Techniques For High Order Adaptive Discontinuous Galerkin Discretizations In Fluid Dynamics

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Techniques for High-order Adaptive Discontinuous Galerkin Discretizations in Fluid Dynamics

Author : Li Wang
Publisher :
ISBN 13 : 9781109532913
Total Pages : 178 pages
Book Rating : 4.5/5 (329 download)

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Book Synopsis Techniques for High-order Adaptive Discontinuous Galerkin Discretizations in Fluid Dynamics by : Li Wang

Download or read book Techniques for High-order Adaptive Discontinuous Galerkin Discretizations in Fluid Dynamics written by Li Wang and published by . This book was released on 2009 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of high-order discontinuous Galerkin (DG) discretizations has become more widespread over the last decade for solving convection-dominated computational fluid dynamics problems. The appeal of these methods relates to their favorable asymptotic accuracy properties, combined with compact stencils and favorable scalability properties on parallel computing architectures. This work covers advances in several areas of high-order DG discretizations, including the development of implicit solvers, discrete adjoint methods for shape optimization, and output-based error estimation and mesh and time-step adaptation. For time-dependent problems, high-order implicit time-integration schemes are considered exclusively to avoid the stability restrictions of explicit methods, with particular emphasis on balancing spatial and temporal accuracy of the overall approach. In order to make the high-order schemes competitive, efficient solution techniques consisting of a p -multigrid approach driven by element Jacobi smoothers are investigated and developed to accelerate convergence of the non-linear systems, in which the results demonstrate h independent convergence rates, while remaining relatively insensitive to time-step sizes. A framework based on discrete adjoint sensitivity analysis has also been developed for applications in shape optimization and goal-oriented error estimation. An adaptive discontinuous Galerkin algorithm driven by an adjoint-based error estimation procedure has been developed, which incorporates both h-, p- and combined hp -adaptive schemes, for producing accurate simulations at optimal cost in the objective functional of interest. Current results show superior performance of these adaptive schemes over uniform mesh refinement methods, as well as the potential of the hp refinement approach to capture strong shocks without limiters. Finally, the adjoint-based error estimation strategy is successfully extended to unsteady flow problems, where the time-dependent flow solution is solved in a forward manner in time but the corresponding unsteady adjoint solution is evaluated as a backward time integration. Results demonstrate that this methodology provides accurate global temporal error prediction, and may be employed to drive an adaptive time-step refinement strategy for improving the accuracy of specified time-dependent functionals of interest.

Adaptive High-order Methods in Computational Fluid Dynamics

Author : Z. J. Wang
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 Methods for Computational Physics

Author : Timothy J. Barth
Publisher : Springer Science & Business Media
ISBN 13 : 366203882X
Total Pages : 594 pages
Book Rating : 4.6/5 (62 download)

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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.

An Adaptive Discontinuous Galerkin Solver for Aerodynamic Flows

Author : Nicholas K. Burgess
Publisher :
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.

Discontinuous Galerkin Methods

Author : Bernardo Cockburn
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.

Efficient High-Order Discretizations for Computational Fluid Dynamics

Author : Martin Kronbichler
Publisher : Springer Nature
ISBN 13 : 3030606104
Total Pages : 314 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Efficient High-Order Discretizations for Computational Fluid Dynamics by : Martin Kronbichler

Download or read book Efficient High-Order Discretizations for Computational Fluid Dynamics written by Martin Kronbichler and published by Springer Nature. This book was released on 2021-01-04 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces modern high-order methods for computational fluid dynamics. As compared to low order finite volumes predominant in today's production codes, higher order discretizations significantly reduce dispersion errors, the main source of error in long-time simulations of flow at higher Reynolds numbers. A major goal of this book is to teach the basics of the discontinuous Galerkin (DG) method in terms of its finite volume and finite element ingredients. It also discusses the computational efficiency of high-order methods versus state-of-the-art low order methods in the finite difference context, given that accuracy requirements in engineering are often not overly strict. The book mainly addresses researchers and doctoral students in engineering, applied mathematics, physics and high-performance computing with a strong interest in the interdisciplinary aspects of computational fluid dynamics. It is also well-suited for practicing computational engineers who would like to gain an overview of discontinuous Galerkin methods, modern algorithmic realizations, and high-performance implementations.

Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows

Author : Murat Uzunca
Publisher : Birkhäuser
ISBN 13 : 3319301306
Total Pages : 111 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows by : Murat Uzunca

Download or read book Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows written by Murat Uzunca and published by Birkhäuser. This book was released on 2016-05-17 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way. After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence.As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.

