Development of a High-order Discontinuous Galerkin CFD Solver for Moving Bodies

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ISBN 13 : 9783843930970
Total Pages : pages
Book Rating : 4.9/5 (39 download)

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Book Synopsis Development of a High-order Discontinuous Galerkin CFD Solver for Moving Bodies by : Michael Wurst

Download or read book Development of a High-order Discontinuous Galerkin CFD Solver for Moving Bodies written by Michael Wurst and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Development of the Discontinuous Galerkin Method for High-resolution, Large Scale CFD and Acoustics in Industrial Geometries

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Publisher : Presses univ. de Louvain
ISBN 13 : 2875581198
Total Pages : 173 pages
Book Rating : 4.8/5 (755 download)

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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.

An Adaptive Discontinuous Galerkin Solver for Aerodynamic Flows

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ISBN 13 : 9781267110817
Total Pages : 325 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis An Adaptive Discontinuous Galerkin Solver for Aerodynamic Flows by : Nicholas K. Burgess

Download or read book An Adaptive Discontinuous Galerkin Solver for Aerodynamic Flows written by Nicholas K. Burgess and published by . This book was released on 2011 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work considers the accuracy, efficiency, and robustness of an unstructured high-order accurate discontinuous Galerkin (DG) solver for computational fluid dynamics (CFD). Recently, there has been a drive to reduce the discretization error of CFD simulations using high-order methods on unstructured grids. However, high-order methods are often criticized for lacking robustness and having high computational cost. The goal of this work is to investigate methods that enhance the robustness of high-order discontinuous Galerkin (DG) methods on unstructured meshes, while maintaining low computational cost and high accuracy of the numerical solutions. This work investigates robustness enhancement of high-order methods by examining effective non-linear solvers, shock capturing methods, turbulence model discretizations and adaptive refinement techniques. The goal is to develop an all encompassing solver that can simulate a large range of physical phenomena, where all aspects of the solver work together to achieve a robust, efficient and accurate solution strategy. The components and framework for a robust high-order accurate solver that is capable of solving viscous, Reynolds Averaged Navier-Stokes (RANS) and shocked flows is presented. In particular, this work discusses robust discretizations of the turbulence model equation used to close the RANS equations, as well as stable shock capturing strategies that are applicable across a wide range of discretization orders and applicable to very strong shock waves. Furthermore, refinement techniques are considered as both efficiency and robustness enhancement strategies. Additionally, efficient non-linear solvers based on multigrid and Krylov subspace methods are presented. The accuracy, efficiency, and robustness of the solver is demonstrated using a variety of challenging aerodynamic test problems, which include turbulent high-lift and viscous hypersonic flows. Adaptive mesh refinement was found to play a critical role in obtaining a robust and efficient high-order accurate flow solver. A goal-oriented error estimation technique has been developed to estimate the discretization error of simulation outputs. For high-order discretizations, it is shown that functional output error super-convergence can be obtained, provided the discretization satisfies a property known as dual consistency. The dual consistency of the DG methods developed in this work is shown via mathematical analysis and numerical experimentation. Goal-oriented error estimation is also used to drive an hp -adaptive mesh refinement strategy, where a combination of mesh or h -refinement, and order or p -enrichment, is employed based on the smoothness of the solution. The results demonstrate that the combination of goal-oriented error estimation and hp-adaptation yield superior accuracy, as well as enhanced robustness and efficiency for a variety of aerodynamic flows including flows with strong shock waves. This work demonstrates that DG discretizations can be the basis of an accurate, efficient, and robust CFD solver. Furthermore, enhancing the robustness of DG methods does not adversely impact the accuracy or efficiency of the solver for challenging and complex flow problems. In particular, when considering the computation of shocked flows, this work demonstrates that the available shock capturing techniques are sufficiently accurate and robust, particularly when used in conjunction with adaptive mesh refinement . This work also demonstrates that robust solutions of the Reynolds Averaged Navier-Stokes (RANS) and turbulence model equations can be obtained for complex and challenging aerodynamic flows. In this context, the most robust strategy was determined to be a low-order turbulence model discretization coupled to a high-order discretization of the RANS equations. Although RANS solutions using high-order accurate discretizations of the turbulence model were obtained, the behavior of current-day RANS turbulence models discretized to high-order was found to be problematic, leading to solver robustness issues. This suggests that future work is warranted in the area of turbulence model formulation for use with high-order discretizations. Alternately, the use of Large-Eddy Simulation (LES) subgrid scale models with high-order DG methods offers the potential to leverage the high accuracy of these methods for very high fidelity turbulent simulations. This thesis has developed the algorithmic improvements that will lay the foundation for the development of a three-dimensional high-order flow solution strategy that can be used as the basis for future LES simulations.

