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Numerical Solution Of The Riemann Problem For Two Dimensional Gas Dynamics
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Book Synopsis The Two-Dimensional Riemann Problem in Gas Dynamics by : Jiequan Li
Download or read book The Two-Dimensional Riemann Problem in Gas Dynamics written by Jiequan Li and published by Routledge. This book was released on 2022-02-13 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in 1860, great progress has been achieved in the one-dimensional case. However, the two-dimensional case is substantially different. Although research interest in it has lasted more than a century, it has yielded almost no analytical demonstration. It remains a great challenge for mathematicians. This volume presents work on the two-dimensional Riemann problem carried out over the last 20 years by a Chinese group. The authors explore four models: scalar conservation laws, compressible Euler equations, zero-pressure gas dynamics, and pressure-gradient equations. They use the method of generalized characteristic analysis plus numerical experiments to demonstrate the elementary field interaction patterns of shocks, rarefaction waves, and slip lines. They also discover a most interesting feature for zero-pressure gas dynamics: a new kind of elementary wave appearing in the interaction of slip lines-a weighted Dirac delta shock of the density function. The Two-Dimensional Riemann Problem in Gas Dynamics establishes the rigorous mathematical theory of delta-shocks and Mach reflection-like patterns for zero-pressure gas dynamics, clarifies the boundaries of interaction of elementary waves, demonstrates the interesting spatial interaction of slip lines, and proposes a series of open problems. With applications ranging from engineering to astrophysics, and as the first book to examine the two-dimensional Riemann problem, this volume will prove fascinating to mathematicians and hold great interest for physicists and engineers.
Book Synopsis Numerical Solution of the Riemann Problem for Two-dimensional Gas Dynamics by : Carsten Werner Schulz-Rinne
Download or read book Numerical Solution of the Riemann Problem for Two-dimensional Gas Dynamics written by Carsten Werner Schulz-Rinne and published by . This book was released on 1992 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Front Tracking and Two Dimensional Riemann Problems (Classic Reprint) by : James Glimm
Download or read book Front Tracking and Two Dimensional Riemann Problems (Classic Reprint) written by James Glimm and published by Forgotten Books. This book was released on 2016-11-13 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Front Tracking and Two Dimensional Riemann Problems A substantial improvement in resolution has been achieved for the computation of jump discontinuities in gas dynamics using the method of front tracking. The essential feature of this method is that a lower dimensional grid is fitted to and follows the discontinuous waves. At the intersection points of these discontinuities, two-dimensional Riemann problems occur. In this paper we study such two-dimensional Riemann problems from both numerical and theoretical points of view. Specifically included is a numerical solution for the Mach reflection, a general classification scheme for two-dimensional elementary waves, and a discussion of problems and conjectures in this area. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Book Synopsis The Two-Dimensional Riemann Problem in Gas Dynamics by : Jiequan Li
Download or read book The Two-Dimensional Riemann Problem in Gas Dynamics written by Jiequan Li and published by Taylor & Francis. This book was released on 2022-02-13 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in 1860, great progress has been achieved in the one-dimensional case. However, the two-dimensional case is substantially different. Although research interest in it has lasted more than a century, it has yielded almost no analytical demonstration. It remains a great challenge for mathematicians. This volume presents work on the two-dimensional Riemann problem carried out over the last 20 years by a Chinese group. The authors explore four models: scalar conservation laws, compressible Euler equations, zero-pressure gas dynamics, and pressure-gradient equations. They use the method of generalized characteristic analysis plus numerical experiments to demonstrate the elementary field interaction patterns of shocks, rarefaction waves, and slip lines. They also discover a most interesting feature for zero-pressure gas dynamics: a new kind of elementary wave appearing in the interaction of slip lines-a weighted Dirac delta shock of the density function. The Two-Dimensional Riemann Problem in Gas Dynamics establishes the rigorous mathematical theory of delta-shocks and Mach reflection-like patterns for zero-pressure gas dynamics, clarifies the boundaries of interaction of elementary waves, demonstrates the interesting spatial interaction of slip lines, and proposes a series of open problems. With applications ranging from engineering to astrophysics, and as the first book to examine the two-dimensional Riemann problem, this volume will prove fascinating to mathematicians and hold great interest for physicists and engineers.
