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Author: Koen Hillewaert
Publisher: Presses univ. de Louvain
Published: 2013-02-10
Total Pages: 173
ISBN-13: 2875581198
DOWNLOAD EBOOK →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.
Author: Jens M. Melenk
Publisher: Springer Nature
Published: 2023-06-30
Total Pages: 571
ISBN-13: 3031204328
DOWNLOAD EBOOK →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.
Author: Charles Hirsch
Publisher: Springer Nature
Published: 2021-06-28
Total Pages: 550
ISBN-13: 3030620484
DOWNLOAD EBOOK →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.
Author: Norbert Kroll
Publisher: Springer
Published: 2015-01-02
Total Pages: 683
ISBN-13: 3319128868
DOWNLOAD EBOOK →The book describes the main findings of the EU-funded project IDIHOM (Industrialization of High-Order Methods – A Top-Down Approach). The goal of this project was the improvement, utilization and demonstration of innovative higher-order simulation capabilities for large-scale aerodynamic application challenges in the aircraft industry. The IDIHOM consortium consisted of 21 organizations, including aircraft manufacturers, software vendors, as well as the major European research establishments and several universities, all of them with proven expertise in the field of computational fluid dynamics. After a general introduction to the project, the book reports on new approaches for curved boundary-grid generation, high-order solution methods and visualization techniques. It summarizes the achievements, weaknesses and perspectives of the new simulation capabilities developed by the project partners for various industrial applications, and includes internal- and external-aerodynamic as well as multidisciplinary test cases.
Author: Rolf Radespiel
Publisher: Springer
Published: 2015-07-09
Total Pages: 404
ISBN-13: 3319211277
DOWNLOAD EBOOK →The book reports on advanced solutions to the problem of simulating wing and nacelle stall, as presented and discussed by internationally recognized researchers at the Closing Symposium of the DFG Research Unit FOR 1066. Reliable simulations of flow separation on airfoils, wings and powered engine nacelles at high Reynolds numbers represent great challenges in defining suitable mathematical models, computing numerically accurate solutions and providing comprehensive experimental data for the validation of numerical simulations. Additional problems arise from the need to consider airframe-engine interactions and inhomogeneous onset flow conditions, as real aircraft operate in atmospheric environments with often-large distortions. The findings of fundamental and applied research into these and other related issues are reported in detail in this book, which targets all readers, academics and professionals alike, interested in the development of advanced computational fluid dynamics modeling for the simulation of complex aircraft flows with flow separation.
Author: Bernardo Cockburn
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 468
ISBN-13: 3642597211
DOWNLOAD EBOOK →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.
Author: Mostafa Javadzadeh Moghtader
Publisher:
Published: 2017
Total Pages: 125
ISBN-13:
DOWNLOAD EBOOK →Computational Fluid Dynamics (CFD) is an essential tool for engineering design and analysis, especially in applications like aerospace, automotive and energy industries. Nowadays most commercial codes are based on Finite Volume (FV) methods, which are second order accurate, and simulation of viscous compressible flow around complex geometries is still very expensive due to large number of low-order elements required. One the other hand, some sophisticated physical phenomena, like aeroacoustics, vortex dominated flows and turbulence, need very high resolution methods to obtain accurate results. High-order methods with their low spatial discretization errors, are a possible remedy for shortcomings of the current CFD solvers. Discontinuous Galerkin (DG) methods have emerged as a successful approach for non-linear hyperbolic problems and are widely regarded very promising for next generation CFD solvers. Their efficiency for high-order discretization makes them suitable for advanced physical models like DES and LES, while their stability in convection dominated regimes is also a merit of them. The compactness of DG methods, facilitate the parallelization and their element-by-element discontinuous nature is also helpful for adaptivity. This PhD thesis focuses on the development of an efficient and robust high-order Hybridizable Discontinuous Galerkin (HDG) Finite Element Method (FEM) for compressible viscous flow computations. HDG method is a new class of DG family which enjoys from merits of DG but has significantly less globally coupled unknowns compared to other DG methods. Its features makes HDG a possible candidate to be investigated as next generation high-order tools for CFD applications. The first part of this thesis recalls the basics of high-order