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Development Of A High Order Implicit Discontinuous Galerkin Method On Unstructured Meshes For Turbomachinery Flow
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Book Synopsis Development of a High-order Implicit Discontinuous Galerkin Method on Unstructured Meshes for Turbomachinery Flow by : Min Yao
Download or read book Development of a High-order Implicit Discontinuous Galerkin Method on Unstructured Meshes for Turbomachinery Flow written by Min Yao and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Development of the Discontinuous Galerkin Method for High-resolution, Large Scale CFD and Acoustics in Industrial Geometries by : Koen Hillewaert
Download or read book Development of the Discontinuous Galerkin Method for High-resolution, Large Scale CFD and Acoustics in Industrial Geometries written by Koen Hillewaert and published by Presses univ. de Louvain. This book was released on 2013-02-10 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this work is the practical development of the discontinuous Galerkin method, arguably the most mature high-order discretisation, for the scale resolving simulations of turbomachinery flows.
Book Synopsis Computational Fluid Dynamics by : Jiri Blazek
Download or read book Computational Fluid Dynamics written by Jiri Blazek and published by Butterworth-Heinemann. This book was released on 2015-04-23 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics. By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques. This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization. An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques. - Will provide you with the knowledge required to develop and understand modern flow simulation codes - Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics - Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques
Book Synopsis High-order Methods for Unsteady Flows on Unstructured Dynamic Meshes by : Kui Ou
Download or read book High-order Methods for Unsteady Flows on Unstructured Dynamic Meshes written by Kui Ou and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive study of discontinuous finite element based high-order methods has been performed in this thesis, addressing a wide range of important issues related to high-order methods. The thesis starts with a detailed discussion of nodal based high-order methods and careful analysis of their stability properties. In particular, the formulations of nodal Discontinuous Galerkin method, Spectral Difference method, and Flux Reconstruction method for the scalar conservation laws are discussed first. The differences and similarities among these high-order schemes are carefully examined and effectively used to establish the linear stability of these methods. Stability proofs of nodal Discontinuous Galerkin method, Spectral Difference method, and Flux Reconstruction method subsequently lead to a new type of energy stable high-order scheme called Energy Stable Flux Reconstruction scheme. The extension of this new scheme from linear advection equation to the diffusion equation is formulated and discussed. The fundamental study of the high-order methods for scalar conservation laws lays the theoretical foundation for the subsequent extension to include conservation laws for fluid dynamics. The formulation of spectral difference method for the Navier-Stokes equations is first discussed. Validation tests to verify the resulting flow solver are presented. The extension of the spectral difference based Navier-Stokes flow solver from static fixed computational mesh to include dynamic moving deforming mesh is discussed next. An efficient mesh deformation algorithm that can handle substantial boundary movement is proposed and examined. The invariance of conservation laws mapping between coordinate systems allows the high-order scheme to be formulated on dynamic deforming meshes without deteriorating the formal order of accuracy of the underlying scheme. Detailed formulation, analysis, and validation results are presented. As a result of mesh deformation, the issue of geometric conservation needs to be addressed. The definition and origin of the geometric conservation law are discussed. The differential form of the geometric conservation law is derived from first principles for both the scalar conservation law and the fluid dynamic conservation laws. Subsequently a geometric conservative high-order scheme is formulated. The significance of geometric conservation on the stability and accuracy of the flow solution is examined. Finally a wide range of interesting fluid dynamic phenomena have been studied using the resulting high-order flow solver based on dynamic unstructured meshes. The representative test cases cover fluid dynamic phenomena ranging from completely laminar flows, to unsteady vortex dominated flows, and to flows exhibiting mixed regions of laminar, transitional, and turbulent structures. Other work that has been completed in this thesis is included in the appendix. In particular, continuous unsteady adjoint equations for advection and Burger's equations have been derived and solved using the high-order methods. The method of mesh deformation is reformulated as an optimization problem and used to achieve adaptive mesh refinement.
