Download or read book Time Stable Boundary Conditions for Finite Difference Schemes Solving Hyperbolic Systems written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-13 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach. Carpenter, Mark H. and Gottlieb, David and Abarbanel, Saul Unspecified Center NAS1-19480; NAS1-18605; RTOP 505-90-52-01...
Download or read book Time stable Boundary Conditions for Finite difference Schemes Solving Hyperbolic Systems Methodology and Application to High order Compact Schemes written by Mark H. Carpenter and published by . This book was released on 1993 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Higher Order FDTD Schemes for Waveguides and Antenna Structures written by Nikolaos Kantartzis and published by Springer Nature. This book was released on 2022-06-01 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication provides a comprehensive and systematically organized coverage of higher order finite-difference time-domain or FDTD schemes, demonstrating their potential role as a powerful modeling tool in computational electromagnetics. Special emphasis is drawn on the analysis of contemporary waveguide and antenna structures. Acknowledged as a significant breakthrough in the evolution of the original Yee's algorithm, the higher order FDTD operators remain the subject of an ongoing scientific research. Among their indisputable merits, one can distinguish the enhanced levels of accuracy even for coarse grid resolutions, the fast convergence rates, and the adjustable stability. In fact, as the fabrication standards of modern systems get stricter, it is apparent that such properties become very appealing for the accomplishment of elaborate and credible designs.
Download or read book Handbook of Numerical Methods for Hyperbolic Problems written by Remi Abgrall and published by Elsevier. This book was released on 2016-11-17 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. 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 readily understand their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications Written by leading subject experts in each field who provide breadth and depth of content coverage
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 High Order Difference Methods for Time Dependent PDE written by Bertil Gustafsson and published by Springer Science & Business Media. This book was released on 2007-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers high order finite difference methods for time dependent PDE. It gives an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for well-posedness and stability, with inclusion of the three fundamental methods of analysis both for PDE in its original and discretized form: the Fourier transform, the eneregy method and the Laplace transform.
Download or read book Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers written by Christopher A. Kennedy and published by . This book was released on 1997 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Polynomial Chaos Methods for Hyperbolic Partial Differential Equations written by Mass Per Pettersson and published by Springer. This book was released on 2015-03-10 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.
Download or read book High order Schemes for Navier Stokes Equations written by Datta V. Gaitonde and published by . This book was released on 1998 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: A spectrum of higher-order schemes is developed to solve the Navier-Stokes equations in finite-difference formulations. Pade type formulas of up to sixth order with a five-point stencil are developed for the difference scheme. Viscous terms are treated by successive applications of the first derivative operator. However, formulas are also derived for use in a mid-point interpolation-differentiation strategy. For numerical stability, up to tenth-order filtering schemes are developed. The spectral properties of the differentiation and filtering schemes are examined and guidelines are provided to choose proper filter coefficients. Special high-order formulas are obtained for differentiation and filtering in the vicinity of boundaries. The coefficients required for systematic implementation of Neumann-type boundary conditions are also presented. A brief description is provided of the manner in which the FDL3DI code is enhanced by coupling the approximately-factored procedure with these compact-difference based algorithms and by incorporating an explicit fourth-order Runge-Kutta scheme.
Download or read book Spectral and High Order Methods for Partial Differential Equations written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.
Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 written by Robert M. Kirby and published by Springer. This book was released on 2015-11-26 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.
Download or read book Computational Electromagnetic Aerodynamics written by Joseph J. S. Shang and published by John Wiley & Sons. This book was released on 2016-04-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents numerical algorithms, procedures, and techniques required to solve engineering problems relating to the interactions between electromagnetic fields and fluid flow and interdisciplinary technology for aerodynamics, electromagnetics, chemical-physic kinetics, and plasmadynamics Integrates interlinking computational model and simulation techniques of aerodynamics and electromagnetics Combines classic plasma drift-diffusion theory and electron impact ionization modeling for electromagnetic-aerodynamic interactions Describes models of internal degrees of freedom for vibration relaxation and electron excitations
Download or read book Monthly Catalogue United States Public Documents written by and published by . This book was released on 1994 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monthly Catalog of United States Government Publications written by and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Annual Research Briefs written by Center for Turbulence Research (U.S.) and published by . This book was released on 2007 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Time Dependent Problems and Difference Methods written by Bertil Gustafsson and published by John Wiley & Sons. This book was released on 1995 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time Dependent Problems and Difference Methods addresses these various industrial considerations in a pragmatic and detailed manner, giving special attention to time dependent problems in its coverage of the derivation and analysis of numerical methods for computational approximations to Partial Differential Equations (PDEs).
Download or read book Advances in Applied Mathematics Modeling and Computational Science written by Roderick Melnik and published by Springer Science & Business Media. This book was released on 2012-09-22 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume presents a selection of in-depth studies and state-of-the-art surveys of several challenging topics that are at the forefront of modern applied mathematics, mathematical modeling, and computational science. These three areas represent the foundation upon which the methodology of mathematical modeling and computational experiment is built as a ubiquitous tool in all areas of mathematical applications. This book covers both fundamental and applied research, ranging from studies of elliptic curves over finite fields with their applications to cryptography, to dynamic blocking problems, to random matrix theory with its innovative applications. The book provides the reader with state-of-the-art achievements in the development and application of new theories at the interface of applied mathematics, modeling, and computational science. This book aims at fostering interdisciplinary collaborations required to meet the modern challenges of applied mathematics, modeling, and computational science. At the same time, the contributions combine rigorous mathematical and computational procedures and examples from applications ranging from engineering to life sciences, providing a rich ground for graduate student projects.
