An Adaptive Variational Multiscale Method with Discontinuous Subscales for Aerodynamic Flows PDF Download
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Author: Arthur Chan-wei Huang
Publisher:
ISBN:
Category :
Languages : en
Pages : 168
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Book Description
A promising methodology for accurate and efficient simulation of aerodynamic flows is output-based mesh adaptation, which optimizes a mesh to minimize the discretization error in an output of interest. The state of the art in output-based adaptation uses the discontinuous Galerkin (DG) method, which is computationally expensive due to its duplicated degrees of freedom. Existing continuous Galerkin (CG) methods require up to 20 times fewer degrees of freedom, but lack the combination of stability and adjoint consistency required for output-based adaptation. This thesis presents a novel high order continuous Galerkin method, which is both adjoint consistent and stable. The scheme, called Variational Multiscale with Discontinuous subscales (VMSD), models unresolved solution perturbations with a discontinuous representation. The solution discontinuities are then used to stabilize the problem using methods borrowed from discontinuous Galerkin methods. At the same time, the mathematical structure of the discretization allows for the elimination of additional degrees of freedom in a computationally efficient manner, so that the method has a linear system of the same size as a conventional CG discretization. Finally, because the scheme is adjoint consistent, accurate error estimates can be obtained for use in an output-based mesh adaptation process. In this work, the method is derived and its optimal properties demonstrated through analysis and numerical experiment. In particular, the thesis describes the integration of VMSD in a high order adaptive method, namely the Mesh Optimization via Error Sampling and Synthesis (MOESS) algorithm. Adaptive DG and VMSD are compared for 3D RANS simulations. The adaptive VMSD method is shown to produces solutions with the same drag error as the adaptive DG method, with a factor of 3-10 fewer globally coupled degrees of freedom, and an associated factor of three or more reduction in computation time.
Author: Arthur Chan-wei Huang
Publisher:
ISBN:
Category :
Languages : en
Pages : 168
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Book Description
A promising methodology for accurate and efficient simulation of aerodynamic flows is output-based mesh adaptation, which optimizes a mesh to minimize the discretization error in an output of interest. The state of the art in output-based adaptation uses the discontinuous Galerkin (DG) method, which is computationally expensive due to its duplicated degrees of freedom. Existing continuous Galerkin (CG) methods require up to 20 times fewer degrees of freedom, but lack the combination of stability and adjoint consistency required for output-based adaptation. This thesis presents a novel high order continuous Galerkin method, which is both adjoint consistent and stable. The scheme, called Variational Multiscale with Discontinuous subscales (VMSD), models unresolved solution perturbations with a discontinuous representation. The solution discontinuities are then used to stabilize the problem using methods borrowed from discontinuous Galerkin methods. At the same time, the mathematical structure of the discretization allows for the elimination of additional degrees of freedom in a computationally efficient manner, so that the method has a linear system of the same size as a conventional CG discretization. Finally, because the scheme is adjoint consistent, accurate error estimates can be obtained for use in an output-based mesh adaptation process. In this work, the method is derived and its optimal properties demonstrated through analysis and numerical experiment. In particular, the thesis describes the integration of VMSD in a high order adaptive method, namely the Mesh Optimization via Error Sampling and Synthesis (MOESS) algorithm. Adaptive DG and VMSD are compared for 3D RANS simulations. The adaptive VMSD method is shown to produces solutions with the same drag error as the adaptive DG method, with a factor of 3-10 fewer globally coupled degrees of freedom, and an associated factor of three or more reduction in computation time.
Author: Axel Målqvist
Publisher:
ISBN: 9789172916548
Category :
Languages : en
Pages : 13
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Book Description
Author: Volker John
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Ido Akkerman
Publisher:
ISBN: 9789079488421
Category :
Languages : en
Pages : 152
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Book Description
Author: Omer San
Publisher: MDPI
ISBN: 3039364022
Category : Technology & Engineering
Languages : en
Pages : 302
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Book Description
In recent decades, the field of computational fluid dynamics has made significant advances in enabling advanced computing architectures to understand many phenomena in biological, geophysical, and engineering fluid flows. Almost all research areas in fluids use numerical methods at various complexities: from molecular to continuum descriptions; from laminar to turbulent regimes; from low speed to hypersonic, from stencil-based computations to meshless approaches; from local basis functions to global expansions, as well as from first-order approximation to high-order with spectral accuracy. Many successful efforts have been put forth in dynamic adaptation strategies, e.g., adaptive mesh refinement and multiresolution representation approaches. Furthermore, with recent advances in artificial intelligence and heterogeneous computing, the broader fluids community has gained the momentum to revisit and investigate such practices. This Special Issue, containing a collection of 13 papers, brings together researchers to address recent numerical advances in fluid mechanics.
Author: Bernardo Cockburn
Publisher: Springer Science & Business Media
ISBN: 3642597211
Category : Mathematics
Languages : en
Pages : 468
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Book Description
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: A. Bruaset
Publisher: Springer Science & Business Media
ISBN: 1461219868
Category : Computers
Languages : en
Pages : 387
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Book Description
Looking back at the years that have passed since the realization of the very first electronic, multi-purpose computers, one observes a tremendous growth in hardware and software performance. Today, researchers and engi neers have access to computing power and software that can solve numerical problems which are not fully understood in terms of existing mathemati cal theory. Thus, computational sciences must in many respects be viewed as experimental disciplines. As a consequence, there is a demand for high quality, flexible software that allows, and even encourages, experimentation with alternative numerical strategies and mathematical models. Extensibil ity is then a key issue; the software must provide an efficient environment for incorporation of new methods and models that will be required in fu ture problem scenarios. The development of such kind of flexible software is a challenging and expensive task. One way to achieve these goals is to in vest much work in the design and implementation of generic software tools which can be used in a wide range of application fields. In order to provide a forum where researchers could present and discuss their contributions to the described development, an International Work shop on Modern Software Tools for Scientific Computing was arranged in Oslo, Norway, September 16-18, 1996. This workshop, informally referred to as Sci Tools '96, was a collaboration between SINTEF Applied Mathe matics and the Departments of Informatics and Mathematics at the Uni versity of Oslo.
Author: Carl Edward Rasmussen
Publisher: MIT Press
ISBN: 026218253X
Category : Computers
Languages : en
Pages : 266
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Book Description
A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
Author: Timothy J. Barth
Publisher: Springer Science & Business Media
ISBN: 3662051893
Category : Mathematics
Languages : en
Pages : 354
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Book Description
As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers.
Author: Jan S Hesthaven
Publisher: Springer
ISBN: 3319224700
Category : Mathematics
Languages : en
Pages : 139
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Book Description
This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
