Computing Qualitatively Correct Approximations Of Balance Laws

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Computing Qualitatively Correct Approximations of Balance Laws

Author : Laurent Gosse
Publisher : Springer Science & Business Media
ISBN 13 : 8847028922
Total Pages : 346 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Computing Qualitatively Correct Approximations of Balance Laws by : Laurent Gosse

Download or read book Computing Qualitatively Correct Approximations of Balance Laws written by Laurent Gosse and published by Springer Science & Business Media. This book was released on 2013-03-30 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Substantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or space-dependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot curves being deformed by local averaging steps in Godunov-type schemes, low-order errors propagating along expanding characteristics after having hit a discontinuity, exponential amplification of truncation errors in the presence of accretive source terms... This book aims at presenting rigorous derivations of different, sometimes called well-balanced, numerical schemes which succeed in reconciling high accuracy with a stronger robustness even in the aforementioned accretive contexts. It is divided into two parts: one dealing with hyperbolic systems of balance laws, such as arising from quasi-one dimensional nozzle flow computations, multiphase WKB approximation of linear Schrödinger equations, or gravitational Navier-Stokes systems. Stability results for viscosity solutions of onedimensional balance laws are sketched. The other being entirely devoted to the treatment of weakly nonlinear kinetic equations in the discrete ordinate approximation, such as the ones of radiative transfer, chemotaxis dynamics, semiconductor conduction, spray dynamics or linearized Boltzmann models. “Caseology” is one of the main techniques used in these derivations. Lagrangian techniques for filtration equations are evoked too. Two-dimensional methods are studied in the context of non-degenerate semiconductor models.

Error Estimates for Well-Balanced Schemes on Simple Balance Laws

Author : Debora Amadori
Publisher : Springer
ISBN 13 : 3319247859
Total Pages : 119 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Error Estimates for Well-Balanced Schemes on Simple Balance Laws by : Debora Amadori

Download or read book Error Estimates for Well-Balanced Schemes on Simple Balance Laws written by Debora Amadori and published by Springer. This book was released on 2015-10-23 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.

Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy

Author : Gennadii V. Demidenko
Publisher : Springer Nature
ISBN 13 : 3030388700
Total Pages : 378 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy by : Gennadii V. Demidenko

Download or read book Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy written by Gennadii V. Demidenko and published by Springer Nature. This book was released on 2020-04-03 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a liber amicorum to Professor Sergei Konstantinovich Godunov and gathers contributions by renowned scientists in honor of his 90th birthday. The contributions address those fields that Professor Godunov is most famous for: differential and difference equations, partial differential equations, equations of mathematical physics, mathematical modeling, difference schemes, advanced computational methods for hyperbolic equations, computational methods for linear algebra, and mathematical problems in continuum mechanics.

Innovative Algorithms and Analysis

Author : Laurent Gosse
Publisher : Springer
ISBN 13 : 3319492624
Total Pages : 362 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Innovative Algorithms and Analysis by : Laurent Gosse

Download or read book Innovative Algorithms and Analysis written by Laurent Gosse and published by Springer. This book was released on 2016-05-26 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers contributions reflecting topics presented during an INDAM workshop held in Rome in May 2016. The event brought together many prominent researchers in both Mathematical Analysis and Numerical Computing, the goal being to promote interdisciplinary collaborations. Accordingly, the following thematic areas were developed: 1. Lagrangian discretizations and wavefront tracking for synchronization models; 2. Astrophysics computations and post-Newtonian approximations; 3. Hyperbolic balance laws and corrugated isometric embeddings; 4. “Caseology” techniques for kinetic equations; 5. Tentative computations of compressible non-standard solutions; 6. Entropy dissipation, convergence rates and inverse design issues. Most of the articles are presented in a self-contained manner; some highlight new achievements, while others offer snapshots of the “state of the art” in certain fields. The book offers a unique resource, both for young researchers looking to quickly enter a given area of application, and for more experienced ones seeking comprehensive overviews and extensive bibliographic references.

Theory, Numerics and Applications of Hyperbolic Problems I

Author : Christian Klingenberg
Publisher : Springer
ISBN 13 : 3319915452
Total Pages : 685 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Theory, Numerics and Applications of Hyperbolic Problems I by : Christian Klingenberg

Download or read book Theory, Numerics and Applications of Hyperbolic Problems I written by Christian Klingenberg and published by Springer. This book was released on 2018-06-23 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.