Development of High-order Discontinuous Galerkin Methods for Simulations of High-speed Particle-laden Fluid Flows

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (124 download)

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Book Synopsis Development of High-order Discontinuous Galerkin Methods for Simulations of High-speed Particle-laden Fluid Flows by : Eric Jishuan Ching

Download or read book Development of High-order Discontinuous Galerkin Methods for Simulations of High-speed Particle-laden Fluid Flows written by Eric Jishuan Ching and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An encouraging alternative to conventional finite-volume and finite-difference schemes for computational fluid dynamics is the discontinuous Galerkin (DG) method. This method combines aspects of finite-element and finite-volume schemes, employing piecewise polynomials to approximate the solution. It offers a number of advantages, such as arbitrarily high order of accuracy with a compact stencil on unstructured meshes. Furthermore, it is well-suited for advanced mesh adaptation strategies and can achieve great efficiency on graphics processing units (GPUs). However, there are several challenges as well. One of these is the robust capturing of shocks and other flow-field discontinuities. In addition, compared to more mature numerical methods, the DG scheme lacks a well-established infrastructure for handling complex physics, such as particle-laden flows. In light of this, the overarching objective of this work is to develop a DG framework for simulating high-speed particle-laden fluid flows and then apply the resulting methodology to investigate hypersonic dusty flows over blunt bodies, with special focus on Mars atmospheric entry. A simple and robust shock capturing method is first developed. The method employs intra-element variations for shock detection and smooth artificial viscosity for stabilization. We apply the shock capturing method to compute canonical hypersonic test cases, such as flows over a cylinder and a double cone. Quantitative comparisons with state-of-the-art finite-volume codes demonstrate significant benefits of the proposed DG formulation for hypersonic flow computations. In particular, in contrast with finite-volume techniques, the DG method can accurately predict surface heating with strong mesh-shock alignment and with fewer degrees of freedom. We then develop a methodology for simulating particle-laden flows with the DG scheme. The particles are described in a Lagrangian manner. The use of curved elements, which are necessary in high-order DG simulations involving curved geometries, presents significant challenges for tracking and localizing the particles on the Eulerian mesh. We propose strategies to handle particle-wall collisions on arbitrary curved, high-aspect-ratio elements, and we find that curved elements can significantly improve predictions of particle trajectories. In addition, an algorithm is developed for treating interparticle collisions that exploits the geometric mapping from physical space to reference space. The algorithm can significantly reduce computational cost compared to conventional strategies. We also develop smooth anisotropic kernels for projecting the effect of the particle phase onto the Eulerian mesh in a robust, accurate, and efficient manner, particularly on high-aspect-ratio elements. Simulations of shock-particle interaction, sandblasting, and other applications illustrate the ability of the developed algorithms to effectively compute complex multiphase flows. Finally, we apply the resulting Euler-Lagrange methodology to compute hypersonic dusty flows over blunt bodies. To address the overall lack of high-quality experimental data, a parametric study is conducted to investigate the sensitivities of the solution to the physical modeling of the particle phase. We also simulate dusty flows over the full-scale ExoMars Schiaparelli capsule at realistic flow conditions. Detailed analysis of particle trajectories through the shock layer is performed. The effects of the dust particles on heat shields, such as heat flux augmentation and surface recession, are characterized.

High Performance Computing in Science and Engineering '19

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Publisher : Springer Nature
ISBN 13 : 3030667928
Total Pages : 583 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis High Performance Computing in Science and Engineering '19 by : Wolfgang E. Nagel

Download or read book High Performance Computing in Science and Engineering '19 written by Wolfgang E. Nagel and published by Springer Nature. This book was released on 2021-05-29 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2019. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance. The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.

