Analysis and Development of Compact Finite Difference Schemes with Optimized Numerical Dispersion Relation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analysis and Development of Compact Finite Difference Schemes with Optimized Numerical Dispersion Relation write by Yi-Hung Kuo. This book was released on 2014. Analysis and Development of Compact Finite Difference Schemes with Optimized Numerical Dispersion Relation available in PDF, EPUB and Kindle. Finite difference approximation, in addition to Taylor truncation errors, introduces numerical dispersion-and-dissipation errors into numerical solutions of partial differential equations. We analyze a class of finite difference schemes which are designed to minimize these errors (at the expanse of formal order of accuracy), and we give a quantitative analysis of the interplay between the Taylor truncation errors and the dispersion-and-dissipation errors when refining meshes. In particular, we study the numerical dispersion relation of the fully discretized non-dispersive transport equation in one and multi-dimensions. We derive the numerical phase error and the L 2 -norm error of the solution in terms of the dispersion-and-dissipation error. Based on our analysis, we investigate the error dynamics among various optimized compact schemes and the unoptimized higher-order generalized Pad\'e compact schemes, taking into account four important factors, namely, (i) error tolerance, (ii) computer memory capacity, (iii) resolvable wavenumber, and (iv) CPU/GPU time. The dynamics shed light on the principles of designing suitable optimized compact schemes for a given problem. Using these principles as guidelines, we then propose an optimized scheme that prescribes the numerical dispersion relation before finding the corresponding discretization. This approach produces smaller numerical dispersion-and-dissipation errors for linear and nonlinear problems, compared with the unoptimized higher-order compact schemes and other optimized schemes developed in the literature. Finally, we discuss the difficulty of developing an optimized composite boundary scheme for problems with non-trivial boundary conditions. We propose a composite scheme that introduces a buffer zone to connect an optimized interior scheme and an unoptimized boundary scheme. Our numerical experiments show that this strategy produces small L2-norm error when a wave packet passes through the non-periodic boundary.
Analysis and Implementation of High-order Compact Finite Difference Schemes
Analysis and Implementation of High-order Compact Finite Difference Schemes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analysis and Implementation of High-order Compact Finite Difference Schemes write by Jonathan Tyler. This book was released on 2007. Analysis and Implementation of High-order Compact Finite Difference Schemes available in PDF, EPUB and Kindle. The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear problems (convection, heat conduction) and also for nonlinear problems (Burgers' and KdV equations) were performed. The compact solvers were combined with Euler and fourth-order Runge-Kutta time differencing. In most cases, the order of convergence of the numerical solution to the exact solution was the same as the formal order of accuracy of the compact schemes employed.
Finite Difference Schemes for Long-time Integration
Finite Difference Schemes for Long-time Integration - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Difference Schemes for Long-time Integration write by Institute for Computer Applications in Science and Engineering. This book was released on 1993. Finite Difference Schemes for Long-time Integration available in PDF, EPUB and Kindle.
Scientific and Technical Aerospace Reports
Scientific and Technical Aerospace Reports - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Scientific and Technical Aerospace Reports write by . This book was released on 1995. Scientific and Technical Aerospace Reports available in PDF, EPUB and Kindle. 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.
Finite Difference Computing with PDEs
Finite Difference Computing with PDEs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Difference Computing with PDEs write by Hans Petter Langtangen. This book was released on 2017-06-21. Finite Difference Computing with PDEs available in PDF, EPUB and Kindle. This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.
