Download or read book Higher Order Accuracy Finite Difference Algorithms for Quasi Linear Conservation Law Hyperbolic Systems written by S. Abarbanel and published by . This book was released on 1972 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: An explicit algorithm that yields finite difference equations that approximate the quasi-linear hyperbolic system to any desired accuracy, for an arbitrary number of space dimensions, is presented. Analytic stability proofs and criteria, in the case of one dimension for arbitrary order of accuracy, are given. Analytic stability proofs in the higher order dimensional cases, up to and including 3rd order accuracy with sufficient stability conditions, are shown. Numerical examples are compared with analytic solutions and demonstrate that the indicated accuracy was achieved. (Author).
Download or read book Mathematical Aspects of Numerical Solution of Hyperbolic Systems written by A.G. Kulikovskii and published by CRC Press. This book was released on 2000-12-21 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics (MHD), shallow water, and solid dynamics equations. This treatment provides-for the first time in book form-a collection of recipes for applying higher-order non-oscillatory shock-capturing schemes to MHD modelling of physical phenomena. The authors also address a number of original "nonclassical" problems, such as shock wave propagation in rods and composite materials, ionization fronts in plasma, and electromagnetic shock waves in magnets. They show that if a small-scale, higher-order mathematical model results in oscillations of the discontinuity structure, the variety of admissible discontinuities can exhibit disperse behavior, including some with additional boundary conditions that do not follow from the hyperbolic conservation laws. Nonclassical problems are accompanied by a multiple nonuniqueness of solutions. The authors formulate several selection rules, which in some cases easily allow a correct, physically realizable choice. This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. Its unique focus on applications, both traditional and new, makes Mathematical Aspects of Numerical Solution of Hyperbolic Systems particularly valuable not only to those interested the development of numerical methods, but to physicists and engineers who strive to solve increasingly complicated nonlinear equations.
Download or read book An N level Quasi geostrophic Model Suitable for Operational Use written by Samuel Y. K. Yee and published by . This book was released on 1974 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quasi-geostrophic model has been formulated using the potential vorticity as the only time dependent model variable. The model consists of a two-dimensional prognostic equation of the hyperbolic-type and a three-dimensional diagnostic equation of the elliptic-type. This formulation permits the model equations to be solved more efficiently and perhaps also more accurately than any other formulation that has been in operational use. Preliminary numerical tests using observed data, in connection with comparison case studies of the effect of discretization error and the influence of the lower boundary conditions, indicate that the model is realistic enough to warrant further tests for possible operational use.
Download or read book Systems of Quasilinear Equations and Their Applications to Gas Dynamics written by Boris Leonidovich Rozhdestvenski_ and published by American Mathematical Soc.. This book was released on 1983-12-31 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is essentially a new edition, revised and augmented by results of the last decade, of the work of the same title published in 1968 by ``Nauka.'' It is devoted to mathematical questions of gas dynamics. Topics covered include Foundations of the Theory of Systems of Quasilinear Equations of Hyperbolic Type in Two Independent Variables; Classical and Generalized Solutions of One-Dimensional Gas Dynamics; Difference Methods for Solving the Equations of Gas Dynamics; and Generalized Solutions of Systems of Quasilinear Equations of Hyperbolic Type.
Download or read book An Approach to the Development of Numerical Algorithms for First Order Linear Hyperbolic Systems in Multiple Space Dimensions The Constant Coefficient Case written by and published by . This book was released on 1995 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multidimensional Difference Schemes with Fourth Order Accuracy written by E. Turkel and published by . This book was released on 1975 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: An explicit finite difference algorithm for the solution of quasi-linear divergence free multidimensional hyperbolic systems. The method consists of four steps per time level. The resulting scheme is fourth order accurate in both space and time though the intermediate steps are only first order accurate. The family of schemes introduced is dissipative and hence suitable for both smooth flows and flows containing shocks. This method is compared, in several numerical examples, with both second order schemes and others that are fourth order in space but second order in time. (Author).
Download or read book Mathematics of Computation written by and published by . This book was released on 1973 with total page 1084 pages. Available in PDF, EPUB and Kindle. Book excerpt: Original articles on all aspects of numerical mathematics, book reviews, mathematical tables, and technical notes. Covers advances in numerical analysis, application of computer methods, high speed calculating, and other aids to computation.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1973 with total page 1102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book SIAM Journal on Applied Mathematics written by Society for Industrial and Applied Mathematics and published by . This book was released on 1966 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains research articles on mathematical methods and their applications in the physical, engineering, biological, and medical sciences.
Download or read book Proceedings of the International Symposium on Modern Developments in Fluid Dynamics written by Josef Rom and published by . This book was released on 1977 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Volume Methods for Hyperbolic Problems written by Randall J. LeVeque and published by Cambridge University Press. This book was released on 2002-08-26 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book STAR written by and published by . This book was released on 1973 with total page 890 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Accurate Finite Difference Algorithms written by and published by . This book was released on 1996 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book High order finite difference approximations for hyperbolic problems written by Hannes Frenander and published by Linköping University Electronic Press. This book was released on 2017-01-24 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we use finite difference operators with the Summation-By-Partsproperty (SBP) and a weak boundary treatment, known as SimultaneousApproximation Terms (SAT), to construct high-order accurate numerical schemes.The SBP property and the SAT’s makes the schemes provably stable. The numerical procedure is general, and can be applied to most problems, but we focus on hyperbolic problems such as the shallow water, Euler and wave equations. For a well-posed problem and a stable numerical scheme, data must be available at the boundaries of the domain. However, there are many scenarios where additional information is available inside the computational domain. In termsof well-posedness and stability, the additional information is redundant, but it can still be used to improve the performance of the numerical scheme. As a first contribution, we introduce a procedure for implementing additional data using SAT’s; we call the procedure the Multiple Penalty Technique (MPT). A stable and accurate scheme augmented with the MPT remains stable and accurate. Moreover, the MPT introduces free parameters that can be used to increase the accuracy, construct absorbing boundary layers, increase the rate of convergence and control the error growth in time. To model infinite physical domains, one need transparent artificial boundary conditions, often referred to as Non-Reflecting Boundary Conditions (NRBC). In general, constructing and implementing such boundary conditions is a difficult task that often requires various approximations of the frequency and range of incident angles of the incoming waves. In the second contribution of this thesis,we show how to construct NRBC’s by using SBP operators in time. In the final contribution of this thesis, we investigate long time error bounds for the wave equation on second order form. Upper bounds for the spatial and temporal derivatives of the error can be obtained, but not for the actual error. The theoretical results indicate that the error grows linearly in time. However, the numerical experiments show that the error is in fact bounded, and consequently that the derived error bounds are probably suboptimal.
Download or read book Advanced Numerical Approximation of Nonlinear Hyperbolic Equations written by B. Cockburn and published by Springer. This book was released on 2006-11-14 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.
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.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1804 pages. Available in PDF, EPUB and Kindle. Book excerpt:
