Numerical Methods For Eulerian And Lagrangian Conservation Laws
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| Author | : Bruno Després |
| Publisher | : Birkhäuser |
| Total Pages | : 361 |
| Release | : 2017-07-09 |
| Genre | : Mathematics |
| ISBN | : 3319503553 |
This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.
| Author | : F. Angrand |
| Publisher | : SIAM |
| Total Pages | : 524 |
| Release | : 1985-01-01 |
| Genre | : Science |
| ISBN | : 9780898712001 |
| Author | : Giacomo Albi |
| Publisher | : Springer Nature |
| Total Pages | : 241 |
| Release | : 2023-06-02 |
| Genre | : Mathematics |
| ISBN | : 3031298756 |
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.
| Author | : Remi Abgrall |
| Publisher | : Elsevier |
| Total Pages | : 668 |
| Release | : 2016-11-17 |
| Genre | : Mathematics |
| ISBN | : 0444637958 |
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
| Author | : Erwin Stein |
| Publisher | : |
| Total Pages | : 870 |
| Release | : 2004 |
| Genre | : Dynamics |
| ISBN | : |
The Encyclopedia of Computational Mechanics provides a comprehensive collection of knowledge about the theory and practice of computational mechanics.
| Author | : Edwige Godlewski |
| Publisher | : Springer Nature |
| Total Pages | : 846 |
| Release | : 2021-08-28 |
| Genre | : Mathematics |
| ISBN | : 1071613448 |
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.
| Author | : Dale R. Durran |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 527 |
| Release | : 2010-09-14 |
| Genre | : Mathematics |
| ISBN | : 1441964126 |
This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean
| Author | : Andrew J. Majda |
| Publisher | : Cambridge University Press |
| Total Pages | : 562 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9780521639484 |
This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprise a modern applied mathematics graduate course on the weak solution theory for incompressible flow.
| Author | : Philippe G. LeFloch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1010 |
| Release | : 2002-07-01 |
| Genre | : Mathematics |
| ISBN | : 9783764366872 |
This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.
| Author | : Taras Gerya |
| Publisher | : Cambridge University Press |
| Total Pages | : 359 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0521887542 |
This user-friendly reference for students and researchers presents the basic mathematical theory, before introducing modelling of key geodynamic processes.
