Download or read book Conjecture on Structure of Solutions of Riemann Problem for 2 D Gasdynamic System written by Tong Zhang and published by . This book was released on 1989 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conjecture on Structure of Solutions of Riemann Problem for 2 D Gasdynamic Systems written by T. Zhang and published by . This book was released on 1989 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Conjecture on structure of solutions of Riemann problem for 2 D gasdynamic systems written by Tong Zhang and published by . This book was released on 1989 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
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.
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.
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.
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."
Download or read book Construction of Solutions for Two Dimensional Riemann Problems Classic Reprint written by W. BRENT. LINDQUIST and published by Forgotten Books. This book was released on 2016-09-17 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Construction of Solutions for Two Dimensional Riemann Problems In 52, the two dimensional nonlinear waves are described for the class of problems f, fz. In 53 a method for explicitly constructing the 2-dimensional solutions in this class from the nonlinear waves is described. Complete solutions for 2-dimensional Riemann problems for representative forms of the function f are given. Solutions to the problem of water/oil bank interactions in two phase, incompressible, gravity free, flow in reservoirs can be obtained from the study of these 2-dimensional Riemann problems. The results for this physical problem are presented in 54. Conclusions and conjectures for the solutions to 2-dimensional Riemann problems for the casef having more than one inflection points orf1 at [2 are presented in 55. 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.
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:
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
Download or read book The Riemann Problem Complete Integrability and Arithmetic Applications written by David Chudnovsky and published by Springer. This book was released on 1982 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solution of a Riemann Problem for a 2 X 2 System of Conservation Laws Possessing No Classical Weak Solution written by Dennis James Korchinski and published by . This book was released on 2005 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyperbolic Problems Theory Numerics Applications written by Michael Fey and published by Springer Science & Business Media. This book was released on 1999-04-01 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Infotext]((Kurztext))These are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and contributors have been rigorously selected and present the state of the art in this field. The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics. ((Volltext))These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.
Download or read book Hyperbolic Problems Theory Numerics Applications written by Heinrich Freistühler and published by Birkhäuser. This book was released on 2013-12-01 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Eighth International Conference on Hyperbolic Problems - Theory, Nu merics, Applications, was held in Magdeburg, Germany, from February 27 to March 3, 2000. It was attended by over 220 participants from many European countries as well as Brazil, Canada, China, Georgia, India, Israel, Japan, Taiwan, und the USA. There were 12 plenary lectures, 22 further invited talks, and around 150 con tributed talks in parallel sessions as well as posters. The speakers in the parallel sessions were invited to provide a poster in order to enhance the dissemination of information. Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. Despite considerable progress, the mathematical theory is still strug gling with fundamental open problems concerning systems of such equations in multiple space dimensions. For various applications the development of accurate and efficient numerical schemes for computation is of fundamental importance. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended ther modynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability ofshock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite ele ment schemes, adaptive, multiresolution, and artificial dissipation methods.
Download or read book Front Tracking and Two Dimensional Riemann Problems written by Courant Mathematics and Computing Laboratory and published by . This book was released on 1984 with total page 0 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 the discontinuities, two-dimensional Riemann problems occur. In this paper we studied 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. (Author).
