numerical Methods for Hyperbolic Problems

Remi Abgrall,Chi-Wang Shu
Handbook of Numerical Methods for Hyperbolic Problems Book PDF

Author : Remi Abgrall,Chi-Wang Shu
Publisher : Elsevier
Page : 610 pages
File Size : 54,9 Mb
Release : 2017-01-16
Category : Mathematics
ISBN : 9780444639110

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Handbook of Numerical Methods for Hyperbolic Problems by Remi Abgrall,Chi-Wang Shu Pdf

Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage

Finite Volume Methods for Hyperbolic Problems

Randall J. LeVeque
Finite Volume Methods for Hyperbolic Problems Book PDF

Author : Randall J. LeVeque
Publisher : Cambridge University Press
Page : 582 pages
File Size : 55,6 Mb
Release : 2002-08-26
Category : Mathematics
ISBN : 0521009243

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Finite Volume Methods for Hyperbolic Problems by Randall J. LeVeque Pdf

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Advanced Numerical Approximation of Nonlinear Hyperbolic Equations

B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor
Advanced Numerical Approximation of Nonlinear Hyperbolic Equations Book PDF

Author : B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor
Publisher : Springer
Page : 446 pages
File Size : 55,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540498049

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Advanced Numerical Approximation of Nonlinear Hyperbolic Equations by B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor Pdf

This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Mass Per Pettersson,Gianluca Iaccarino,Jan Nordström
Polynomial Chaos Methods for Hyperbolic Partial Differential Equations Book PDF

Author : Mass Per Pettersson,Gianluca Iaccarino,Jan Nordström
Publisher : Springer
Page : 214 pages
File Size : 40,9 Mb
Release : 2015-03-10
Category : Technology & Engineering
ISBN : 9783319107141

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Polynomial Chaos Methods for Hyperbolic Partial Differential Equations by Mass Per Pettersson,Gianluca Iaccarino,Jan Nordström Pdf

This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.

Numerical Approximation of Hyperbolic Systems of Conservation Laws

Edwige Godlewski,Pierre-Arnaud Raviart
Numerical Approximation of Hyperbolic Systems of Conservation Laws Book PDF

Author : Edwige Godlewski,Pierre-Arnaud Raviart
Publisher : Springer Nature
Page : 846 pages
File Size : 43,5 Mb
Release : 2021-08-28
Category : Mathematics
ISBN : 9781071613443

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Numerical Approximation of Hyperbolic Systems of Conservation Laws by Edwige Godlewski,Pierre-Arnaud Raviart Pdf

This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.

Partial Differential Equations with Numerical Methods

Stig Larsson,Vidar Thomee
Partial Differential Equations with Numerical Methods Book PDF

Author : Stig Larsson,Vidar Thomee
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 42,9 Mb
Release : 2008-12-05
Category : Mathematics
ISBN : 9783540887058

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Partial Differential Equations with Numerical Methods by Stig Larsson,Vidar Thomee Pdf

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. 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. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. 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. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems

Giacomo Albi,Walter Boscheri,Mattia Zanella
Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems Book PDF

Author : Giacomo Albi,Walter Boscheri,Mattia Zanella
Publisher : Springer Nature
Page : 241 pages
File Size : 46,8 Mb
Release : 2023-06-02
Category : Mathematics
ISBN : 9783031298752

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Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems by Giacomo Albi,Walter Boscheri,Mattia Zanella Pdf

A broad range of phenomena in science and technology can be described by non-linear partial differential equations characterized by systems of conservation laws with source terms. Well known examples are hyperbolic systems with source terms, kinetic equations, and convection-reaction-diffusion equations. This book collects research advances in numerical methods for hyperbolic balance laws and kinetic equations together with related modelling aspects. All the contributions are based on the talks of the speakers of the Young Researchers’ Conference “Numerical Aspects of Hyperbolic Balance Laws and Related Problems”, hosted at the University of Verona, Italy, in December 2021.

Analytic Methods for Partial Differential Equations

G. Evans,J. Blackledge,P. Yardley
Analytic Methods for Partial Differential Equations Book PDF

Author : G. Evans,J. Blackledge,P. Yardley
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447103790

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Analytic Methods for Partial Differential Equations by G. Evans,J. Blackledge,P. Yardley Pdf

This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.

Solving Hyperbolic Equations with Finite Volume Methods

M. Elena Vázquez-Cendón
Solving Hyperbolic Equations with Finite Volume Methods Book PDF

Author : M. Elena Vázquez-Cendón
Publisher : Springer
Page : 188 pages
File Size : 55,5 Mb
Release : 2015-04-16
Category : Computers
ISBN : 9783319147840

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Solving Hyperbolic Equations with Finite Volume Methods by M. Elena Vázquez-Cendón Pdf

Finite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields. The selection of content is based on the author’s experience giving PhD and master courses in different universities. In the book the introduction of new concepts and numerical methods go together with simple exercises, examples and applications that contribute to reinforce them. In addition, some of them involve the execution of MATLAB codes. The author promotes an understanding of common terminology with a balance between mathematical rigor and physical intuition that characterizes the origin of the methods. This book aims to be a first contact with finite volume methods. Once readers have studied it, they will be able to follow more specific bibliographical references and use commercial programs or open source software within the framework of Computational Fluid Dynamics (CFD).