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High Order Spectral Methods On Unstructured Grids
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Book Synopsis High-Order/Spectral Methods on Unstructured Grids by : J. S. Hesthaven
Download or read book High-Order/Spectral Methods on Unstructured Grids written by J. S. Hesthaven and published by . This book was released on 2001 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an ab initio development of a convergent high-order accurate scheme for the solution of linear conservation laws in geometrically complex domains. As our main example we present a detailed development and analysis of a scheme suitable for the time-domain solution of Maxwell's equations in a three-dimensional domain. The fully unstructured spatial discretization is made possible by the use of high-order nodal basis, employing multivariate Lagrange polynomials defined on the triangles and tetrahedra. Careful choices of the unstructured nodal grid points ensure high-order/spectral accuracy, while the equations themselves are satisfied in a discontinuous Galerkin form with the boundary conditions being enforced weakly through a penalty term. Accuracy, stability, and convergence of the semi-discrete approximation to Maxwell's equations is established rigorously and bounds on the global divergence error are provided. Concerns related to efficient implementations are discussed in detail. This sets the stage for the presentation of examples, verifying the theoretical results, as well as illustrating the versatility, flexibility, and robustness when solving two-and three- dimensional benchmarks in computational electromagnetic. Pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated.
Book Synopsis High-order/spectral Methods on Unstructured Grids by : J. S. Hesthaven
Download or read book High-order/spectral Methods on Unstructured Grids written by J. S. Hesthaven and published by . This book was released on 2001 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an ab initio development of a convergent high-order accurate scheme for the solution of linear conservation laws in geometrically complex domains. As our main example we present a detailed development and analysis of a scheme suitable for the time-domain solution of Maxwell's equations in a three-dimensional domain. The fully unstructured spatial discretization is made possible by the use of high-order nodal basis, employing multivariate Lagrange polynomials defined on the triangles and tetrahedra. Careful choices of the unstructured nodal grid points ensure high-order/spectral accuracy, while the equations themselves are satisfied in a discontinuous Galerkin form with the boundary conditions being enforced weakly through a penalty term. Accuracy, stability, and convergence of the semi-discrete approximation to Maxwell's equations is established rigorously and bounds on the global divergence error are provided. Concerns related to efficient implementations are discussed in detail. This sets the stage for the presentation of examples, verifying the theoretical results, as well as illustrating the versatility, flexibility, and robustness when solving two-and three- dimensional benchmarks in computational electromagnetic. Pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated.
Book Synopsis High-order/spectral Methods on Unstructured Grids by : J. S. Hesthaven
Download or read book High-order/spectral Methods on Unstructured Grids written by J. S. Hesthaven and published by . This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High Order Spectral Volume and Spectral Difference Methods on Unstructured Grids by : Ravishekar Kannan
Download or read book High Order Spectral Volume and Spectral Difference Methods on Unstructured Grids written by Ravishekar Kannan and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spectral and High Order Methods for Partial Differential Equations by : Jan S. Hesthaven
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.
Book Synopsis Implementing Spectral Methods for Partial Differential Equations by : David A. Kopriva
Download or read book Implementing Spectral Methods for Partial Differential Equations written by David A. Kopriva and published by Springer Science & Business Media. This book was released on 2009-05-27 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.
Book Synopsis Spectral Methods in Fluid Dynamics by : Claudio Canuto
Download or read book Spectral Methods in Fluid Dynamics written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.
Book Synopsis Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 by : Marco L. Bittencourt
Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 written by Marco L. Bittencourt and published by Springer. This book was released on 2017-11-07 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
Book Synopsis Efficient Implementation of High-Order Accurate Numerical Methods on Unstructured Grids by : Wanai Li
Download or read book Efficient Implementation of High-Order Accurate Numerical Methods on Unstructured Grids written by Wanai Li and published by Springer. This book was released on 2014-05-23 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on the development of high-order finite volume methods and discontinuous Galerkin methods, and presents possible solutions to a number of important and common problems encountered in high-order methods, such as the shock-capturing strategy and curved boundary treatment, then applies these methods to solve compressible flows.
Book Synopsis Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 by : Mejdi Azaïez
Download or read book Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 written by Mejdi Azaïez and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 421 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 (2012), and provides an overview of the depth and breath 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.