High-order (hybridized) Discontinuous Galerkin Method for Geophysical Flows

Author : Shinhoo Kang
Publisher :
ISBN 13 :
Total Pages : 384 pages
Book Rating : 4.:/5 (112 download)

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Book Synopsis High-order (hybridized) Discontinuous Galerkin Method for Geophysical Flows by : Shinhoo Kang

Download or read book High-order (hybridized) Discontinuous Galerkin Method for Geophysical Flows written by Shinhoo Kang and published by . This book was released on 2019 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: As computational research has grown, simulation has become a standard tool in many fields of academic and industrial areas. For example, computational fluid dynamics (CFD) tools in aerospace and research facilities are widely used to evaluate the aerodynamic performance of aircraft or wings. Weather forecasts are highly dependent on numerical weather prediction (NWP) model. However, it is still difficult to simulate the complex physical phenomena of a wide range of length and time scales with modern computational resources. In this study, we develop a robust, efficient and high-order accurate numerical methods and techniques to tackle the challenges. First, we use high-order spatial discretization using (hybridized) discontinuous Galerkin (DG) methods. The DG method combines the advantages of finite volume and finite element methods. As such, it is well-suited to problems with large gradients including shocks and with complex geometries, and large-scale simulations. However, DG typically has many degrees-of-freedoms. To mitigate the expense, we use hybridized DG (HDG) method that introduces new “trace unknowns” on the mesh skeleton (mortar interfaces) to eliminate the local “volume unknowns” with static condensation procedure and reduces globally coupled system when implicit time-stepping is required. Also, since the information between the elements is exchanged through the mesh skeleton, the mortar interfaces can be used as a glue to couple multi-phase regions, e.g., solid and fluid regions, or non-matching grids, e.g., a rotating mesh and a stationary mesh. That is the HDG method provides an efficient and flexible coupling environment compared to standard DG methods. Second, we develop an HDG-DG IMEX scheme for an efficient time integrating scheme. The idea is to divide the governing equations into stiff and nonstiff parts, implicitly treat the former with HDG methods, and explicitly treat the latter with DG methods. The HDG-DG IMEX scheme facilitates high-order temporal and spatial solutions, avoiding too small a time step. Numerical results show that the HDG-DG IMEX scheme is comparable to an explicit Runge-Kutta DG scheme in terms of accuracy while allowing for much larger timestep sizes. We also numerically observe that IMEX HDG-DG scheme can be used as a tool to suppress the high-frequency modes such as acoustic waves or fast gravity waves in atmospheric or ocean models. In short, IMEX HDG-DG methods are attractive for applications in which a fast and stable solution is important while permitting inaccurate processing of the fast modes. Third, we also develop an EXPONENTIAL DG scheme for an efficient time integrators. Similar to the IMEX method, the governing equations are separated into linear and nonlinear parts, then the two parts are spatially discretized with DG methods. Next, we analytically integrate the linear term and approximate the nonlinear term with respect to time. This method accurately handles the fast wave modes in the linear operator. To efficiently evaluate a matrix exponential, we employ the cutting-edge adaptive Krylov subspace method. Finally, we develop a sliding-mesh interface by combining nonconforming treatment and the arbitrary Lagrangian-Eulerian (ALE) scheme for simulating rotating flows, which are important to estimate the characteristics of a rotating wind turbine or understanding vortical structures shown in atmospheric or astronomical phenomena. To integrate the rotating motion of the domain, we use the ALE formulation to map the governing equation to the stationary reference domain and introduce mortar interfaces between the stationary mesh and the rotating mesh. The mortar structure on the sliding interface changes dynamically as the mesh rotates

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

Author : Norbert Kroll
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.

A Time-spectral Hybridizable Discontinuous Galerkin Method for Periodic Flow Problems

Author : Hemant Kumar Chaurasia
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis A Time-spectral Hybridizable Discontinuous Galerkin Method for Periodic Flow Problems by : Hemant Kumar Chaurasia

