Abstract not found

The complex-step derivative approximation and its application to numerical algorithms are presented. Improvements to the basic method are suggested that further increase its accuracy and robustness and unveil the connection to algorithmic differentiation theory. A general procedure for the implementation of the complex-step method is described in detail and a script is developed that automates its implementation. Automatic implementations of the complex-step method for Fortran and C/C++ are presented and compared to existing algorithmic differentiation tools. The complex-step method is tested in two large multidisciplinary solvers and the resulting sensitivities are compared to results given by finite differences. The resulting sensitivities are shown to be as accurate as the analyses. Accuracy, robustness, ease of implementation and maintainability make these complex-step derivative approximation tools very attractive options for sensitivity analysis.

This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed

A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena. As evidenced by the papers, which appear in the biannual AIAA/USAF/NASA/ISSMO Symposia on Multidisciplinary Analysis and Optimization, the MDO technical community focuses on vehicle and system design issues. This paper provides an overview of the MDO technology field from a fluid dynamics perspective, giving emphasis to suggestions of specific applications of recent MDO technologies that can enhance fluid dynamics research itself across the spectrum, from basic flow physics to full configuration aerodynamics.

This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed. With a new iterative procedure for solving the adjoint equaitons, exact numerical equivalence is maintained between the linear and adjoint discretisations. The incorporation of strong boundary conditions within the discrete approach is discussed, as well as a new application of adjoint methods to linear unsteady ow in turbomachinery

This paper discusses the role that computational fluid dynamics plays in the design of aircraft. An overview of the design process is provided, covering some of the typical decisions that a design team addresses within a multi-disciplinary environment. On a very regular basis trade-offs between disciplines have to be made where a set of conflicting requirements exist. Within an aircraft development project, we focus on the aerodynamic design problem and review how this process has been advanced, first with the improving capabilities of traditional computational fluid dynamics analyses, and then with aerodynamic optimizations based on these increasingly accurate methods. The optimization method of the present work is based on the use of the adjoint of the flow equations to compute the gradient of the cost function. Then, we use this gradient to navigate the design space in an efficient manner to find a local minimum. The computational costs of the present method are compared with that of other approaches to aerodynamic optimization. A brief discussion regarding the formulation of a continuous adjoint, as opposed to a discrete one, is also included. Two case studies are provided...

This paper presents improvements to the complexstep derivative approximation method which increase its accuracy and robustness. These improvements unveil the connection to algorithmic differentiation theory. The choice between these two methods then hinges on a trade-off between ease of implementation and execution efficiency. Automatic implementations for Fortran and C/C++ are presented and their relative merits are discussed. These new methods were successfully implemented in two very large multidisciplinary programs and the resulting sensitivities are shown to be as accurate as the analyses. Accuracy and ease of implementation make these tools very attractive options for sensitivity analysis.

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 su#cient accuracy. The opportunities are addressed only at a general level here, but an extensive list of references containing further details is included. The opportunities discussed are being addressed through the Fast Adaptive Aerospace Tools (FAAST) element of the Advanced Systems Concept to Test (ASCoT) and the 3rd Generation Reusable Launch Vehicles (RLV) projects at NASA Langley Research Center. The overall goal is to enable greater inroads into the design process with large-scale simulations.

Abstract not found

Since the present author first became involved in computational fluid dynamics, around 1970, the landscape has changed dramatically. At that time, panel methods had just come into use, and the world’s fastest super computer, the Control data 6600, had only 131000 words of memory (about 1 megabyte). Prior to the break-through of Murman and Cole [1970], no viable algorithms for computing transonic flow with shock