Download or read book Adjoint based Error Estimation and Grid Adaptation for Functional Outputs from CFD Simulations written by Ravishankar Balasubramanian and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This study seeks to reduce the degree of uncertainty that often arises in computational fluid dynamics simulations about the computed accuracy of functional outputs. An error estimation methodology based on discrete adjoint sensitivity analysis is developed to provide a quantitative measure of the error in computed outputs. The developed procedure relates the local residual errors to the global error in output function via adjoint variables as weight functions. The three major steps in the error estimation methodology are: (1) development of adjoint sensitivity analysis capabilities; (2) development of an efficient error estimation procedure; (3) implementation of an output-based grid adaptive scheme. Each of these steps are investigated. For the first step, parallel discrete adjoint capabilities are developed for the variable Mach version of the U2NCLE flow solver. To compare and validate the implementation of adjoint solver, this study also develops direct sensitivity capabilities. A modification is proposed to the commonly used unstructured flux-limiters, specifically, those of Barth-Jespersen and Venkatakrishnan, to make them piecewise continuous and suitable for sensitivity analysis. A distributed-memory message-passing model is employed for the parallelization of sensitivity analysis solver and the consistency of linearization is demonstrated in sequential and parallel environments. In the second step, to compute the error estimates, the flow and adjoint solutions are prolongated from a coarse-mesh to a fine-mesh using the meshless Moving Least Squares (MLS) approximation. These error estimates are used as a correction to obtain highly-accurate functional outputs and as adaptive indicators in an iterative grid adaptive scheme to enhance the accuracy of the chosen output to a prescribed tolerance. For the third step, an output-based adaptive strategy that takes into account the error in both the primal (flow) and dual (adjoint) solutions is implemented. A second adaptive strategy based on physics-based feature detection is implemented to compare and demonstrate the robustness and effectiveness of the output-based adaptive approach. As part of the study, a general-element unstructured mesh adaptor employing h-refinement is developed using Python and C++. Error estimation and grid adaptation results are presented for inviscid, laminar and turbulent flows.
Download or read book ADJOINT BASED ERROR ESTIMATION AND GRID ADAPTATION FOR FUNCTIONAL OUTPUTS FROM CFD SIMULATIONS written by and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This study seeks to reduce the degree of uncertainty that often arises in computational fluid dynamics simulations about the computed accuracy of functional outputs. An error estimation methodology based on discrete adjoint sensitivity analysis is developed to provide a quantitative measure of the error in computed outputs. The developed procedure relates the local residual errors to the global error in output function via adjoint variables as weight functions. The three major steps in the error estimation methodology are: (1) development of adjoint sensitivity analysis capabilities; (2) development of an efficient error estimation procedure; (3) implementation of an output-based grid adaptive scheme. Each of these steps are investigated. For the first step, parallel discrete adjoint capabilities are developed for the variable Mach version of the U2NCLE flow solver. To compare and validate the implementation of adjoint solver, this study also develops direct sensitivity capabilities. A modification is proposed to the commonly used unstructured flux-limiters, specifically, those of Barth-Jespersen and Venkatakrishnan, to make them piecewise continuous and suitable for sensitivity analysis. A distributed-memory message-passing model is employed for the parallelization of sensitivity analysis solver and the consistency of linearization is demonstrated in sequential and parallel environments. In the second step, to compute the error estimates, the flow and adjoint solutions are prolongated from a coarse-mesh to a fine-mesh using the meshless Moving Least Squares (MLS) approximation. These error estimates are used as a correction to obtain highly-accurate functional outputs and as adaptive indicators in an iterative grid adaptive scheme to enhance the accuracy of the chosen output to a prescribed tolerance. For the third step, an output-based adaptive strategy that takes into account the error in both the primal (flow) and dual (adjoint) solutions is implemented. A secon.