Download or read book A Time-spectral Hybridizable Discontinuous Galerkin Method for Periodic Flow Problems written by Hemant Kumar Chaurasia and published by . This book was released on 2014 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulations of time-periodic flows are an essential design tool for a wide range of engineered systems, including jet engines, wind turbines and flapping wings. Conventional solvers for time-periodic flows are limited in accuracy and efficiency by the low-order Finite Volume and time-marching methods they typically employ. These methods introduce significant numerical dissipation in the simulated flow, and can require hundreds of timesteps to describe a periodic flow with only a few harmonic modes. However, recent developments in high-order methods and Fourier-based time discretizations present an opportunity to greatly improve computational performance. This thesis presents a novel Time-Spectral Hybridizable Discontinuous Galerkin (HDG) method for periodic flow problems, together with applications to flow through cascades and rotor/stator assemblies in aeronautical turbomachinery. The present work combines a Fourier-based Time-Spectral discretization in time with an HDG discretization in space, realizing the dual benefits of spectral accuracy in time and high-order accuracy in space. Low numerical dissipation and favorable stability properties are inherited from the high-order HDG method, together with a reduced number of globally coupled degrees of freedom compared to other DG methods. HDG provides a natural framework for treating boundary conditions, which is exploited in the development of a new high-order sliding mesh interface coupling technique for multiple-row turbomachinery problems. A regularization of the Spalart-Allmaras turbulence model is also employed to ensure numerical stability of unsteady flow solutions obtained with high-order methods. Turning to the temporal discretization, the Time-Spectral method enables direct solution of a periodic flow state, bypasses initial transient behavior, and can often deliver substantial savings in computational cost compared to implicit time-marching. An important driver of computational efficiency is the ability to select and resolve only the most important frequencies of a periodic problem, such as the blade-passing frequencies in turbomachinery flows. To this end, the present work introduces an adaptive frequency selection technique, using the Time-Spectral residual to form an inexpensive error indicator. Having selected a set of frequencies, the accuracy of the Time-Spectral solution is greatly improved by using optimally selected collocation points in time. For multi-domain problems such as turbomachinery flows, an anti-aliasing filter is also needed to avoid errors in the transfer of the solution across the sliding interface. All of these aspects contribute to the Adaptive Time-Spectral HDG method developed in this thesis. Performance characteristics of the method are demonstrated through applications to periodic ordinary differential equations, a convection problem, laminar flow over a pitching airfoil, and turbulent flow through a range of single- and multiple-row turbomachinery configurations. For a 2:1 rotor/stator flow problem, the Adaptive Time-Spectral HDG method correctly identifies the relevant frequencies in each blade row. This leads to an accurate periodic flow solution with greatly reduced computational cost, when compared to sequentially selected frequencies or a time-marching solution. For comparable accuracy in prediction of rotor loading, the Adaptive Time- Spectral HDG method incurs 3 times lower computational cost (CPU time) than time-marching, and for prediction of only the 1st harmonic amplitude, these savings rise to a factor of 200. Finally, in three-row compressor flow simulations, a high-order HDG method is shown to achieve significantly greater accuracy than a lower-order method with the same computational cost. For example, considering error in the amplitude of the 1st harmonic mode of total rotor loading, a p = 1 computation results in 20% error, in contrast to only 1% error in a p = 4 solution with comparable cost. This highlights the benefits that can be obtained from higher-order methods in the context of turbomachinery flow problems.

Computational Fluid Dynamics 2010

Author : Alexander Kuzmin
Publisher : Springer Science & Business Media
ISBN 13 : 3642178847
Total Pages : 902 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Computational Fluid Dynamics 2010 by : Alexander Kuzmin

Download or read book Computational Fluid Dynamics 2010 written by Alexander Kuzmin and published by Springer Science & Business Media. This book was released on 2011-05-03 with total page 902 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Computational Fluid Dynamics is held every two years and brings together physicists, mathematicians and engineers to review and share recent advances in mathematical and computational techniques for modeling fluid flow. The proceedings of the 2010 conference (ICCFD6) held in St Petersburg, Russia, contain a selection of refereed contributions and are meant to serve as a source of reference for all those interested in the state of the art in computational fluid dynamics.

An Adaptive Space-time Discontinuous Galerkin Method for Reservoir Flows

Author : Yashod Savithru Jayasinghe
Publisher :
ISBN 13 :
Total Pages : 216 pages
Book Rating : 4.:/5 (112 download)

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Book Synopsis An Adaptive Space-time Discontinuous Galerkin Method for Reservoir Flows by : Yashod Savithru Jayasinghe

