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Anisotropic hp-Mesh Adaptation Methods

Author: Vít Dolejší

Publisher: Springer Nature

Published: 2022-06-06

Total Pages: 258

ISBN-13: 3031042794

Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations. If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods. A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques. This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.

Unstructured Anisotropic All-quad Mesh Adaptation Based on a Continuous Local Error Model for the Discontinuous Galerkin Method

Author: Keigan MacLean

Publisher:

Published: 2021

Total Pages:

ISBN-13:

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"This thesis will present a method of unstructured anisotropic adaptation for all-quad mesh suitable for use with high-order methods. The overall goal is to minimize the computational cost needed to perform highly accurate Computational Fluid Dynamics (CFD) simulations. With adaptive methods this can be accomplished through modifying the underlying spatial discretization of the domain. Here, this will be tailored to the particular problem at hand through a continuous local error model. In this form, the physical mesh geometry is replaced by the notion of a frame field, allowing us to extend previous ideas from metric-based adaptation methods. This will serve as a means to restate the discrete error minimization problem in order to determine the target element size and shape based on an optimal distribution of degrees of freedom.Furthermore, the goal of most CFD simulations is to measure some particular output of interest (e.g. such as lift or drag). Therefore, extensions to the method will be examined for goal-oriented adaptation. This involves using the adjoint problem solution and dual-weighted residuals to target mesh refinement in areas most crucial to the accuracy of these measurements.Finally, this work will also consider the implementation of a fully unstructured and anisotropic all-quad mesh generator capable of conforming to the aforementioned target elements. Here, the procedure is based on an Lp-CVT energy minimization problem used to determine updated node positions. Overall, this work will combine each of these aspects in order to establish a complete adaptive framework for use in solving high-order problems with the Discontinuous Galerkin method"--

Anisotropic Mesh Adaptation for Transient Problems and Functional-output Variables

Author: Mostafa Najafiyazdi

Publisher:

Published: 2011

Total Pages:

ISBN-13:

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L'adaptation de maillage est la modification d'un maillage existant afin de saisir avec précision les phénomènes physiques sans augmentation excessive du coût de calcul. Parmi les nombreux défis qui demeurent dans ce domaine, l'adaptation de maillage de manière instable et l'adaptation de maillage selon un ± functional-output » sont les deux thèmes abordés dans ce travail. La méthode ± Transient-Fixed-point » est une nouvelle approche pour l'adaptation de maillage de manière instable. Cette méthode consiste à formée un lien entre le maillage et la solution. Ce qui différencie la méthode ± Transient-Fixed-point » de méthodes d'adaptation constante est l'intersection des métriques à travers le temps. Dans cet ouvrage, un nouveau régime pour l'intersection de métriques transitoire est proposé afin de préserver l'orthogonalité des données. Un autre défi de l'adaptation de maillage est de contrôler les modifications apporté à la ...

Mesh Adaptation for Computational Fluid Dynamics, Volume 2

Author: Alain Dervieux

Publisher: John Wiley & Sons

Published: 2022-09-21

Total Pages: 244

ISBN-13: 1786308320

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Simulation technology, and computational fluid dynamics (CFD) in particular, is essential in the search for solutions to the modern challenges faced by humanity. Revolutions in CFD over the last decade include the use of unstructured meshes, permitting the modeling of any 3D geometry. New frontiers point to mesh adaptation, allowing not only seamless meshing (for the engineer) but also simulation certification for safer products and risk prediction. Mesh Adaptation for Computational Dynamics 2 is the second of two volumes and introduces topics including optimal control formulation, minimizing a goal function, and extending the steady algorithm to unsteady physics. Also covered are multi-rate strategies, steady inviscid flows in aeronautics and an extension to viscous flows. This book will be useful to anybody interested in mesh adaptation pertaining to CFD, especially researchers, teachers and students.

Mesh Adaptation for Computational Fluid Dynamics, Volume 1

Author: Alain Dervieux

Publisher: John Wiley & Sons

Published: 2022-08-30

Total Pages: 260

ISBN-13: 1394163983

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Simulation technology, and computational fluid dynamics (CFD) in particular, is essential in the search for solutions to the modern challenges faced by humanity. Revolutions in CFD over the last decade include the use of unstructured meshes, permitting the modeling of any 3D geometry. New frontiers point to mesh adaptation, allowing not only seamless meshing (for the engineer) but also simulation certification for safer products and risk prediction. Mesh Adaptation for Computational Dynamics 1 is the first of two volumes and introduces basic methods such as feature-based and multiscale adaptation for steady models. Also covered is the continuous Riemannian metrics formulation which models the optimally adapted mesh problem into a pure partial differential statement. A number of mesh adaptative methods are defined based on a particular feature of the simulation solution. This book will be useful to anybody interested in mesh adaptation pertaining to CFD, especially researchers, teachers and students.

Two-dimensional, Three-dimensional and Four-dimensional Anisotropic Mesh Adaptation for the Time-continuous Space-time Finite Element Method with Applications to the Incompressible Navier-Stokes Equations

Author: Pascal Tremblay

Publisher:

Published: 2007

Total Pages: 544

ISBN-13:

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3D Anisotropic Mesh Adaptation for Reynolds Averaged Navier-Stokes Simulations

Author: Loïc Frazza

Publisher:

Published: 2018

Total Pages: 0

ISBN-13:

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The fast and reliable simulation of turbulent flow using Reynolds Averaged Navier Stokes (RANS) models is a major financial issue for many industries. With the increasing complexity of geometries and simulated flows, as well as requirements in terms of fidelity, the generation of appropriate meshes has become a key link in the chain of computation. We show in this thesis the ability of modern numerical schemes to simulate turbulent flows on fully unstructured meshes generated automatically using mesh adaptation methods. We present the implementation of different versions of the Spalart-Allmaras model as well as the numerical choices guaranteeing a sufficient robustness of the solver in order to not require a structured boundary layer. We then introduce the error analysis necessary to propose different error estimators for mesh optimization. This methodology is tested on various external aerodynamic and turbomachinery test cases and compared to traditional mesh generation methods. We show the ability of mesh adaptation methods to automatically generate optimal mesh sizes for RANS simulations on realistic and complex geometries.

Fast Solvers for Mesh-Based Computations

Author: Maciej Paszynski

Publisher: CRC Press

Published: 2016-01-05

Total Pages: 350

ISBN-13: 1498754201

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Fast Solvers for Mesh-Based Computations presents an alternative way of constructing multi-frontal direct solver algorithms for mesh-based computations. It also describes how to design and implement those algorithms.The book's structure follows those of the matrices, starting from tri-diagonal matrices resulting from one-dimensional mesh-based meth

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1

Author: Jens M. Melenk

Publisher: Springer Nature

Published: 2023-06-30

Total Pages: 571

ISBN-13: 3031204328

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The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles cover state of the art topics in high order discretizations of partial differential equations. The volume presents a wide range of topics including the design and analysis of high order methods, the development of fast solvers on modern computer architecture, and the application of these methods in fluid and structural mechanics computations.

Error Control, Adaptive Discretizations, and Applications, Part 1

Author:

Publisher: Elsevier

Published: 2024-06-29

Total Pages: 446

ISBN-13: 0443294496

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Error Control, Adaptive Discretizations, and Applications, Volume 58, Part One highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems, An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations. Covers multi-scale modeling Includes updates on data-driven modeling Presents the latest information on large deformations of multi-scale materials