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Author: Carmen-Ioana Ursachi Publisher: ISBN: Category : Languages : en Pages : 87
Book Description
Higher-order methods in computational fluid dynamics have the potential to provide accurate solutions at lower computational costs than traditional methods. Obtaining accurate flow solutions requires the use of computational meshes that resolve relevant solution features, but generating such meshes a priori is difficult. In this thesis, the effects of adaptivity and discretization order are studied on the solutions of a 2D multi-element high-lift airfoil test case. The flow in this test case is simulated by the RANS equations and Spalart-Allmaras turbulence model. Numerical flow solutions are obtained using both stabilized continuous Galerkin and discontinuous Galerkin finite element frameworks. For both discretizations, a series of increasingly refined adapted meshes are generated using the Metric Optimization via Error Sampling and Synthesis algorithm. The convergence of aerodynamic coefficients, surface pressure, and skin friction on these meshes are studied in order to evaluate the accuracy and cost of the solution. This study is done for several discretization orders, and for both linear and curved meshes. In addition, the characteristics of the adapted meshes for different discretization orders are investigated at a prescribed error level. This analysis provides insight into how the discretization order affects the mesh, along with the resulting solution accuracy and cost. The conclusions of this study indicate that higher-order methods, in particular the p = 2 and p = 3 Continuous Galerkin Variational Multi-Scale with Discontinuous subscales discretizations, provide accurate outputs with an order of magnitude less computational time than p = 1 methods.
Author: Carmen-Ioana Ursachi Publisher: ISBN: Category : Languages : en Pages : 87
Book Description
Higher-order methods in computational fluid dynamics have the potential to provide accurate solutions at lower computational costs than traditional methods. Obtaining accurate flow solutions requires the use of computational meshes that resolve relevant solution features, but generating such meshes a priori is difficult. In this thesis, the effects of adaptivity and discretization order are studied on the solutions of a 2D multi-element high-lift airfoil test case. The flow in this test case is simulated by the RANS equations and Spalart-Allmaras turbulence model. Numerical flow solutions are obtained using both stabilized continuous Galerkin and discontinuous Galerkin finite element frameworks. For both discretizations, a series of increasingly refined adapted meshes are generated using the Metric Optimization via Error Sampling and Synthesis algorithm. The convergence of aerodynamic coefficients, surface pressure, and skin friction on these meshes are studied in order to evaluate the accuracy and cost of the solution. This study is done for several discretization orders, and for both linear and curved meshes. In addition, the characteristics of the adapted meshes for different discretization orders are investigated at a prescribed error level. This analysis provides insight into how the discretization order affects the mesh, along with the resulting solution accuracy and cost. The conclusions of this study indicate that higher-order methods, in particular the p = 2 and p = 3 Continuous Galerkin Variational Multi-Scale with Discontinuous subscales discretizations, provide accurate outputs with an order of magnitude less computational time than p = 1 methods.
Author: Todd A. Oliver Publisher: ISBN: Category : Languages : en Pages : 182
Book Description
This thesis presents high-order, discontinuous Galerkin (DG) discretizations of the Reynolds-Averaged Navier-Stokes (RANS) equations and an output-based error estimation and mesh adaptation algorithm for these discretizations. In particular, DG discretizations of the RANS equations with the Spalart-Allmaras (SA) turbulence model are examined. The dual consistency of multiple DG discretizations of the RANS-SA system is analyzed. The approach of simply weighting gradient dependent source terms by a test function and integrating is shown to be dual inconsistent. A dual consistency correction for this discretization is derived. The analysis also demonstrates that discretizations based on the popular mixed formulation, where dependence on the state gradient is handled by introducing additional state variables, are generally asymptotically dual consistent. Numerical results are presented to confirm the results of the analysis. The output error estimation and output-based adaptation algorithms used here are extensions of methods previously developed in the finite volume and finite element communities. In particular, the methods are extended for application on the curved, highly anisotropic meshes required for boundary conforming, high-order RANS simulations. Two methods for generating such curved meshes are demonstrated. One relies on a user-defined global mapping of the physical domain to a straight meshing domain. The other uses a linear elasticity node movement scheme to add curvature to an initially linear mesh. Finally, to improve the robustness of the adaptation process, an "unsteady" algorithm, where the mesh is adapted at each time step, is presented. The goal of the unsteady procedure is to allow mesh adaptation prior to converging a steady state solution, not to obtain a time-accurate solution of an unsteady problem. Thus, an estimate of the error due to spatial discretization in the output of interest averaged over the current time step is developed. This error estimate is then used to drive an h-adaptation algorithm. Adaptation results demonstrate that the high-order discretizations are more efficient than the second-order method in terms of degrees of freedom required to achieve a desired error tolerance. Furthermore, using the unsteady adaptation process, adaptive RANS simulations may be started from extremely coarse meshes, significantly decreasing the mesh generation burden to the user.