New Results in Numerical and Experimental Fluid Mechanics XIII

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Publisher : Springer Nature
ISBN 13 : 3030795616
Total Pages : 787 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis New Results in Numerical and Experimental Fluid Mechanics XIII by : Andreas Dillmann

Download or read book New Results in Numerical and Experimental Fluid Mechanics XIII written by Andreas Dillmann and published by Springer Nature. This book was released on 2021-07-13 with total page 787 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers timely insights into research on numerical and experimental fluid mechanics and aerodynamics, mainly for (but not limited to) aerospace applications. It reports on findings by members of the STAB (German Aerospace Aerodynamics Association) and DGLR (German Society for Aeronautics and Astronautics) and covers both nationally and EC-funded projects. Continuing on the tradition of the previous volumes, the book highlights innovative solutions, promoting translation from fundamental research to industrial applications. It addresses academics and professionals in the field of aeronautics, astronautics, ground transportation, and energy alike.

High Performance Computing in Science and Engineering ’22

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Publisher : Springer Nature
ISBN 13 : 3031468708
Total Pages : 467 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis High Performance Computing in Science and Engineering ’22 by : Wolfgang E. Nagel

Download or read book High Performance Computing in Science and Engineering ’22 written by Wolfgang E. Nagel and published by Springer Nature. This book was released on with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Towards High-performance Discontinuous Galerkin Simulations of Reacting Flows Using Legion

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (138 download)

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Book Synopsis Towards High-performance Discontinuous Galerkin Simulations of Reacting Flows Using Legion by : Kihiro Bando

Download or read book Towards High-performance Discontinuous Galerkin Simulations of Reacting Flows Using Legion written by Kihiro Bando and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

High-order Hybridizable Discontinuous Galerkin Method for Viscous Compressible Flows

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Publisher :
ISBN 13 :
Total Pages : 125 pages
Book Rating : 4.:/5 (112 download)

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Book Synopsis High-order Hybridizable Discontinuous Galerkin Method for Viscous Compressible Flows by : Mostafa Javadzadeh Moghtader

Download or read book High-order Hybridizable Discontinuous Galerkin Method for Viscous Compressible Flows written by Mostafa Javadzadeh Moghtader and published by . This book was released on 2017 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

OpenACC Acceleration of an Unstructured CFD Solver Based on a Reconstructed Discontinuous Galerkin Method for Compressible Flows

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Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (951 download)

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Book Synopsis OpenACC Acceleration of an Unstructured CFD Solver Based on a Reconstructed Discontinuous Galerkin Method for Compressible Flows by :

Download or read book OpenACC Acceleration of an Unstructured CFD Solver Based on a Reconstructed Discontinuous Galerkin Method for Compressible Flows written by and published by . This book was released on 2015 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, an OpenACC directive-based graphics processing unit (GPU) parallel scheme is presented for solving the compressible Navier-Stokes equations on 3D hybrid unstructured grids with a third-order reconstructed discontinuous Galerkin method. The developed scheme requires the minimum code intrusion and algorithm alteration for upgrading a legacy solver with the GPU computing capability at very little extra effort in programming, which leads to a unified and portable code development strategy. A face coloring algorithm is adopted to eliminate the memory contention because of the threading of internal and boundary face integrals. A number of flow problems are presented to verify the implementation of the developed scheme. Timing measurements were obtained by running the resulting GPU code on one Nvidia Tesla K20c GPU card (Nvidia Corporation, Santa Clara, CA, USA) and compared with those obtained by running the equivalent Message Passing Interface (MPI) parallel CPU code on a compute node (consisting of two AMD Opteron 6128 eight-core CPUs (Advanced Micro Devices, Inc., Sunnyvale, CA, USA)). Speedup factors of up to 24× and 1.6× for the GPU code were achieved with respect to one and 16 CPU cores, respectively. The numerical results indicate that this OpenACC-based parallel scheme is an effective and extensible approach to port unstructured high-order CFD solvers to GPU computing.

Adaptive High-order Methods in Computational Fluid Dynamics

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Publisher : World Scientific
ISBN 13 : 9814313181
Total Pages : 471 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Adaptive High-order Methods in Computational Fluid Dynamics by : Z. J. Wang

Download or read book Adaptive High-order Methods in Computational Fluid Dynamics written by Z. J. Wang and published by World Scientific. This book was released on 2011 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD

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Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (317 download)

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Book Synopsis High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD by : Chi-Wang Shu

Download or read book High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD written by Chi-Wang Shu and published by . This book was released on 2001 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years high order numerical methods have been widely used in computational fluid dynamics (CFD), to effectively resolve complex flow features using meshes which are reasonable for today's computers. In this paper we review and compare three types of high order methods being used in CFD, namely the weighted essentially non-oscillatory (WENO) finite difference methods, the WENO finite volume methods, and the discontinuous Galerkin (DG) finite element methods. We summarize the main features of these methods, from a practical user's point of view, indicate their applicability and relative strength, and show a few selected numerical examples to demonstrate their performance on illustrative model CFD problems.

