Download or read book An Adaptive Finite Difference Method for Hyperbolic Systems on One Space Dimension Revision written by John H. Bolstad and published by . This book was released on 1982 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we develop and partially analyze an adaptive finite difference mesh refinement algorithm for the initial boundary value problem for hyperbolic systems in one space dimension. The method uses clusters uniform grids which can move along with pulses or steep gradients appearing in the calculation, and which are superimposed over a uniform coarse grid. Such refinements are created, destroyed, merged, separated, recursively nested or moved based on estimates of the local truncation error. We use a four-way linked tree and sequentially allocated deques (double-ended queues) to perform these operations efficiently. The local truncation error is estimated using a three-step Richardson extrapolation procedure in the interior of the region, and differences at the boundaries. Our algorithm was implemented using a portable, extensible Fortran preprocessor, to which we added records and pointers. The method is applied to two model problems: the second order wave equation with counterstreaming Gaussian pulses, and the Riemann shock-tube problem. For both problems our algorithm is shown to be three to five times more efficient (in computing time) than the use of a uniform coarse mesh, for the same accuracy.

Download or read book An Adaptive Finite Difference Method for Hyperbolic Systems in One Space Dimension written by J. H. Bolstad and published by . This book was released on 1982 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Adaptive Finite Difference Method for Hyperbolic Systems in OneSpace Dimension written by and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems of physical interest have solutions which are generally quite smooth in a large portion of the region of interest, but have local phenomena such as shocks, discontinuities or large gradients which require much more accurate approximations or finer grids for reasonable accuracy. Examples are atmospheric fronts, ocean currents, and geological discontinuities. In this thesis we develop and partially analyze an adaptive finite difference mesh refinement algorithm for the initial boundary value problem for hyperbolic systems in one space dimension. The method uses clusters of uniform grids which can ''move'' along with pulses or steep gradients appearing in the calculation, and which are superimposed over a uniform coarse grid. Such refinements are created, destroyed, merged, separated, recursively nested or moved based on estimates of the local truncation error. We use a four-way linked tree and sequentially allocated deques (double-ended queues) to perform these operations efficiently. The local truncation error in the interior of the region is estimated using a three-step Richardson extrapolation procedure, which can also be considered a deferred correction method. At the boundaries we employ differences to estimate the error. Our algorithm was implemented using a portable, extensible Fortran preprocessor, to which we added records and pointers. The method is applied to three model problems: the first order wave equation, the second order wave equation, and the inviscid Burgers equation. For the first two model problems our algorithm is shown to be three to five times more efficient (in computing time) than the use of a uniform coarse mesh, for the same accuracy. Furthermore, to our knowledge, our algorithm is the only one which adaptively treats time-dependent boundary conditions for hyperbolic systems.

Download or read book An Adaptative Finite difference Method for Hyperbolic Systems in One Space Dimension written by John H.. Bolstad and published by . This book was released on 1982 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Download or read book Stable Implicit Finite difference Methods for Three dimensional Hyperbolic Systems written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1982 with total page 32 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 A Posteriori Error Estimation of Adaptive Finite Difference Schemes for Hyperbolic Systems written by David C. Arney and published by . This book was released on 1988 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe several techniques that are based on Richardson's extrapolation for estimating discretization errors of finite difference solutions of one- and two-dimensional hyperbolic systems. These a posteriori error estimates are intended for use with adaptive mesh moving and local refinement procedures. Mesh moving algorithms produce nonuniform grids which necessitate special treatment of solution and error estimation techniques. The required adjustments are discussed using a two-step MacCormack method as a model finite difference scheme. We also discuss automatic time step selection procedures and the effects of artificial viscosity. Extrapolation schemes that produce separate estimates of the temporal and spatial discretization errors are presented and we show how these may be used to control local mesh refinement procedures. Several examples illustrating these procedures are presented. Keywords: Hyperbolic systems, Adaptive methods, Posteriori error estimation, Finite difference methods. (mjm).

Download or read book Energy Research Abstracts written by and published by . This book was released on 1982 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Numerical Methods for Hyperbolic Problems written by Remi Abgrall and published by Elsevier. This book was released on 2017-01-16 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. 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 become familiar with their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage

Download or read book Adaptive mesh refinement for hyperbolic partial differential equations written by Stanford University. Computer Science Department. Numerical Analysis Project and published by . This book was released on 1983 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques. Based upon Richardson-type estimates of the truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. Their approach is recursive in that fine grids can themselves contain even finer grids. The grids with finer mesh width in space also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. This document includes algorithm, data structures and grid generation procedure, and concludes with numerical examples in one and two space dimensions. (Author).

Download or read book Finite Difference Methods Theory and Applications written by Ivan Dimov and published by Springer. This book was released on 2015-06-16 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Finite Difference Methods, FDM 2014, held in Lozenetz, Bulgaria, in June 2014. The 36 revised full papers were carefully reviewed and selected from 62 submissions. These papers together with 12 invited papers cover topics such as finite difference and combined finite difference methods as well as finite element methods and their various applications in physics, chemistry, biology and finance.

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 Selected Papers from the Second Conference on Parallel Processing for Scientific Computing written by Charles William Gear and published by SIAM. This book was released on 1987-01-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Parallel Computing.

Download or read book An Adaptive Stencil Finite Difference Method for First Order Linear Hyperbolic Systems written by Robert Henry Hoar and published by . This book was released on 1995 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Difference Methods for 1st Order in Time 2nd Order in Space Hyperbolic Systems Used in Numerical Relativity written by Mihaela Chirvasa and published by . This book was released on 2009 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 560 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,