Numerical Methods for Eulerian and Lagrangian Conservation Laws

Author : Bruno Després
Publisher : Birkhäuser
ISBN 13 : 3319503553
Total Pages : 361 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Numerical Methods for Eulerian and Lagrangian Conservation Laws by : Bruno Després

Download or read book Numerical Methods for Eulerian and Lagrangian Conservation Laws written by Bruno Després and published by Birkhäuser. This book was released on 2017-07-09 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Uncertainty Quantification for Hyperbolic and Kinetic Equations

Author : Shi Jin
Publisher : Springer
ISBN 13 : 3319671103
Total Pages : 282 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Uncertainty Quantification for Hyperbolic and Kinetic Equations by : Shi Jin

Download or read book Uncertainty Quantification for Hyperbolic and Kinetic Equations written by Shi Jin and published by Springer. This book was released on 2018-03-20 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

The Application of Mathematics to Physics and Nonlinear Science

Author : Andrei Ludu
Publisher : MDPI
ISBN 13 : 3039287265
Total Pages : 122 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis The Application of Mathematics to Physics and Nonlinear Science by : Andrei Ludu

Download or read book The Application of Mathematics to Physics and Nonlinear Science written by Andrei Ludu and published by MDPI. This book was released on 2020-04-16 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear science is the science of, among other exotic phenomena, unexpected and unpredictable behavior, catastrophes, complex interactions, and significant perturbations. Ocean and atmosphere dynamics, weather, many bodies in interaction, ultra-high intensity excitations, life, formation of natural patterns, and coupled interactions between components or different scales are only a few examples of systems where nonlinear science is necessary. All outstanding, self-sustained, and stable structures in space and time exist and protrude out of a regular linear background of states mainly because they identify themselves from the rest by being highly localized in range, time, configuration, states, and phase spaces. Guessing how high up you drive toward the top of the mountain by compiling your speed, road slope, and trip duration is a linear model, but predicting the occurrence around a turn of a boulder fallen on the road is a nonlinear phenomenon. In an effort to grasp and understand nonlinear phenomena, scientists have developed several mathematical approaches including inverse scattering theory, Backlund and groups of transformations, bilinear method, and several other detailed technical procedures. In this Special Issue, we introduce a few very recent approaches together with their physical meaning and applications. We present here five important papers on waves, unsteady flows, phases separation, ocean dynamics, nonlinear optic, viral dynamics, and the self-appearance of patterns for spatially extended systems, which are problems that have aroused scientists’ interest for decades, yet still cannot be predicted and have their generating mechanism and stability open to debate. The aim of this Special Issue was to present these most debated and interesting topics from nonlinear science for which, despite the existence of highly developed mathematical tools of investigation, there are still fundamental open questions.

Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Author : Robert Klöfkorn
Publisher : Springer Nature
ISBN 13 : 3030436519
Total Pages : 727 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples by : Robert Klöfkorn

Download or read book Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples written by Robert Klöfkorn and published by Springer Nature. This book was released on 2020-06-09 with total page 727 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dispersive Shallow Water Waves

Author : Gayaz Khakimzyanov
Publisher : Springer Nature
ISBN 13 : 3030462676
Total Pages : 296 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Dispersive Shallow Water Waves by : Gayaz Khakimzyanov

Download or read book Dispersive Shallow Water Waves written by Gayaz Khakimzyanov and published by Springer Nature. This book was released on 2020-09-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves. Including both an overview of existing dispersive models, as well as recent breakthroughs, the authors maintain an ideal balance between theory and applications. From modelling tsunami waves to smaller scale coastal processes, this book will be an indispensable resource for those looking to be brought up-to-date in this active area of scientific research. Beginning with an introduction to various dispersive long wave models on the flat space, the authors establish a foundation on which readers can confidently approach more advanced mathematical models and numerical techniques. The first two chapters of the book cover modelling and numerical simulation over globally flat spaces, including adaptive moving grid methods along with the operator splitting approach, which was historically proposed at the Institute of Computational Technologies at Novosibirsk. Later chapters build on this to explore high-end mathematical modelling of the fluid flow over deformed and rotating spheres using the operator splitting approach. The appendices that follow further elaborate by providing valuable insight into long wave models based on the potential flow assumption, and modified intermediate weakly nonlinear weakly dispersive equations. Dispersive Shallow Water Waves will be a valuable resource for researchers studying theoretical or applied oceanography, nonlinear waves as well as those more broadly interested in free surface flow dynamics.

Convection-Diffusion Problems

Author : Martin Stynes
Publisher : American Mathematical Soc.
ISBN 13 : 1470448688
Total Pages : 168 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Convection-Diffusion Problems by : Martin Stynes

Download or read book Convection-Diffusion Problems written by Martin Stynes and published by American Mathematical Soc.. This book was released on 2018-11-21 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical problems involve diffusive and convective (transport) processes. When diffusion dominates convection, standard numerical methods work satisfactorily. But when convection dominates diffusion, the standard methods become unstable, and special techniques are needed to compute accurate numerical approximations of the unknown solution. This convection-dominated regime is the focus of the book. After discussing at length the nature of solutions to convection-dominated convection-diffusion problems, the authors motivate and design numerical methods that are particularly suited to this class of problems. At first they examine finite-difference methods for two-point boundary value problems, as their analysis requires little theoretical background. Upwinding, artificial diffusion, uniformly convergent methods, and Shishkin meshes are some of the topics presented. Throughout, the authors are concerned with the accuracy of solutions when the diffusion coefficient is close to zero. Later in the book they concentrate on finite element methods for problems posed in one and two dimensions. This lucid yet thorough account of convection-dominated convection-diffusion problems and how to solve them numerically is meant for beginning graduate students, and it includes a large number of exercises. An up-to-date bibliography provides the reader with further reading.