Download or read book Error Estimation and Grid Adaptation for Functional Outputs Using Discrete adjoint Sensitivity Analysis written by Ravishankar Balsubramanian and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the design process, computational fluid dynamics is typically used to compute specific quantities that assess the performance of the apparatus under investigation. These quantities are usually integral output functions such as force and moment coefficients. However, to accurately model the configuration, the geometric features and the resulting physical phenomena must be adequately resolved. Due to limited computational resources a compromise must be made between the fidelity of the solution obtained and the available resources. This creates a degree of uncertainty about the error in the computed output functions. To this end, the current study attempts to address this problem for two-dimensional inviscid, incompressible flows on unstructured grids. The objective is to develop an error estimation and grid adaptive strategy for improving the accuracy of output functions from computational fluid dynamic codes. The present study employs a discrete adjoint formulation to arrive at the error estimates in which the global error in the output function is related to the local residual errors in the flow solution via adjoint variables as weighting functions. This procedure requires prolongation of the flow solution and adjoint solution from coarse to finer grids and, thus, different prolongation operators are studied to evaluate their influence on the accuracy of the error correction terms. Using this error correction procedure, two different adaptive strategies may be employed to enhance the accuracy of the chosen output to a prescribed tolerance. While both strategies strive to improve the accuracy of the computed output, the means by which the adaptation parameters are formed differ. The first strategy improves the computable error estimates by forming adaptation parameters based on the level of error in the computable error estimates. A grid adaptive scheme is then implemented that takes into account the error in both the primal and dual solutions. The second strategy uses the computable error estimates as indicators in an iterative grid adaptive scheme to generate grids that produce accurate estimates of the chosen output. Several test cases are provided to demonstrate the effectiveness and robustness of the error correction procedure and the grid adaptive methods.
Download or read book ERROR ESTIMATION AND GRID ADAPTATION FOR FUNCTIONAL OUTPUTS USING DISCRETE ADJOINT SENSITIVITY ANALYSIS written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the design process, computational fluid dynamics is typically used to compute specific quantities that assess the performance of the apparatus under investigation. These quantities are usually integral output functions such as force and moment coefficients. However, to accurately model the configuration, the geometric features and the resulting physical phenomena must be adequately resolved. Due to limited computational resources a compromise must be made between the fidelity of the solution obtained and the available resources. This creates a degree of uncertainty about the error in the computed output functions. To this end, the current study attempts to address this problem for two-dimensional inviscid, incompressible flows on unstructured grids. The objective is to develop an error estimation and grid adaptive strategy for improving the accuracy of output functions from computational fluid dynamic codes. The present study employs a discrete adjoint formulation to arrive at the error estimates in which the global error in the output function is related to the local residual errors in the flow solution via adjoint variables as weighting functions. This procedure requires prolongation of the flow solution and adjoint solution from coarse to finer grids and, thus, different prolongation operators are studied to evaluate their influence on the accuracy of the error correction terms. Using this error correction procedure, two different adaptive strategies may be employed to enhance the accuracy of the chosen output to a prescribed tolerance. While both strategies strive to improve the accuracy of the computed output, the means by which the adaptation parameters are formed differ. The first strategy improves the computable error estimates by forming adaptation parameters based on the level of error in the computable error estimates. A grid adaptive scheme is then implemented that takes into account the error in both the primal and dual solutions. The second stra.
Download or read book Opportunities for Breakthroughs in Large Scale Computational Simulation and Design written by and published by . This book was released on 2002 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Opportunities for breakthroughs in the large-scale computational simulation and design of aerospace vehicles are presented. Computational fluid dynamics tools to be used within multidisciplinary analysis and design methods are emphasized. The opportunities stem from speedups and robustness improvements in the underlying unit operations associated with simulation (geometry modeling, grid generation, physical modeling, analysis, etc.). Further, an improved programming environment can synergistically integrate these unit operations to leverage the gains. The speedups result from reducing the problem setup time through geometry modeling and grid generation operations, and reducing the solution time through the operation counts associated with solving the discretized equations to a sufficient accuracy. The opportunities are addressed only at a general level here, but an extensive list of references containing further details is included.