Book Synopsis An Adaptive Quadrature-free Implementation of the High-order Spectral Volume Method on Unstructured Grids by : Robert Evan Harris
Download or read book An Adaptive Quadrature-free Implementation of the High-order Spectral Volume Method on Unstructured Grids written by Robert Evan Harris and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High-order Numerical Methods for Unstructured Grids and Sliding Mesh by : Gonzalo Sáez Mischlich
Download or read book High-order Numerical Methods for Unstructured Grids and Sliding Mesh written by Gonzalo Sáez Mischlich and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-order numerical methods have proven to be an essential tool to improve the accuracy of simulations involving turbulent flows through the solution of conservation laws. Such flows appear in a wide variety of industrial applications and its correct prediction is crucial to reduce the power consumption and improve the efficiency of these processes. The present study implements and analyzes different types of high-order spatial discretization schemes for unstructured grids to assess and quantify their accuracy in simulations of turbulent flows. In particular, high-order Finite Volume methods (FVM) based on least squares and fully constrained deconvolution operators are considered and their accuracy is evaluated in a variety of linear and non-linear test cases and throughanalytical analysis. Special emphasis is placed on the comparison of formally second-order and high-order FVM, showing that the former can over-perform the latter in terms of accuracy and computational performance in under-resolved configurations. High-order Spectral Element methods (SEM), including Spectral Difference (SD) and Flux Reconstruction (FR), are compared in different linear and non-linear configurations. Furthermore, a SD GPU-based solver (based on the open-source PyFR solver) is developed and its performance with respect to other state of the art CPU-based solvers will be discussed, showing that the developed GPU-based solver outperforms other state of the art CPU-based solvers in terms of performance-per-euro and performance-per-watt. The accuracy and behavior of SEM under aliasing are assessed in linear test cases using analytical tools. The use of grids with high-order cells, which allow to better describe the surfaces of interests of a given simulation, in combination with SEM is also analyzed. The latter analysis demonstrates that special care must be taken to ensure appropriate numerical accuracy when utilizing meshes with such elements. This document also presents the development and the analysis of the Spectral Difference Raviart-Thomas (SDRT) method for two and three-dimensional tensor product and simplex elements. This method is equivalent to the SD formulation for tensor product elements and it can be considered as a natural extension of the SD formulation for simplex elements. Additionally, a new family of FR methods, which is equivalent to the SDRT method under certain circumstances, is described. All these developments were implemented in the open-source PyFR solver and are compatible with CPU and GPU architectures. In the context of high-order simulations of turbulent flows found in rotor-stator interaction test cases, a sliding mesh method (which involves non-conformal grids and mesh motion) specifically tailored for massivelyparallel simulations is implemented within a CPU-based solver. The developed method is compatible with second-order and high-order FVM and SEM. Grid movement, needed to simulate rotor-stator test cases due to the relative movement of each domain zone, is treated using the Arbitrary-Lagrangian-Eulerian (ALE) formulation. The analysis of such formulation depicts its important influence on the numerical accuracy and stability of numerical simulations with mesh motion. Moreover, specific non-conformal discretization methodscompatible with second-order and high-order FVM and SEM are developed and their accuracy is assessed on different non-linear test cases. The parallel scalability of the method is assessed with up to 11000 cores, proving appropriate computational efficiency. The accuracy of the implementation is assessed through a set of linear and non-linear test cases. Preliminary results of the turbulent flow around a DGEN 380 fan stage in an under-resolved configuration are shown and compared to available experimental data.
Book Synopsis Spectral Methods on Arbitrary Grids by : Mark H. Carpenter
Download or read book Spectral Methods on Arbitrary Grids written by Mark H. Carpenter and published by . This book was released on 1995 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High-Order Methods for Computational Physics by : Timothy J. Barth
Download or read book High-Order Methods for Computational Physics written by Timothy J. Barth and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order ac curacy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence sug gests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Cen ter. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18,1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25,1998 at the NASA Ames Research Center in the United States.
Book Synopsis Spectral Methods And Their Applications by : Ben-yu Guo
Download or read book Spectral Methods And Their Applications written by Ben-yu Guo and published by World Scientific. This book was released on 1998-05-05 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.The book consists of three parts. The first part deals with orthogonal approximations in Sobolev spaces and the stability and convergence of approximations for nonlinear problems, as the mathematical foundation of spectral methods. In the second part, various spectral methods are described, with some applications. It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method. The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.
Book Synopsis Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 by : Jens M. Melenk
Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 written by Jens M. Melenk and published by Springer Nature. This book was released on 2023-06-30 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles cover state of the art topics in high order discretizations of partial differential equations. The volume presents a wide range of topics including the design and analysis of high order methods, the development of fast solvers on modern computer architecture, and the application of these methods in fluid and structural mechanics computations.
Book Synopsis High-Order Methods for Incompressible Fluid Flow by : M. O. Deville
Download or read book High-Order Methods for Incompressible Fluid Flow written by M. O. Deville and published by Cambridge University Press. This book was released on 2002-08-15 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