Author: Publisher: Elsevier ISBN: 0443294496 Category : Science Languages : en Pages : 446
Book Description
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
Author: James M. Modisette Publisher: ISBN: Category : Languages : en Pages : 180
Book Description
The development of computational fluid dynamics algorithms and increased computational resources have led to the ability to perform complex aerodynamic simulations. Obstacles remain which prevent autonomous and reliable simulations at accuracy levels required for engineering. To consider the solution strategy autonomous and reliable, high quality solutions must be provided without user interaction or detailed previous knowledge about the flow to facilitate either adaptation or solver robustness. One such solution strategy is presented for two-dimensional Reynolds-averaged Navier-Stokes (RANS) flows and is based on: a higher-order discontinuous Galerkin finite element method which enables higher accuracy with fewer degrees of freedom than lower-order methods; an output-based error estimation and adaptation scheme which provides quantifiable measure of solution accuracy and autonomously drives toward an improved discretization; a non-linear solver technique based on pseudo-time continuation and line-search update limiting which improves the robustness for solutions to the RANS equations; and a simplex cut-cell mesh generation which autonomously provides higher-order meshes of complex geometries. The simplex cut-cell mesh generation method presented here extends methods previously developed to improve robustness with the goal of RANS simulations. In particular, analysis is performed to expose the impact of small volume ratios between arbitrarily cut elements on linear system conditioning and solution quality. Merging of the small cut element into its larger neighbor is identified as a solution to alleviate the consequences of small volume ratios. For arbitrarily cut elements randomness in the algorithm for generating integration rules is identified as a limiting factor for accuracy and recognition of canonical element shapes are introduced to remove the randomness. The cut-cell method is linked with line-search based update limiting for improved non-linear solver robustness and Riemannian metric based anisotropic adaptation to efficiently resolve anisotropic features with arbitrary orientations in RANS flows. A fixed-fraction marking strategy is employed to redistribute element areas and steps toward meshes which equidistribute elemental errors at a fixed degree of freedom. The benefit of the higher spatial accuracy and the solution efficiency (defined as accuracy per degree of freedom) is exhibited for a wide range of RANS applications including subsonic through supersonic flows. The higher-order discretizations provide more accurate solutions than second-order methods at the same degree of freedom. Furthermore, the cut-cell meshes demonstrate comparable solution efficiency to boundary-conforming meshes while significantly decreasing the burden of mesh generation for a CFD user.
Author: Rémi Abgrall Publisher: Springer ISBN: 3319054554 Category : Mathematics Languages : en Pages : 220
Book Description
This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.
Author: E. Arge Publisher: Springer Science & Business Media ISBN: 9780817639747 Category : Computers Languages : en Pages : 400
Book Description
The purpose of this book is to survey some recent advances in the development of software tools for scientific computing. This book presents 17 carefully selected and refereed chapters originally presented at the SciTools '96 Workshop in Oslo, Norway. The chapters emphasize the design of large software codes, computational efficiency, object-oriented programming in scientific computing, reliability of numerical software, and parallel computing.
Author: Anders Logg Publisher: Springer Science & Business Media ISBN: 3642230997 Category : Computers Languages : en Pages : 723
Book Description
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Author: Omer San Publisher: MDPI ISBN: 3039364022 Category : Technology & Engineering Languages : en Pages : 302
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: Carmen-Ioana Ursachi
Author: Carmen-Ioana Ursachi
Author: Todd A. Oliver
Author: 
Author: James M. Modisette
Author: Rémi Abgrall
Author: E. Arge
Author: 
Author: Anders Logg
Author: 
Author: Omer San