Download or read book An Adaptive Space-time Discontinuous Galerkin Method for Reservoir Flows written by Yashod Savithru Jayasinghe and published by . This book was released on 2018 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation has become a vital tool for predicting engineering quantities of interest in reservoir flows. However, the general lack of autonomy and reliability prevents most numerical methods from being used to their full potential in engineering analysis. This thesis presents work towards the development of an efficient and robust numerical framework for solving reservoir flow problems in a fully-automated manner. In particular, a space-time discontinuous Galerkin (DG) finite element method is used to achieve a high-order discretization on a fully unstructured space-time mesh, instead of a conventional time-marching approach. Anisotropic mesh adaptation is performed to reduce the error of a specified output of interest, by using a posteriori error estimates from the dual weighted residual method to drive a metric-based mesh optimization algorithm. An analysis of the adjoint equations, boundary conditions and solutions of the Buckley-Leverett and two-phase flow equations is presented, with the objective of developing a theoretical understanding of the adjoint behaviors of porous media models. The intuition developed from this analysis is useful for understanding mesh adaptation behaviors in more complex flow problems. This work also presents a new bottom-hole pressure well model for reservoir simulation, which relates the volumetric flow rate of the well to the reservoir pressure through a distributed source term that is independent of the discretization. Unlike Peaceman-type models which require the definition of an equivalent well-bore radius dependent on local grid length scales, this distributed well model is directly applicable to general discretizations on unstructured meshes. We show that a standard DG diffusive flux discretization of the two-phase flow equations in mass conservation form results in an unstable semi-discrete system in the advection-dominant limit, and hence propose modifications to linearly stabilize the discretization. Further, an artificial viscosity method is presented for the Buckley-Leverett and two-phase flow equations, as a means of mitigating Gibbs oscillations in high-order discretizations and ensuring convergence to physical solutions. Finally, the proposed adaptive solution framework is demonstrated on compressible two-phase flow problems in homogeneous and heterogeneous reservoirs. Comparisons with conventional time-marching methods show that the adaptive space-time DG method is significantly more efficient at predicting output quantities of interest, in terms of degrees-of-freedom required, execution time and parallel scalability.

ADIGMA – A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications

Author : Norbert Kroll
Publisher : Springer Science & Business Media
ISBN 13 : 3642037070
Total Pages : 498 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis ADIGMA – A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications by : Norbert Kroll

Download or read book ADIGMA – A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications written by Norbert Kroll and published by Springer Science & Business Media. This book was released on 2010-09-18 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains results gained from the EU-funded 6th Framework project ADIGMA (Adaptive Higher-order Variational Methods for Aerodynamic Applications in Industry). The goal of ADIGMA was the development and utilization of innovative adaptive higher-order methods for the compressible flow equations enabling reliable, mesh independent numerical solutions for large-scale aerodynamic applications in aircraft industry. The ADIGMA consortium was comprised of 22 organizations which included the main European aircraft manufacturers, the major European research establishments and several universities, all with well proven expertise in Computational Fluid Dynamics (CFD). The book presents an introduction to the project, exhibits partners’ methods and approaches and provides a critical assessment of the newly developed methods for industrial aerodynamic applications. The best numerical strategies for integration as major building blocks for the next generation of industrial flow solvers are identified.

An Adaptive High Order Discontinuous Galerkin Method with Error Control for the Hamilton-Jacobi Equations

Author : Yanlai Chen
Publisher :
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis An Adaptive High Order Discontinuous Galerkin Method with Error Control for the Hamilton-Jacobi Equations by : Yanlai Chen

Download or read book An Adaptive High Order Discontinuous Galerkin Method with Error Control for the Hamilton-Jacobi Equations written by Yanlai Chen and published by . This book was released on 2007 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Error Control, Adaptive Discretizations, and Applications, Part 1

Author :
Publisher : Elsevier
ISBN 13 : 0443294488
Total Pages : 430 pages
Book Rating : 4.4/5 (432 download)

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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 2024-06-21 with total page 430 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.

Robust and Accurate Shock-capturing in Discontinuous Galerkin Discretizations

Author : Jae Hwan Choi
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (113 download)

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Book Synopsis Robust and Accurate Shock-capturing in Discontinuous Galerkin Discretizations by : Jae Hwan Choi

