The papers presented at the AGARD Fluid Dynamics Panel Specialists' Meeting on 'Computational Methods for Aerodynamic Design (Inverse) and Optimization' are reviewed. Strengths and weaknesses are identified for many of the contributions as each is reviewed. The reviewer closes with some general comments. The 23 papers presented at the Meeting have been collected in AGARD CP 463 (ADA220870). Keywords: Computer aided design; Computational fluid dynamics; Inverse methods; Aerodynamic characteristics/optimization. (edc).
Beaucoup de méthodes de dessin utilisées par les ingénieurs en matière de conception d'éléments de turbomachines sont basées sur les hypothèses classiques 'quasi-tridimensionnelles' (surfaces aube à aube axisymétrique). Il a été montré récement que cette hypothèse n'était pas pertinente pour certains éléments de turbomachines, et qu'il pouvait être plus axact de les considérer comme des canaux isolés. La nécessité d'une méthode inverse pour de tels passges est alors clairement apparue, la présente étude tente de satisfaire cette nécessité. la méthode développée dans le cadre de ce travail, repose sur le calcul du champ aérodynamique (vitesse, pression statique) autour d'une ligne moyenne. Pour cela, un développement en série de Taylor est effectué sur les composantes du champ. les termes du développement sont calculés jusqu'à un degré fixé par l'utilisateur. Les équations d'Euler sont dérivées autant de fois que nécessite le degré imposé puis sont discrétisées par une méthode aux différences finies. Le système résultant n'est pas fermé. Cette non fermeture est utilisée pour imposéz à l'écoulement certains desiderata par le biais de relations dites arbitraires. Ces relations peuvent prendre la forme de minimisation d'une vitesse de transpiration, on obtient alors un calcul direct. Ainsi, il a été possible de rendre compte de l'importance des effets des écoulements secondaires et de la validité limitée des hypothèses quasi-3D. D'autres types de relations conduisent à des calculs inverses ou semi-inverse. Ainsi, il a été possible d'imposer à l'écoulement à titre d'exemple, une rotation solide, une réduction de charge sur les cotés d'un coude , ou encore une distribution de charge variable. une expérimentation numérique a été faite afin de mieux cerner le comportement du code et d'acquérir une expérience de son utilisation. Plusieurs cas tests ont été effectués aussi bien en inverse qu'en direct. Ils permettent une confrontation avec des calculs Euler 3D directs ou des résultats expérimentaux. Quelques voies pouvant conduire au desin d'un canal de retour ont été également explorées.
The European Community on Computational Methods in Applied Science (ECCOMAS) has been created with the aim of providing a co-ordination of international scientific conferences and other activities in the field of computational methods in applied sciences. The main objective of the joint conferences on computational fluid dynamics and numerical methods in engineering is to provide a common forum for the presentation and discussion of scientific computing applied to engineering sciences. Equal emphasis is to be given to basic methodologies, scientific developments and industrial applications. These conferences are presented in three volumes. Volume one, Computational Fluid Dynamics '96, covers the proceedings of the Third ECCOMAS Conference on Computational Fluid Dynamics; Volume two, Numerical Methods in Engineering '96, covers the proceedings of the second ECCOMAS Conference on Numerical Methods in Engineering; and Volume three, Computational Methods in Applied Sciences '96, which presents invited lectures and special technical sessions of both the Third ECCOMAS Computational Fluid Dynamics Conference and the Second ECCOMAS Conference on Numerical Methods in Engineering.
This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.
This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. However, thorough parameter studies are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are an emerging set of dimension reduction tools that identify important directions in the parameter space. This book describes techniques for discovering a model's active subspace and proposes methods for exploiting the reduced dimension to enable otherwise infeasible parameter studies. Readers will find new ideas for dimension reduction, easy-to-implement algorithms, and several examples of active subspaces in action.