HDG method. It is presented for the two-dimensional linear convection-diffusion equation, and its accuracy and features are investigated. Then, the method is used to solve compressible viscous flow problems modelled by non-linear compressible Navier-Stokes equations; and finally a new linearized HDG formulation is proposed and implemented for that problem, all using high-order approximations. The accuracy and efficiency of high-order HDG method to tackle viscous compressible flow problems is investigated, and both steady and unsteady solvers are developed for this purpose. The second part is the core of this thesis, proposing a novel shock-capturing method for HDG solution of viscous compressible flow problems, in the presence of shock waves. The main idea is to utilize the stabilization of numerical fluxes, via a discontinuous space of approximation inside the elements, to diminish or remove the oscillations in the vicinity of discontinuity. This discontinuous nodal basis functions, leads to a modified weak form of the HDG local problem in the stabilized elements. First, the method is applied to convection-diffusion problems with Bassi-Rebay and LDG fluxes inside the elements, and then, the strategy is extended to the compressible Navier-Stokes equations using LDG and Lax-Friedrichs fluxes. Various numerical examples, for both convection-diffusion and compressible Navier-Stokes equations, demonstrate the ability of the proposed method, to capture shocks in the solution, and its excellent performance in eliminating oscillations is the vicinity of shocks to obtain a spurious-free high-order solution.
Author: Kihiro Bando
Publisher:
Published: 2023
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOK →High-fidelity scale-resolving computational fluid dynamics (CFD) simulations may provide a path towards predictive capabilities for many engineering-relevant applications, in particular those involving the interaction between multiple physics such as turbulent multi-component reacting flows. However, their routine use is hindered by their cost. The throughput of the fastest supercomputers is fortunately still increasing but this comes at the cost of specialized devices and hardware heterogeneity. Modern supercomputing thus imposes new requirements onto numerical algorithms and their implementation for leveraging the available compute while significantly complicating the design, development, and maintenance of massively parallel computational physics software. This dissertation focuses on addressing numerical and implementation challenges of CFD of multi-component reacting flows. It considers high-order discontinuous Galerkin (DG) discretization methods as a way towards a more efficient use of modern compute architectures for performing high-fidelity simulations of configurations involving complex geometries. Both the high accuracy requirement and the ability to accommodate unstructured meshes are key motivations for investigating this class of numerical schemes. The entire content of this manuscript is based on DG-Legion, a novel unstructured DG CFD solver for the compressible Navier-Stokes equations written on top of the Legion system for targeting distributed heterogeneous architectures. The main challenge related to the computer science aspect was to scale the code on GPU supercomputers. An explicit ghost formulation is proposed which results in performance competitive with state-of-the-art solvers based on the message-passing interface (MPI) system while the application code remains free of explicit communication and synchronization, i.e. it has sequential semantics. The contribution related to the numerics addresses two important questions. First, the issue of spurious pressure oscillations generated by fully-conservative schemes for thermally perfect mixtures is analyzed in detail. A generic framework is developed in order to generate systematic variations of the baseline scheme with improved properties. When applied to the problem at hand, several techniques that were previously proposed independently are recovered as special cases in a rigorous way. Finally, a hybrid strategy for preserving the positivity of DG solutions for the composition-describing scalars is introduced. The method based on the composition of subcell finite volume schemes and linear-scaling limiters leads to an overall positivity-preserving scheme in the inviscid limit, compatible with higher-order quadrature rules, and better preserving the subcell resolution compared to only using rescaling techniques.
Author: Shukai Du
Publisher:
Published: 2019
Total Pages:
ISBN-13: 9783030272319
DOWNLOAD EBOOK →This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second year graduate student who has already taken a non necessarily advanced class in the Finite Element method.
Author: Z. J. Wang
Publisher: World Scientific
Published: 2011
Total Pages: 471
ISBN-13: 9814313181
DOWNLOAD EBOOK →This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.
