Finite Volume Methods for Hyperbolic Problems PDF Download
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Author: Randall J. LeVeque
Publisher: Cambridge University Press
ISBN: 1139434187
Category : Mathematics
Languages : en
Pages : 582
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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.
Author: Randall J. LeVeque
Publisher: Cambridge University Press
ISBN: 1139434187
Category : Mathematics
Languages : en
Pages : 582
Get Book Here
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.
Author: Alain Dervieux
Publisher: Springer Science & Business Media
ISBN: 3322878759
Category : Technology & Engineering
Languages : en
Pages : 369
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Book Description
The numerical simulation of the Euler equations of Fluid Dynamics has been these past few years a challenging problem both for research scientists and aerospace engineers. The increasing interest of more realistic models such as the Euler equations originates in Aerodynamics and also Aerothermics where aerospace applications such as military aircrafts and also space vehicles require accurate and efficient Euler solvers (which can be extended to more complicated modelisations including non-equilibrium chemistry) for su personic and hypersonic flows at high angles of attack and Mach number regimes involving strong shocks and vorticity. This book contains the proceedings of the GAMM Workshop on the Numerical Simu lation of Compressible Euler Flows. that W:LS held at INRIA, Rocquencourt (France), on June 10-13, 1986. The purpose of this event was to compare in terms of accuracy and efficiency several codes for solving compressible inviscid, mainly steady, Euler flows. This workshop was a sequel of the GAMM workshop held in 1979 in Stockholm; this time, though, because of the present strong activity in numerical methods for the Euler equat.ions, the full-potential approach was not included. Since 1979, other Eulpr workshops have been organised, sev eral of them focussed on airfoil calculations; however, many recently derived methods were not presented at these workshops, because, among other reasons, the methods were not far enough developed, or had not been applied to flow problems of sufficient complexity. In fact, the 1986 GAMM workshop scored very high as regards to the novelty of methods.
Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Author: Antony Jameson
Publisher: Cambridge University Press
ISBN: 1108837883
Category : Science
Languages : en
Pages : 627
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Book Description
Learn the design and analysis of numerical algorithms for aerodynamics. Ideal for graduates, researchers, and professionals in the field.
Author: Bernardo Cockburn
Publisher: Springer Science & Business Media
ISBN: 3642597211
Category : Mathematics
Languages : en
Pages : 468
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Book Description
A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Author: H. Lomax
Publisher: Springer Science & Business Media
ISBN: 3662046547
Category : Science
Languages : en
Pages : 256
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Book Description
The chosen semi-discrete approach of a reduction procedure of partial differential equations to ordinary differential equations and finally to difference equations gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.
Author: F. Angrand
Publisher: SIAM
ISBN: 9780898712001
Category : Science
Languages : en
Pages : 524
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Book Description
Author: Eleuterio F. Toro
Publisher: Springer Science & Business Media
ISBN: 366203915X
Category : Technology & Engineering
Languages : en
Pages : 635
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Book Description
High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows.
Author: Robert Klöfkorn
Publisher: Springer Nature
ISBN: 3030436519
Category : Computers
Languages : en
Pages : 727
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Book Description
The proceedings of the 9th conference on "Finite Volumes for Complex Applications" (Bergen, June 2020) are structured in two volumes. The first volume collects the focused invited papers, as well as the reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods. Topics covered include convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. Altogether, a rather comprehensive overview is given on the state of the art in the field. The properties of the methods considered in the conference give them distinguished advantages for a number of applications. These include fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory, carbon capture utilization and storage, geothermal energy and further topics. The second volume covers reviewed contributions reporting successful applications of finite volume and related methods in these fields. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability, making the finite volume methods compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is a valuable resource for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.
Author: Jean Donea
Publisher: John Wiley & Sons
ISBN: 9780471496663
Category : Science
Languages : en
Pages : 366
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Book Description
Die Finite-Elemente-Methode, eines der wichtigsten in der Technik verwendeten numerischen Näherungsverfahren, wird hier gründlich und gut verständlich, aber ohne ein Zuviel an mathematischem Formalismus abgehandelt. Insbesondere geht es um die Anwendung der Methode auf Strömungsprobleme. Alle wesentlichen aktuellen Forschungsergebnisse wurden in den Band aufgenommen; viele davon sind bisher nur verstreut in der Originalliteratur zu finden.
