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Handbook of Numerical Methods for Hyperbolic Problems

Author : Remi Abgrall

Publisher : Elsevier

Page : 668 pages

File Size : 36,11 MB

Release : 2016-11-17

Category : Mathematics

ISBN : 0444637958

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Book Description

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



Handbook of Numerical Methods for Hyperbolic Problems

Author : Remi Abgrall

Publisher : Elsevier

Page : 612 pages

File Size : 10,77 MB

Release : 2017-01-16

Category : Mathematics

ISBN : 044463911X

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Book Description

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

Author : Randall J. LeVeque

Publisher : Cambridge University Press

Page : 582 pages

File Size : 47,4 MB

Release : 2002-08-26

Category : Mathematics

ISBN : 1139434187

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Book Description

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.



Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems

Author : Giacomo Albi

Publisher : Springer Nature

Page : 241 pages

File Size : 33,20 MB

Release : 2023-06-02

Category : Mathematics

ISBN : 3031298756

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Book Description

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.



Handbook of Numerical Heat Transfer

Author : W. J. Minkowycz

Publisher : Wiley

Page : 0 pages

File Size : 40,74 MB

Release : 2006-03-24

Category : Science

ISBN : 9780471348788

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Book Description

A completely updated edition of the acclaimed single-volume reference for heat transfer and the thermal sciences This Second Edition of Handbook of Numerical Heat Transfer covers the basic equations for numerical method calculations regarding heat transfer problems and applies these to problems encountered in aerospace, nuclear power, chemical processes, electronic packaging, and other related areas of mechanical engineering. As with the first edition, this complete revision presents comprehensive but accessible coverage of the necessary formulations, numerical schemes, and innovative solution techniques for solving problems of heat and mass transfer and related fluid flows. Featuring contributions from some of the most prominent authorities in the field, articles are grouped by major sets of methods and functions, with the text describing new and improved, as well as standard, procedures. Handbook of Numerical Heat Transfer, Second Edition includes: * Updated coverage of parabolic systems, hyperbolic systems, integral-and integro-differential systems, Monte Carlo and perturbation methods, and inverse problems * Usable computer programs that allow quick applications to aerospace, chemical, nuclear, and electronic packaging industries * User-friendly nomenclature listings include all the symbols used in each chapter so that chapter-specific symbols are readily available



Handbook of Computational Fluid Mechanics

Author : Roger Peyret

Publisher : Academic Press

Page : 479 pages

File Size : 47,19 MB

Release : 1996

Category : Computers

ISBN : 0125530102

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Book Description

This handbook covers computational fluid dynamics from fundamentals to applications. This text provides a well documented critical survey of numerical methods for fluid mechanics, and gives a state-of-the-art description of computational fluid mechanics, considering numerical analysis, computer technology, and visualization tools. The chapters in this book are invaluable tools for reaching a deeper understanding of the problems associated with the calculation of fluid motion in various situations: inviscid and viscous, incompressible and compressible, steady and unsteady, laminar and turbulent flows, as well as simple and complex geometries. Each chapter includes a related bibliography Covers fundamentals and applications Provides a deeper understanding of the problems associated with the calculation of fluid motion



Recent Advances in Numerical Methods for Hyperbolic PDE Systems

Author : María Luz Muñoz-Ruiz

Publisher : Springer Nature

Page : 269 pages

File Size : 10,69 MB

Release : 2021-05-25

Category : Mathematics

ISBN : 3030728501

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Book Description

The present volume contains selected papers issued from the sixth edition of the International Conference "Numerical methods for hyperbolic problems" that took place in 2019 in Málaga (Spain). NumHyp conferences, which began in 2009, focus on recent developments and new directions in the field of numerical methods for hyperbolic partial differential equations (PDEs) and their applications. The 11 chapters of the book cover several state-of-the-art numerical techniques and applications, including the design of numerical methods with good properties (well-balanced, asymptotic-preserving, high-order accurate, domain invariant preserving, uncertainty quantification, etc.), applications to models issued from different fields (Euler equations of gas dynamics, Navier-Stokes equations, multilayer shallow-water systems, ideal magnetohydrodynamics or fluid models to simulate multiphase flow, sediment transport, turbulent deflagrations, etc.), and the development of new nonlinear dispersive shallow-water models. The volume is addressed to PhD students and researchers in Applied Mathematics, Fluid Mechanics, or Engineering whose investigation focuses on or uses numerical methods for hyperbolic systems. It may also be a useful tool for practitioners who look for state-of-the-art methods for flow simulation.



Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws

Author : Philipp Öffner

Publisher : Springer Nature

Page : 486 pages

File Size : 33,94 MB

Release : 2023-09-17

Category : Mathematics

ISBN : 3658426209

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Book Description

The book focuses on stability and approximation results concerning recent numerical methods for the numerical solution of hyperbolic conservation laws. The work begins with a detailed and thorough introduction of hyperbolic conservation/balance laws and their numerical treatment. In the main part, recent results in such context are presented focusing on the investigation of approximation properties of discontinuous Galerkin and flux reconstruction methods, the construction of (entropy) stable numerical methods and the extension of existing (entropy) stability results for both semidiscrete and fully discrete schemes, and development of new high-order methods.



Handbook of Linear Partial Differential Equations for Engineers and Scientists

Author : Andrei D. Polyanin

Publisher : CRC Press

Page : 800 pages

File Size : 43,89 MB

Release : 2001-11-28

Category : Mathematics

ISBN : 1420035320

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Book Description

Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering. Parabolic, hyperbolic, and elliptic equations with



Numerical Approximation of Hyperbolic Systems of Conservation Laws

Author : Edwige Godlewski

Publisher : Springer Nature

Page : 846 pages

File Size : 20,57 MB

Release : 2021-08-28

Category : Mathematics

ISBN : 1071613448

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Book Description

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.