Theory, Numerics and Applications of Hyperbolic Problems II

Author : Christian Klingenberg
Publisher : Springer
ISBN 13 : 3319915487
Total Pages : 698 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Theory, Numerics and Applications of Hyperbolic Problems II by : Christian Klingenberg

Download or read book Theory, Numerics and Applications of Hyperbolic Problems II written by Christian Klingenberg and published by Springer. This book was released on 2018-06-27 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.

Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems

Author : Jürgen Fuhrmann
Publisher : Springer
ISBN 13 : 3319055917
Total Pages : 499 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems by : Jürgen Fuhrmann

Download or read book Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems written by Jürgen Fuhrmann and published by Springer. This book was released on 2014-05-16 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics. 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. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of 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. Researchers, PhD and masters level students in numerical analysis, scientific computing and related fields such as partial differential equations will find this volume useful, as will engineers working in numerical modeling and simulations.

Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects

Author : Clément Cancès
Publisher : Springer
ISBN 13 : 3319573977
Total Pages : 457 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects by : Clément Cancès

Download or read book Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects written by Clément Cancès and published by Springer. This book was released on 2017-05-23 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier–Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. 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, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asy mptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of 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.

New Frontiers in Computational Intelligence and Its Applications

Author : Masoud Mohammadian
Publisher : IOS Press
ISBN 13 : 9789051994766
Total Pages : 396 pages
Book Rating : 4.9/5 (947 download)

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Book Synopsis New Frontiers in Computational Intelligence and Its Applications by : Masoud Mohammadian

Download or read book New Frontiers in Computational Intelligence and Its Applications written by Masoud Mohammadian and published by IOS Press. This book was released on 2000 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Intelligence is a broad and active research area that is growing rapidly due to the many successful applications of these new techniques in very diverse problems. Many industries have benefited from adopting this technology. The increased number of patents and diverse range of products developed using computational intelligence methods is evidence of this fact. The goal of this book is to provide highlights of the current research in computational intelligence area. The book consists of research papers in the fields of neural networks, fuzzy logic, evolutionary computing, hybrid evolutionary computing-fuzzy logic systems, hybrid neural networks-evolutionary computing and fuzzy logic systems, image processing and vision, advances in robotics, control and manufacturing, and rough sets.

Fuzzy Systems and Soft Computing in Nuclear Engineering

Author : Da Ruan
Publisher : Springer Science & Business Media
ISBN 13 : 9783790812510
Total Pages : 506 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Fuzzy Systems and Soft Computing in Nuclear Engineering by : Da Ruan

Download or read book Fuzzy Systems and Soft Computing in Nuclear Engineering written by Da Ruan and published by Springer Science & Business Media. This book was released on 2000-01-14 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an organized edited collection of twenty-one contributed chapters covering nuclear engineering applications of fuzzy systems, neural networks, genetic algorithms and other soft computing techniques. All chapters are either updated review or original contributions by leading researchers written exclusively for this volume. The volume highlights the advantages of applying fuzzy systems and soft computing in nuclear engineering, which can be viewed as complementary to traditional methods. As a result, fuzzy sets and soft computing provide a powerful tool for solving intricate problems pertaining in nuclear engineering. Each chapter of the book is self-contained and also indicates the future research direction on this topic of applications of fuzzy systems and soft computing in nuclear engineering.

Computational Intelligence for Modelling, Control & Automation

Author : Masoud Mohammadian
Publisher : IOS Press
ISBN 13 : 9789051994742
Total Pages : 550 pages
Book Rating : 4.9/5 (947 download)

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Book Synopsis Computational Intelligence for Modelling, Control & Automation by : Masoud Mohammadian

Download or read book Computational Intelligence for Modelling, Control & Automation written by Masoud Mohammadian and published by IOS Press. This book was released on 1999 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited Book is dedicated to the theory and applications of Evolutionary Computation and Fuzzy Logic for Intelligent Control, Knowledge Acquisition and Information Retrieval. The book consists of 86 selected research papers from the 1999 International Conference on Computational Intelligence for Modelling, Control and Automation - CIMCA'99 The research papers presented in this book cover new techniques and applications in the following research areas: Evolutionary Computation, Fuzzy Logic and Expert Systems with their applications for Optimisation, Learning, Control, Scheduling and Multi-Criteria Analysis as well as Reliability Assessment, Information Retrieval and Knowledge Acquisition.