Discontinuous Galerkin Methods

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Publisher : Springer Science & Business Media
ISBN 13 : 3642597211
Total Pages : 468 pages
Book Rating : 4.6/5 (425 download)

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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.

A High-order Discontinuous Galerkin Multigrid Solver for Aerodynamic Applications

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Publisher :
ISBN 13 :
Total Pages : 90 pages
Book Rating : 4.:/5 (565 download)

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Book Synopsis A High-order Discontinuous Galerkin Multigrid Solver for Aerodynamic Applications by : Krzysztof J. Fidkowski

Download or read book A High-order Discontinuous Galerkin Multigrid Solver for Aerodynamic Applications written by Krzysztof J. Fidkowski and published by . This book was released on 2004 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results are presented from the development of a high-order discontinuous Galerkin finite element solver using p-multigrid with line Jacobi smoothing. The line smoothing algorithm is presented for unstructured meshes, and p-multigrid is outlined for the nonlinear Euler equations of gas dynamics. Analysis of 2-D advection shows the improved performance of line implicit versus block implicit relaxation. Through a mesh refinement study, the accuracy of the discretization is determined to be the optimal O(h[superscript]P+l) for smooth problems in 2-D and 3-D. The multigrid convergence rate is found to be independent of the interpolation order but weakly dependent on the grid size. Timing studies for each problem indicate that higher order is advantageous over grid refinement when high accuracy is required. Finally, parallel versions of the 2-D and 3-D solvers demonstrate close to ideal coarse-grain scalability.

Nodal Discontinuous Galerkin Methods

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Publisher : Springer Science & Business Media
ISBN 13 : 0387720650
Total Pages : 507 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Nodal Discontinuous Galerkin Methods by : Jan S. Hesthaven

Download or read book Nodal Discontinuous Galerkin Methods written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.

Visualization for High-order DG Computational Fluid Dynamics Results

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Publisher :
ISBN 13 :
Total Pages : 71 pages
Book Rating : 4.:/5 (23 download)

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Book Synopsis Visualization for High-order DG Computational Fluid Dynamics Results by : David Walfisch

Download or read book Visualization for High-order DG Computational Fluid Dynamics Results written by David Walfisch and published by . This book was released on 2007 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis demonstrates a technique that reduces the perceived error introduced in the visualization of higher-order DG solutions with traditional tools. Most visualization techniques work by using the solution at the mesh vertices and linearly interpolating to color the interior of the element. For higher-order solutions (where the visualization mesh is the same as the solution mesh) this method renders the high-order solution linear. By inserting new nodes at element quadrature points where the difference between the actual solution and the linear rendering is above a user-defined tolerance, additional elements are created and used for the visualization process. In order to keep the counts low for this new mesh, after each insertion a local rearrangement is performed to readapt the parent element so that the total visualization error is reduced. The method introduced here has many advantages over isotropic adaptation used by some higher-order visualization techniques. Isotropic adaptation adapts all the elements regardless of error, thus creating a higher total element count and therefore requiring more memory and rendering time. In some cases isotropic elements are not ideal in representing the solution (ie: boundary layers, shocks, wakes, etc.). Lastly, by providing an option to define the maximum visualization error allows the user to specify how close the visualized solution is to the actual calculated one (at the expense of a denser visualization mesh). Second, this work introduces a new method to apply an accuracy maintaining post-processor on DG vector fields to improve on the standard streamlining algorithms. Time integration methods do not work accurately and may even fail on discontinuos fields. The post-processor smoothens the field and eliminates the discontinuity between elements thus resulting in more accurate streamlines. To keep down the computational cost of the method, the post-processing is done in a one dimensional manner along the streamline.

IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach

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Publisher : Springer
ISBN 13 : 3319128868
Total Pages : 683 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach by : Norbert Kroll

Download or read book IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach written by Norbert Kroll and published by Springer. This book was released on 2015-01-02 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.