Optimal design methods involving the solution of an adjoint system of equations are an active area of research in computational fluid dynamics, particularly for aeronautical applications. This paper presents an introduction to the subject, emphasising the simplicity of the ideas when viewed in the context of linear algebra. Detailed discussions also include the extension to p.d.e.'s, the construction of the adjoint p.d.e. and its boundary conditions, and the physical significance of the adjoint solution. The paper concludes with examples of the use of adjoint methods for optimising the design of business jets.

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An Introduction to the Adjoint Approach to Design

Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.

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Verification and Validation in Scientific Computing

https://www.southampton.ac.uk/~nwb/lectures/GoodPracticeCFD/Articles/Validation_SAND2002-0529.pdf

Verification and Validation in Computational Fluid Dynamics

Developers of computer codes, analysts who use the codes, and decision makers who rely on the results of the analyses face a critical question: How should confidence in modeling and simulation be critically assessed? Verification and validation (V&V) of computational simulations are the primary methods for building and quantifying this confidence. Briefly, verification is the assessment of the accuracy of the solution to a computational model. Validation is the assessment of the accuracy of a computational simulation by comparison with experimental data. In verification, the relationship of the simulation to the real world is not an issue. In validation, the relationship between computation and the real world, i.e., experimental data, is the issue.

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Verification, Validation, and Predictive Capability in Computational Engineering and Physics

This report documents the results of a study to address the long range, strategic planning required by NASA's Revolutionary Computational Aerosciences (RCA) program in the area of computational fluid dynamics (CFD), including future software and hardware requirements for High Performance Computing (HPC). Specifically, the "Vision 2030" CFD study is to provide a knowledge-based forecast of the future computational capabilities required for turbulent, transitional, and reacting flow simulations across a broad Mach number regime, and to lay the foundation for the development of a future framework and/or environment where physics-based, accurate predictions of complex turbulent flows, including flow separation, can be accomplished routinely and efficiently in cooperation with other physics-based simulations to enable multi-physics analysis and design. Specific technical requirements from the aerospace industrial and scientific communities were obtained to determine critical capability gaps, anticipated technical challenges, and impediments to achieving the target CFD capability in 2030. A preliminary development plan and roadmap were created to help focus investments in technology development to help achieve the CFD vision in 2030.

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CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences

Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows

Grid adaptation for functional outputs: application to two-dimensional inviscid flows

Adjoint error estimation and grid adaptation for functional outputs: application to quasi-one-dimensional flow

An inexpensive error estimation and grid adaptive strategy is presented for estimating and reducing simulation errors in specific engineering outputs (functionals) such as lift or drag. These error estimates are directly related to the local residual errors of both the primal and adjoint solutions. This relationship allows the local error contributions to be used as indicators in a grid-adaptive strategy designed to produce specially tuned grids for accurately estimating the error in the chosen functional. Results are presented for the quasi-l-D Euler equations both isentropic and shocked flows. The remaining error in the functional, after correction, is superconvergent in all test cases. Additional improvements in the error estimates are obtained after applying the current adaptive strategy to an initially uniform grid.

David A. Venditti

Papers

Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows

Grid adaptation for functional outputs: application to two-dimensional inviscid flows

Adjoint error estimation and grid adaptation for functional outputs: application to quasi-one-dimensional flow

A multilevel error estimation and grid adaptive strategy for improving the accuracy of integral outputs

AIAA 2001-2659 A Grid Adaptive Methodology for Functional Outputs of Compressible Flow Simulations