Download or read book Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics written by Timothy J. Barth and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book AIAA Journal written by American Institute of Aeronautics and Astronautics and published by . This book was released on 2004 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Uncertainty Management for Robust Industrial Design in Aeronautics written by Charles Hirsch and published by Springer. This book was released on 2018-07-21 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers cutting-edge findings related to uncertainty quantification and optimization under uncertainties (i.e. robust and reliable optimization), with a special emphasis on aeronautics and turbomachinery, although not limited to these fields. It describes new methods for uncertainty quantification, such as non-intrusive polynomial chaos, collocation methods, perturbation methods, as well as adjoint based and multi-level Monte Carlo methods. It includes methods for characterization of most influential uncertainties, as well as formulations for robust and reliable design optimization. A distinctive element of the book is the unique collection of test cases with prescribed uncertainties, which are representative of the current engineering practice of the industrial consortium partners involved in UMRIDA, a level 1 collaborative project within the European Commission's Seventh Framework Programme (FP7). All developed methods are benchmarked against these industrial challenges. Moreover, the book includes a section dedicated to Best Practice Guidelines for uncertainty quantification and robust design optimization, summarizing the findings obtained by the consortium members within the UMRIDA project. All in all, the book offers a authoritative guide to cutting-edge methodologies for uncertainty management in engineering design, covers a wide range of applications and discusses new ideas for future research and interdisciplinary collaborations.
Download or read book Grid quality Measures for Error Estimation and Solution adaptive Mesh Refinement in CFD written by Xubin Gu and published by . This book was released on 2002 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Engineering Optimization 2014 written by Hélder Rodrigues and published by CRC Press. This book was released on 2014-09-26 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern engineering processes and tasks are highly complex, multi- and interdisciplinary, requiring the cooperative effort of different specialists from engineering, mathematics, computer science and even social sciences. Optimization methodologies are fundamental instruments to tackle this complexity, giving the possibility to unite synergistically team members’ inputs and thus decisively contribute to solving new engineering technological challenges. With this context in mind, the main goal of Engineering Optimization 2014 is to unite engineers, applied mathematicians, computer and other applied scientists working on research, development and practical application of optimization methods applied to all engineering disciplines, in a common scientific forum to present, analyze and discuss the latest developments in this area. Engineering Optimization 2014 contains the edited papers presented at the 4th International Conference on Engineering Optimization (ENGOPT2014, Lisbon, Portugal, 8-11 September 2014). ENGOPT2014 is the fourth edition of the biennial “International Conference on Engineering Optimization”. The first conference took place in 2008 in Rio de Janeiro, the second in Lisbon in 2010 and the third in Rio de Janeiro in 2012. The contributing papers are organized around the following major themes: - Numerical Optimization Techniques - Design Optimization and Inverse Problems - Effi cient Analysis and Reanalysis Techniques - Sensitivity Analysis - Industrial Applications - Topology Optimization For Structural Static and Dynamic Failures - Optimization in Oil and Gas Industries - New Advances in Derivative-Free Optimization Methods for Engineering Optimization - Optimization Methods in Biomechanics and Biomedical Engineering - Optimization of Laminated Composite Materials - Inverse Problems in Engineering Engineering Optimization 2014 will be of great interest to engineers and academics in engineering, mathematics and computer science.
Download or read book 2023 Asia Pacific International Symposium on Aerospace Technology APISAT 2023 Proceedings written by Song Fu and published by Springer Nature. This book was released on with total page 1991 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book TILDA Towards Industrial LES DNS in Aeronautics written by Charles Hirsch and published by Springer Nature. This book was released on 2021-06-28 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers detailed insights into new methods for high-fidelity CFD, and their industrially relevant applications in aeronautics. It reports on the H2020 TILDA project, funded by the European Union in 2015-2018. The respective chapters demonstrate the potential of high-order methods for enabling more accurate predictions of non-linear, unsteady flows, ensuring enhanced reliability in CFD predictions. The book highlights industrially relevant findings and representative test cases on the development of high-order methods for unsteady turbulence simulations on unstructured grids; on the development of the LES/DNS methodology by means of multilevel, adaptive, fractal and similar approaches for applications on unstructured grids; and on leveraging existent large-scale HPC networks to facilitate the industrial applications of LES/DNS in daily practice. Furthermore, the book discusses multidisciplinary applications of high-order methods in the area of aero-acoustics. All in all, it offers timely insights into the application and performance of high-order methods for CFD, and an extensive reference guide for researchers, graduate students, and industrial engineers whose work involves CFD and turbulence modeling.