Book Synopsis Implementation of Discontinuous Galerkin Methods for the Level Set Equation on Unstructured Meshes by : Matthew W. Farthing
Download or read book Implementation of Discontinuous Galerkin Methods for the Level Set Equation on Unstructured Meshes written by Matthew W. Farthing and published by . This book was released on 2008 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A high-order discontinuous Galerkin method for unsteady compressible flows with immersed boundaries by : Stephan Krämer-Eis
Download or read book A high-order discontinuous Galerkin method for unsteady compressible flows with immersed boundaries written by Stephan Krämer-Eis and published by Cuvillier Verlag. This book was released on 2017-10-20 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Um die komplexe Physik in kompressiblen Strömungen genauer zu verstehen, kommen vermehrt Simulationen zum Einsatz. Jedoch können weit verbreitete kommerzielle Softwarepakete die Physik aufgrund ihrer niedrigen Genauigkeit oft nicht korrekt erfassen. In dieser Arbeit wird eine diskontinuierliche Galerkin Methode mit hoher Ordnung entwickelt, welche eine hohe Genauigkeit erzielt. Dabei werden insbesondere zwei Probleme, die im Kontext von Verfahren mit hoher Ordnung auftreten, behandelt. Zum einen wird die Gittergenerierung durch das Verwenden einer Immersed Boundary Methode deutlich vereinfacht. Dies bedeutet, dass die Problemgeometrie aus einem deutlich einfacheren Hintergrundgitter herausgeschnitten wird. Die Geometrie wird mit Hilfe einer Level-Set Funktion dargestellt, und die Integration auf den entstehenden geschnittenen Zellen wird mittels einer hierarchischen Moment-Fitting Quadratur durchgeführt. Das Problem der sehr kleinen oder stark gekrümmten Zellen wird durch Zellagglomeration gelöst. Zum zweiten wird die starke Zeitschrittbeschränkung durch anisotrope Gitter mit Hilfe eines lokalen Zeitschrittverfahrens behoben. Diverse numerische Experimente bestätigen die hohe Genauigkeit, Effizienz und geometrische Flexibilität der vorgestellten Methode.
Book Synopsis Discontinuous Galerkin Methods by : Bernardo Cockburn
Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Book Synopsis hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes by : Andrea Cangiani
Download or read book hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes written by Andrea Cangiani and published by Springer. This book was released on 2017-11-27 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios.
Book Synopsis Error Control, Adaptive Discretizations, and Applications, Part 1 by :
Download or read book Error Control, Adaptive Discretizations, and Applications, Part 1 written by and published by Elsevier. This book was released on 2024-06-29 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Error Control, Adaptive Discretizations, and Applications, Volume 58, Part One highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems, An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations. - Covers multi-scale modeling - Includes updates on data-driven modeling - Presents the latest information on large deformations of multi-scale materials
Book Synopsis A High-Order Finite Volume Method for 3D Elastic Modelling on Unstructured Meshes by : Wensheng Zhang
Download or read book A High-Order Finite Volume Method for 3D Elastic Modelling on Unstructured Meshes written by Wensheng Zhang and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, a new efficient high-order finite volume method for 3D elastic modelling on unstructured meshes is developed. The stencil for the high-order polynomial reconstruction is generated by subdividing the relative coarse tetrahedrons. The reconstruction on the stencil is performed by using cell-averaged quantities represented by the hierarchical orthonormal basis functions. Unlike the traditional high-order finite volume method, the new method has a very local property like the discontinuous Galerkin method. Furthermore, it can be written as an inner-split computational scheme which is beneficial to reducing computational amount. The reconstruction matrix is invertible and remains unchanged for all tetrahedrons, and thus it can be pre-computed and stored before time evolution. These special advantages facilitate the parallelization and high-order computations. The high-order accuracy in time is obtained by the Runge-Kutta method. Numerical computations including a 3D real model with complex topography demonstrate the effectiveness and good adaptability to complex topography.
Book Synopsis TILDA: Towards Industrial LES/DNS in Aeronautics by : Charles Hirsch
Download or read book TILDA: Towards Industrial LES/DNS in Aeronautics written by Charles Hirsch and published by Springer Nature. This book was released on 2021-06-28 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers detailed insights into new methods for high-fidelity CFD, and their industrially relevant applications in aeronautics. It reports on the H2020 TILDA project, funded by the European Union in 2015-2018. The respective chapters demonstrate the potential of high-order methods for enabling more accurate predictions of non-linear, unsteady flows, ensuring enhanced reliability in CFD predictions. The book highlights industrially relevant findings and representative test cases on the development of high-order methods for unsteady turbulence simulations on unstructured grids; on the development of the LES/DNS methodology by means of multilevel, adaptive, fractal and similar approaches for applications on unstructured grids; and on leveraging existent large-scale HPC networks to facilitate the industrial applications of LES/DNS in daily practice. Furthermore, the book discusses multidisciplinary applications of high-order methods in the area of aero-acoustics. All in all, it offers timely insights into the application and performance of high-order methods for CFD, and an extensive reference guide for researchers, graduate students, and industrial engineers whose work involves CFD and turbulence modeling.