Book Synopsis Methods for the Localization of Singularities in Numerical Solutions of Gas Dynamics Problems by : E.V. Vorozhtsov
Download or read book Methods for the Localization of Singularities in Numerical Solutions of Gas Dynamics Problems written by E.V. Vorozhtsov and published by Springer. This book was released on 1990-01-11 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a result of the numerical simulation of multidimensional gas dynamics problems on a computer, the output information is obtained in the form of immense arrays of numerical data. In this connection, there arises the problem of extracting the actually needed information from these arrays; in other words, it is necessary to solve the problem of information compression. In particular, the numerical solution of gas dynamics problems often aims at the information on the solution singularities-the shock waves, contact interfaces, slip lines, etc. Our book is devoted to the development and investigation of accuracy of the algorithms for the localization of such singularities. In addi tion, the questions of development of the algorithms for the classification of singularities into several types (on the basis of shock-capturing numerical solutions of two-dimensional gas dynamics problems) are considered for the first time in the monographic literature. For this purpose, some ideas and methods of the modern theory of digital-image processing and of the pattern recognition theory are used. The information obtained at the output of the systems of the singularities classification presented in this book is rich in content, because it contains both physical and geometrical characteristics of recognized objects. Therefore, such "intellectual" systems of information ex traction may be used in the expert systems of automated design of aero dynamic bodies which meet some optimality requirements. This is, in our opinion, very attractive from the point of view of applications.
Book Synopsis Front Tracking and Two Dimensional Riemann Problems by : James Glimm
Download or read book Front Tracking and Two Dimensional Riemann Problems written by James Glimm and published by . This book was released on 1984 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Riemann Solvers and Numerical Methods for Fluid Dynamics by : Eleuterio F. Toro
Download or read book Riemann Solvers and Numerical Methods for Fluid Dynamics written by Eleuterio F. Toro and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Systems of Conservation Laws by : Yuxi Zheng
Download or read book Systems of Conservation Laws written by Yuxi Zheng and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work should serve as an introductory text for graduate students and researchers working in the important area of partial differential equations with a focus on problems involving conservation laws. The only requisite for the reader is a knowledge of the elementary theory of partial differential equations. Key features of this work include: * broad range of topics, from the classical treatment to recent results, dealing with solutions to 2D compressible Euler equations * good review of basic concepts (1-D Riemann problems) * concrete solutions presented, with many examples, over 100 illustrations, open problems, and numerical schemes * numerous exercises, comprehensive bibliography and index * appeal to a wide audience of applied mathematicians, graduate students, physicists, and engineers Written in a clear, accessible style, the book emphasizes more recent results that will prepare readers to meet modern challenges in the subject, that is, to carry out theoretical, numerical, and asymptotical analysis.
Book Synopsis The Riemann Problem for the Transportation Equations in Gas Dynamics by : Wancheng Sheng
Download or read book The Riemann Problem for the Transportation Equations in Gas Dynamics written by Wancheng Sheng and published by American Mathematical Soc.. This book was released on 1999 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which has been merely discussed so far. The generalized Rankine-Hugoniot and entropy conditions for Dirac delta waves are clarified with viscous vanishing method. All of the existence, uniqueness and stability for viscous perturbations are proved analytically
Book Synopsis Front Tracking and Two Dimensional Riemann Problems by :
Download or read book Front Tracking and Two Dimensional Riemann Problems written by and published by . This book was released on 1984 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A substantial improvement in resolution has been achieved for the computation of jump discontinuities in gas dynamics using the method of front tracking. The essential feature of this method is that a lower dimensional grid is fitted to and follows the discontinuous waves. At the intersection points of these discontinuities, two-dimensional Riemann problems occur. In this paper we study such two-dimensional Riemann problems from both numerical and theoretical points of view. Specifically included is a numerical solution for the Mach reflection, a general classification scheme for two-dimensional elementary waves, and a discussion of problems and conjectures in this area.