Download or read book Robust and Accurate Shock-capturing in Discontinuous Galerkin Discretizations written by Jae Hwan Choi and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Fluid Dynamics (CFD) has become a critical component in analyzing fluid flows and designing industrial products. Among various numerical methods in CFD, second-order numerical schemes have been widely used in both industry and academia. Second-order methods are robust enough to use on complex geometries and usually provide a sufficient amount of accuracy in flow simulations. However, second-order accurate solutions may not be sufficient for many aerodynamic applications such as vortex flows, Large Eddy Simulations (LES), and aeroacoustics problems. As a consequence, researchers have sought high-order numerical methods to simulate complex flows with low dissipation over the past few decades. Many approaches have been suggested including Finite Difference (FD), Finite Volume (FV), and Finite Element (FE) frameworks for CFD. In the group of high-order methods, discontinuous Galerkin (DG) methods have become popular in academia because of their distinctive benefits. For DG methods, high-order accuracy in flow solutions can be easily achieved by just adding more degrees of freedom in each element. Furthermore, DG methods are well suited to modern computer hardware, even on GPUs, due to high arithmetic intensity and the locality of operations. Despite their numerous benefits, DG methods are not widely adopted because of some remaining challenges, especially in industry. One of these difficulties is shock-capturing. Similarly to other numerical methods in CFD, DG methods also suffer from spurious oscillations if discontinuities arise during flow simulations. The accuracy of solutions will degrade significantly, or solutions may diverge unless these discontinuities are captured appropriately. Therefore, a shock-capturing capability becomes necessary for DG methods to simulate compressible flows with shocks. In this work, robust and accurate shock-capturing approaches for DG methods will be demonstrated. To precisely capture various strengths of shocks, a simple shock-detector is first proposed for DG discretizations, which only relies on local flow information. Additionally, filtering strengths are precalculated to avoid parameter tuning procedures and are optimized to achieve maximum accuracy while capturing shocks. The proposed methods are then applied to two- and three-dimensional canonical problems to demonstrate the shock-capturing capabilities of the proposed methods.

Fast and Scalable Solvers for High-order Hybridized Discontinuous Galerkin Methods with Applications to Fluid Dynamics and Magnetohydrodynamics

Download Fast and Scalable Solvers for High-order Hybridized Discontinuous Galerkin Methods with Applications to Fluid Dynamics and Magnetohydrodynamics PDF Online Free

Author : Sriramkrishnan Muralikrishnan
Publisher :
ISBN 13 :
Total Pages : 498 pages
Book Rating : 4.:/5 (112 download)

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Book Synopsis Fast and Scalable Solvers for High-order Hybridized Discontinuous Galerkin Methods with Applications to Fluid Dynamics and Magnetohydrodynamics by : Sriramkrishnan Muralikrishnan

Download or read book Fast and Scalable Solvers for High-order Hybridized Discontinuous Galerkin Methods with Applications to Fluid Dynamics and Magnetohydrodynamics written by Sriramkrishnan Muralikrishnan and published by . This book was released on 2019 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: The hybridized discontinuous Galerkin methods (HDG) introduced a decade ago is a promising candidate for high-order spatial discretization combined with implicit/implicit-explicit time stepping. Roughly speaking, HDG methods combines the advantages of both discontinuous Galerkin (DG) methods and hybridized methods. In particular, it enjoys the benefits of equal order spaces, upwinding and ability to handle large gradients of DG methods as well as the smaller globally coupled linear system, adaptivity, and multinumeric capabilities of hybridized methods. However, the main bottleneck in HDG methods, limiting its use to small to moderate sized problems, is the lack of scalable linear solvers. In this thesis we develop fast and scalable solvers for HDG methods consisting of domain decomposition, multigrid and multilevel solvers/preconditioners with an ultimate focus on simulating large scale problems in fluid dynamics and magnetohydrodynamics (MHD). First, we propose a domain decomposition based solver namely iterative HDG for partial differential equations (PDEs). It is a fixed point iterative scheme, with each iteration consisting only of element-by-element and face-by-face embarrassingly parallel solves. Using energy analysis we prove the convergence of the schemes for scalar and system of hyperbolic PDEs and verify the results numerically. We then propose a novel geometric multigrid approach for HDG methods based on fine scale Dirichlet-to-Neumann maps. The algorithm combines the robustness of algebraic multigrid methods due to operator dependent intergrid transfer operators and at the same time has fixed coarse grid construction costs due to its geometric nature. For diffusion dominated PDEs such as the Poisson and the Stokes equations the algorithm gives almost perfect hp--scalability. Next, we propose a multilevel algorithm by combining the concepts of nested dissection, a fill-in reducing ordering strategy, variational structure and high-order properties of HDG, and domain decomposition. Thanks to its root in direct solver strategy the performance of the solver is almost independent of the nature of the PDEs and mostly depends on the smoothness of the solution. We demonstrate this numerically with several prototypical PDEs. Finally, we propose a block preconditioning strategy for HDG applied to incompressible visco-resistive MHD. We use a least squares commutator approximation for the inverse of the Schur complement and algebraic multigrid or the multilevel preconditioner for the approximate inverse of the nodal block. With several 2D and 3D transient examples we demonstrate the robustness and parallel scalability of the block preconditioner