Download or read book Application of the Discrete Adjoint Method to Coupled Multidisciplinary Unsteady Flow Problems for Error Estimation and Optimization written by Karthik Mani and published by . This book was released on 2009 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adjoint methods have found applications in several key areas of computational fluid dynamics (CFD), namely, shape optimization and goal based adaptive solutions. CFD has become an essential tool in the design process by enabling the rapid testing of multiple designs, and currently it is normal practice to use CFD in conjunction with optimization algorithms for design improvement. In the context of shape optimization problems based on CFD, adjoint methods offer the significant advantage of computing sensitivity derivatives of the optimization cost function with respect to the set of design parameters, at a cost that is essentially independent of the number of design parameters. Adjoint methods reduce the cost of obtaining the complete gradient vector at any point in the design space equivalent to that of a single flow solution at the same point in the design space. This immediately enables the use of all gradient based optimization algorithms and lifts any restrictions on the number of design parameters required for the adequate definition of the optimization problem. Adaptive techniques in CFD constitute the other aspect where adjoint methods have have made great inroads. Typical adaptive solutions of the governing flow equations rely on estimating the local error in an evolving solution to target regions of the computational mesh for increased discrete resolution. The main goal of any adaptive solution method is the overall increase in solution accuracy with minimal increase in computational cost. However, targeting local error in the solution does not translate into efficient use of computational resources, since ultimately it is the accurate estimation of boundary integrated functional quantities such as load coefficients that are of importance to the user. Contrary to local error-based methods, adjoint methods allow the adaptation of the computational mesh specifically for the improvement of functionals such as load coefficients. This is achieved by mathematically establishing a clear relationship between the functional of interest and the regions of the computational mesh that are most relevant to it. The current work extends the use of adjoint methods to multiple governing disciplines that are tightly coupled, and more importantly unsteady in nature. The adjoint method is derived in a very general form for the purpose of computing the gradient vector for use in shape optimization in the context of coupled multidisciplinary unsteady equations. It is shown that computing the gradient vector in unsteady problems involves solving the analysis problem forward in time and then solving the adjoint problem backward in time. While adjoint methods have been used successively to drive spatial mesh adaptation, the current work extends the use of the computed unsteady adjoint variables for estimating temporal discretization error, which is then applied to temporal mesh adaptation. Additionally, the computed adjoint variables are also used for the estimation of algebraic error in the solution arising due to intentional or nonintentional partial convergence of the governing equations. Results indicate that the adaptation of the temporal resolution and convergence tolerance limits using adjoint-based error estimates is able to outperform traditional adaptation methods such as uniform refinement and those based on local error estimates. All of the development is carried out in a fully unstructured mesh framework with dynamic deformation of the computational spatial mesh.
Download or read book Frontiers Of Computational Fluid Dynamics 2006 written by Mohamed M Hafez and published by World Scientific. This book was released on 2005-12-07 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series of volumes to which this book belongs honors contributors who have made a major impact in computational fluid dynamics. This fourth volume in the series is dedicated to David Caughey on the occasion of his 60th birthday. The first volume was published in 1994 and was dedicated to Prof Antony Jameson. The second, dedicated to Earl Murman, was published in 1998. The third volume was dedicated to Robert MacCormack in 2002.Written by leading researchers from academia, government laboratories, and industry, the contributions in this volume present descriptions of the latest developments in techniques for numerical analysis of fluid flow problems, as well as applications to important problems in industry.
Download or read book New Approaches for Adjoint based Error Estimation and Mesh Adaptation in Stabilized Finite Element Methods with an Emphasis on Solid Mechanics Applications written by Brian Neal Granzow and published by . This book was released on 2018 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book MEGADESIGN and MegaOpt German Initiatives for Aerodynamic Simulation and Optimization in Aircraft Design written by Norbert Kroll and published by Springer Science & Business Media. This book was released on 2009-11-18 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains results of the German CFD initiative MEGADESIGN which combines CFD development activities from DLR, universities and aircraft industry. Based on the DLR flow solvers FLOWer and TAU the main objectives of the four-years project is to ensure the prediction accuracy with a guaranteed error bandwidth for certain aircraft configurations at design conditions, to reduce the simulation turn-around time for large-scale applications significantly, to improve the reliability of the flow solvers for full aircraft configurations in the complete flight regime, to extend the flow solvers to allow for multidisciplinary simulations and to establish numerical shape optimization as a vital tool within the aircraft design process. This volume highlights recent improvements and enhancements of the flow solvers as well as new developments with respect to aerodynamic and multidisciplinary shape optimization. Improved numerical simulation capabilities are demonstrated by several industrial applications.
Download or read book 41st AIAA Aerospace Sciences Meeting Exhibit written by and published by . This book was released on 2003 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