Book Synopsis International Aerospace Abstracts by :
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1999 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discontinuous Galerkin Methods on Moving Domains with Large Deformations by : Luming Wang
Download or read book Discontinuous Galerkin Methods on Moving Domains with Large Deformations written by Luming Wang and published by . This book was released on 2015 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present two different numerical approaches for solving compressible flows on moving domains with high-order accuracy. The approaches are base on discontinuous Galerkin (DG) methods and are particularly designed for addressing the large deformation problems as the domain moves. A moving-mesh technique is first introduced to improve the mesh quality with the domain deforming. The technique moves the mesh nodes by DistMesh algorithm and locally changes the mesh topology by flipping edges or faces, which can be applied in both 2D and 3D. Moreover, some local density control operations are also developed to add or remove the mesh nodes to change the mesh adaptivity. Our first numerical scheme is formulated on a space-time framework using a nodal DG discretization on space-time domains with appropriate numerical fluxes for the first and the second-order terms, respectively. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton-Krylov solver. Along with the numerical scheme, two efficient algorithms for constructing globally conforming space-time slab meshes are given, based on our moving-mesh technique. The second approach employs DG discreatization with arbitrary-Eulerian-Lagrangian (ALE) framework by solving equations based on smooth mappings. An efficient local L2 projection is used for transferring solutions when mesh topology change happens. We test our two approaches by a number of numerical cases in both 2D and 3D. The tests involve convergence tests as well as simulations of laminar flows, which shows that the proposed methods achieve high-order accuracy and are able to handle problems with complex geometric motions.
Book Synopsis Runge-Kutta Discontinuous Galerkin Methods for Convection-dominated Problems by : Bernardo Cockburn
Download or read book Runge-Kutta Discontinuous Galerkin Methods for Convection-dominated Problems written by Bernardo Cockburn and published by . This book was released on 2000 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Mesh Quality Considerations for the Discontinuous Galerkin Method by : Eric Michael Collins
Download or read book On Mesh Quality Considerations for the Discontinuous Galerkin Method written by Eric Michael Collins and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: It is widely accepted that the accuracy and efficiency of computational fluid dynamics (CFD) simulations is heavily influenced by the quality of the mesh upon which the solution is computed. Unfortunately, the computational tools available for assessing mesh quality remain rather limited. This report describes a methodology for rigorously investigating the interaction between a flow solver and a variety of mesh configurations for the purposes of deducing which mesh properties produce the best results from the solver. The techniques described herein permit a more detailed exploration of what constitutes a quality mesh in the context of a given solver and a desired flow regime. In the present work, these newly developed tools are used to investigate mesh quality as it pertains to a high-order accurate discontinuous Galerkin solver when it is used to compute inviscid and high-Reynolds number flows in domains possessing smoothly curving boundaries. For this purpose, two flow models have been generated and used to conduct parametric studies of mesh configurations involving curved elements. The results of these studies allow us to make some observations regarding mesh quality when using the discontinuous Galerkin method to solve these types of problems. Briefly, we have found that for inviscid problems, the mesh elements used to resolve curved boundaries should be at least third order accurate. For viscous problems, the domain boundaries must be approximated by mesh elements that are of the same order as the polynomial approximation of the solution if the theoretical order of accuracy of the scheme is to be maintained. Increasing the accuracy of the boundary elements to at least one order higher than the solution approximation typically results in a noticeable improvement in the computed error norms. It is also noted that C1-continuity of the mesh is not required at element interfaces along the boundary.
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 Unstructured Anisotropic All-quad Mesh Adaptation Based on a Continuous Local Error Model for the Discontinuous Galerkin Method by : Keigan MacLean
Download or read book Unstructured Anisotropic All-quad Mesh Adaptation Based on a Continuous Local Error Model for the Discontinuous Galerkin Method written by Keigan MacLean and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "This thesis will present a method of unstructured anisotropic adaptation for all-quad mesh suitable for use with high-order methods. The overall goal is to minimize the computational cost needed to perform highly accurate Computational Fluid Dynamics (CFD) simulations. With adaptive methods this can be accomplished through modifying the underlying spatial discretization of the domain. Here, this will be tailored to the particular problem at hand through a continuous local error model. In this form, the physical mesh geometry is replaced by the notion of a frame field, allowing us to extend previous ideas from metric-based adaptation methods. This will serve as a means to restate the discrete error minimization problem in order to determine the target element size and shape based on an optimal distribution of degrees of freedom.Furthermore, the goal of most CFD simulations is to measure some particular output of interest (e.g. such as lift or drag). Therefore, extensions to the method will be examined for goal-oriented adaptation. This involves using the adjoint problem solution and dual-weighted residuals to target mesh refinement in areas most crucial to the accuracy of these measurements.Finally, this work will also consider the implementation of a fully unstructured and anisotropic all-quad mesh generator capable of conforming to the aforementioned target elements. Here, the procedure is based on an Lp-CVT energy minimization problem used to determine updated node positions. Overall, this work will combine each of these aspects in order to establish a complete adaptive framework for use in solving high-order problems with the Discontinuous Galerkin method"--