Book Synopsis Riemann Problems and Jupyter Solutions by : David I. Ketcheson
Download or read book Riemann Problems and Jupyter Solutions written by David I. Ketcheson and published by SIAM. This book was released on 2020-06-26 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses an important class of mathematical problems (the Riemann problem) for first-order hyperbolic partial differential equations (PDEs), which arise when modeling wave propagation in applications such as fluid dynamics, traffic flow, acoustics, and elasticity. The solution of the Riemann problem captures essential information about these models and is the key ingredient in modern numerical methods for their solution. This book covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem. The emphasis is on the general ideas, but each chapter delves into a particular application. Riemann Problems and Jupyter Solutions is available in electronic form as a collection of Jupyter notebooks that contain executable computer code and interactive figures and animations, allowing readers to grasp how the concepts presented are affected by important parameters and to experiment by varying those parameters themselves. The only interactive book focused entirely on the Riemann problem, it develops each concept in the context of a specific physical application, helping readers apply physical intuition in learning mathematical concepts. Graduate students and researchers working in the analysis and/or numerical solution of hyperbolic PDEs will find this book of interest. This includes mathematicians, as well as scientists and engineers, working on wave propagation problems. Educators interested in developing instructional materials using Jupyter notebooks will also find this book useful. The book is appropriate for courses in Numerical Methods for Hyperbolic PDEs and Analysis of Hyperbolic PDEs, and it can be a great supplement for courses in computational fluid dynamics, acoustics, and gas dynamics.
Book Synopsis The Riemann Problem for Two-dimensional Gas Dynamics and New Limiters for High-order Schemes by : Carsten Werner Schulz-Rinne
Download or read book The Riemann Problem for Two-dimensional Gas Dynamics and New Limiters for High-order Schemes written by Carsten Werner Schulz-Rinne and published by . This book was released on 1993 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The P1-RKDG Method for Two-dimensional Euler Equations of Gas Dynamics by : Bernardo Cockburn
Download or read book The P1-RKDG Method for Two-dimensional Euler Equations of Gas Dynamics written by Bernardo Cockburn and published by . This book was released on 1991 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Conservation Laws by : LEVEQUE
Download or read book Numerical Methods for Conservation Laws written by LEVEQUE and published by Birkhäuser. This book was released on 2013-11-11 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.
Book Synopsis Generalized Riemann Problems in Computational Fluid Dynamics by : Matania Ben-Artzi
Download or read book Generalized Riemann Problems in Computational Fluid Dynamics written by Matania Ben-Artzi and published by Cambridge University Press. This book was released on 2003-04-10 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation of compressible, inviscid time-dependent flow is a major branch of computational fluid dynamics. Its primary goal is to obtain accurate representation of the time evolution of complex flow patterns, involving interactions of shocks, interfaces, and rarefaction waves. The Generalized Riemann Problem (GRP) algorithm, developed by the authors for this purpose, provides a unifying 'shell' which comprises some of the most commonly used numerical schemes of this process. This monograph gives a systematic presentation of the GRP methodology, starting from the underlying mathematical principles, through basic scheme analysis and scheme extensions (such as reacting flow or two-dimensional flows involving moving or stationary boundaries). An array of instructive examples illustrates the range of applications, extending from (simple) scalar equations to computational fluid dynamics. Background material from mathematical analysis and fluid dynamics is provided, making the book accessible to both researchers and graduate students of applied mathematics, science and engineering.
Book Synopsis Riemann Problem for the Transportation Equations in Gas Dynamics by : Wancheng Sheng
Download or read book Riemann Problem for the Transportation Equations in Gas Dynamics written by Wancheng Sheng and published by Oxford University Press, USA. This book was released on 2014-09-11 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which has been merely discussed so far. The generalized Rankine-Hugoniot and entropy conditions for Dirac delta waves are clarified with viscous vanishing method. All of the existence, uniqueness and stability for viscous perturbations are proved analytically
Book Synopsis Numerical Riemann solutions in multi-pieces for 2 D gas dynamics systems I by : Shuli Yang
Download or read book Numerical Riemann solutions in multi-pieces for 2 D gas dynamics systems I written by Shuli Yang and published by . This book was released on 1992 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "The numerical solutions of Riemann problems in three, four, five and six pieces, which only contain contact discontinuities, are presented by using Taylor FVM MmB schemes on regular triangular meshes for 2-D gas dynamics systems. The 2-D Riemann initial data are as defined in [1], under the assumption that each jump in initial data outside of the origin projects exactly one planar wave of shocks, centered rarefaction waves, or contact discontinuities. The main ends of the paper are that spirals will be shown for some configurations and the relations of the solutions between different distibutions [sic] of Riemann initial data are explained by the numerical solutions of modified Riemann problems."
