Flow simulation and shape optimization for aircraft design

AbstractWithin the framework of the German aerospace research program, the CFD project MEGADESIGN was initiated. The main goal of the project is the development of efficient numerical methods for shape design and optimization. In order to meet the requirements of industrial implementations a co-operative effort has been set up which involves the German aircraft industry, the DLR, several universities and some small enterprises specialized in numerical optimization. This paper outlines the planned activities within MEGADESIGN, the status at the beginning of the project and it presents some early results achieved in the project

Numerical parameter identification in multiphase flow through porous media

Multiphase flow is of high interest for the investigation of the behavior of waste in groundwater. The high nonlinearity of the model equations pose special problems. Here, a new parameter identification technique in this context is proposed which takes advantage of recently developed highly efficient numerical simulation techniques. It is based on a reduced Gauss-Newton technique in combination with an efficient gradient computation. Numerical experiments are performed for the McWhorter model problem

Large-Scale PDE-Constrained Optimization in Applications

This book results from the authors work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in his postdoctoral thesis (Habilitationsschrift) accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and algorithms which lead to efficient and high performance computational techniques to solve such optimization problems in real-life applications. Systematic development of the methods and algorithms are presented here. Practical aspects of implementations are discussed at each level as the complexity of the problems increase, supporting with enough number of computational examples. It consists of two parts: first part deals with time dependent optimization problems with applications in environmental engineering and the second part deals with steady state optimization problems, in which the PDEs are solved using semi-iterative or pseudo-time-stepping techniques, with applications in aerodynamics. This book will be useful for scientists and engineers who are looking for efficient numerical methods for PDE-constrained optimization problems. It will be helpful for graduate and Ph.D. students in applied mathematics, aerospace engineering, mechanical engineering, civil engineering and computational engineering during their training and research. This also will provide exciting research and development areas involving realistic applications

Large-Scale PDE-Constrained Optimization in Applications

This book results from the authors work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in his postdoctoral thesis (Habilitationsschrift) accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and algorithms which lead to efficient and high performance computational techniques to solve such optimization problems in real-life applications. Systematic development of the methods and algorithms are presented here. Practical aspects of implementations are discussed at each level as the complexity of the problems increase, supporting with enough number of computational examples. It consists of two parts: first part deals with time dependent optimization problems with applications in environmental engineering and the second part deals with steady state optimization problems, in which the PDEs are solved using semi-iterative or pseudo-time-stepping techniques, with applications in aerodynamics. This book will be useful for scientists and engineers who are looking for efficient numerical methods for PDE-constrained optimization problems. It will be helpful for graduate and Ph.D. students in applied mathematics, aerospace engineering, mechanical engineering, civil engineering and computational engineering during their training and research. This also will provide exciting research and development areas involving realistic applications

An Efficient Method for Aerodynamic Shape Optimization

Abstract. We present simultaneous pseudo-timestepping as an efficient method for aerodynamic shape optimization. In this method, instead of solving the necessary optimality conditions by iterative techniques, pseudo-time embedded nonstationary system is integrated in time until a steady state is reached. The main advantages of this method are that it requires no additional globalization techniques and that a preconditioner can be used for convergence acceleration which stems from the reduced SQP method. The important issue of this method is the trade-off between the accuracy of the forward and adjoint solver and its impact on the computational cost to approach an optimum solution is addressed. The method is applied to a test case of drag reduction for an RAE2822 airfoil, keeping it’s thickness constant. The optimum overall cost of computation that is achieved in this method is less than 4 times that of the forward simulation run. Nomenclature (x, y) ∈ R2:cartesian coordinates H:total enthalpy (ξ,η) ∈ [0, 1] 2:generalized coordinates M:Mach number Ω:flow field domain) ∞:values at free stream ∂Ω �n:=:flow field boundary γ:ratio of specific heats � � nx ny:unit outward normal Cref:chord length α:angle of attack CD:drag coefficient ρ:density I:cost unction u:x-component of velocity w:vector of state variables v:y-component of velocity q:vector of design variables p:pressure λ:vector of adjoint variables E:total energy J:Jacobian Cp:pressure coefficient B:reduced Hessian I

Numerical parameter identification in multiphase flow through porous media

Multiphase flow is of high interest for the investigation of the behavior of waste in groundwater. The high nonlinearity of the model equations pose special problems. Here, a new parameter identification technique in this context is proposed which takes advantage of recently developed highly efficient numerical simulation techniques. It is based on a reduced Gauss–Newton technique in combination with an efficient gradient computation. Numerical experiments are performed for the McWhorter model problem

Simultaneous Pseudo-Time Stepping for 3D Aerodynamic Shape Optimization

This paper presents a numerical method for aerodynamic shape optimization problems with state constraint. It uses a simultaneous semi-iterative technique to solve the equations arising from the first order necessary optimality conditions. The method converges without additional globalization in the design space. A reduced SQP method based preconditioner is used for convergence acceleration. Design examples of drag reduction with constant lift for wing and body of a Supersonic Commercial Transport (SCT) aircraft are included. The overall cost of computation is about 8 forward simlation runs