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 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 Applied Shape Optimization for Fluids written by Bijan Mohammadi and published by Oxford University Press. This book was released on 2010 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: PREFACE; ACKNOWLEDGEMENTS; 1. Introduction; 2. Optimal shape design; 3. Partial differential equations for fluids; 4. Some numerical methods for fluids; 5. Sensitivity evaluation and automatic differentiation; 6. Parameterization and implementation issues; 7. Local and global optimization; 8. Incomplete sensitivities; 9. Consistent approximations and approximate gradients; 10. Numerical results on shape optimization; 11. Control of unsteady flows; 12. From airplane design to microfluidic; 13. Toplogical optimization for fluids; 14. Conclusion and perspectives; INDEX.
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 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 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:
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.
Download or read book Annual Research Briefs written by Center for Turbulence Research (U.S.) and published by . This book was released on 2009 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sensitivity Uncertainty Analysis Volume 1 written by Dan G. Cacuci and published by CRC Press. This book was released on 2003-05-28 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: As computer-assisted modeling and analysis of physical processes have continued to grow and diversify, sensitivity and uncertainty analyses have become indispensable investigative scientific tools in their own right. While most techniques used for these analyses are well documented, there has yet to appear a systematic treatment of the method based on adjoint operators, which is applicable to a much wider variety of problems than methods traditionally used in control theory. This book fills that gap, focusing on the mathematical underpinnings of the Adjoint Sensitivity Analysis Procedure (ASAP) and the use of deterministically obtained sensitivities for subsequent uncertainty analysis.
Download or read book Design Sensitivity Analysis written by Lisa G. Stanley and published by SIAM. This book was released on 2002-01-01 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an understandable introduction to one approach to design sensitivity computation and illustrates some of the important mathematical and computational issues inherent in using the sensitivity equation method (SEM) for partial differential equations. The authors use basic models to illustrate the computational issues that one might encounter when applying the SEM in a laboratory or research setting, while providing an overview of applications and computational issues regarding sensitivity calculations performed by way of continuous sensitivity equation methods (CSEM).
Download or read book Grid Adaptation Using Adjoint Error Analysis with an Application in Computational Flud Dynamics written by Harish Bhanderi and published by . This book was released on 2000 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Enhancing Adaptive Sparse Grid Approximations and Improving Refinement Strategies Using Adjoint based a Posteriori Error Estimates written by and published by . This book was released on 2015 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.
Download or read book Sensitivity Technologies for Large Scale Simulation written by Curtis Curry Ober and published by . This book was released on 2005 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sensitivity analysis is critically important to numerous analysis algorithms, including large scale optimization, uncertainty quantification, reduced order modeling, and error estimation. Our research focused on developing tools, algorithms and standard interfaces to facilitate the implementation of sensitivity type analysis into existing code and equally important, the work was focused on ways to increase the visibility of sensitivity analysis. We attempt to accomplish the first objective through the development of hybrid automatic differentiation tools, standard linear algebra interfaces for numerical algorithms, time domain decomposition algorithms and two level Newton methods. We attempt to accomplish the second goal by presenting the results of several case studies in which direct sensitivities and adjoint methods have been effectively applied, in addition to an investigation of h-p adaptivity using adjoint based a posteriori error estimation. A mathematical overview is provided of direct sensitivities and adjoint methods for both steady state and transient simulations. Two case studies are presented to demonstrate the utility of these methods. A direct sensitivity method is implemented to solve a source inversion problem for steady state internal flows subject to convection diffusion. Real time performance is achieved using novel decomposition into offline and online calculations. Adjoint methods are used to reconstruct initial conditions of a contamination event in an external flow. We demonstrate an adjoint based transient solution. In addition, we investigated time domain decomposition algorithms in an attempt to improve the efficiency of transient simulations. Because derivative calculations are at the root of sensitivity calculations, we have developed hybrid automatic differentiation methods and implemented this approach for shape optimization for gas dynamics using the Euler equations. The hybrid automatic differentiation method was applied to a first order approximation of the Euler equations and used as a preconditioner. In comparison to other methods, the AD preconditioner showed better convergence behavior. Our ultimate target is to perform shape optimization and hp adaptivity using adjoint formulations in the Premo compressible fluid flow simulator. A mathematical formulation for mixed-level simulation algorithms has been developed where different physics interact at potentially different spatial resolutions in a single domain. To minimize the implementation effort, explicit solution methods can be considered, however, implicit methods are preferred if computational efficiency is of high priority. We present the use of a partial elimination nonlinear solver technique to solve these mixed level problems and show how these formulation are closely coupled to intrusive optimization approaches and sensitivity analyses. Production codes are typically not designed for sensitivity analysis or large scale optimization. The implementation of our optimization libraries into multiple production simulation codes in which each code has their own linear algebra interface becomes an intractable problem. In an attempt to streamline this task, we have developed a standard interface between the numerical algorithm (such as optimization) and the underlying linear algebra. These interfaces (TSFCore and TSFCoreNonlin) have been adopted by the Trilinos framework and the goal is to promote the use of these interfaces especially with new developments. Finally, an adjoint based a posteriori error estimator has been developed for discontinuous Galerkin discretization of Poisson's equation. The goal is to investigate other ways to leverage the adjoint calculations and we show how the convergence of the forward problem can be improved by adapting the grid using adjoint-based error estimates. Error estimation is usually conducted with continuous adjoints but if discrete adjoints are available it may be possible to reuse the discrete version for error estimation. We investigate the advantages and disadvantages of continuous and discrete adjoints through a simple example.
