Postdoctoral Research Associateship in Computational Scienceand Engineering: Optimum Design in Fluid Mechanics

所提出的研究旨在开发新的算法 用于解决流体动力学中的形状优化问题。 尽管有几种流动分析技术， 问题，设计技术，是非常需要从一个工程 前景是稀缺的。 在设计方法中，目标是找到 最佳性能的形状。 拟议的工作将 解决如何确定系统几何形状的逆问题 当系统行为由下式描述时， 定常Navier-Stokes方程。 这一问题将 采用约束最优控制的思想。 的NS 方程和一组附加的伴随偏微分 方程需要求解。 在这项研究中，A 计算代码的解决方案的伴随方程将是 编写并开发优化算法。 数值 使用该算法将获得几个样品的结果 问题，以证明该方法的可行性。 的 分析和数值实现也将扩展到 可压缩层流 计算实现将是 在匹兹堡超级计算中心的Cray YMP上执行。

The proposed research is aimed at the development of novel algorithms for the solution of shape optimization problems in fluid dynamics. Despite the availability of several analysis techniques for flow problems, design techniques that are much needed from an engineering perspective are scarce. In a design approach, the goal is to find the shape that gives the best performance. The proposed work will address the inverse problem of how to determine the system geometry for optimum flow performance when the system behavior is described by the steady Navier-Stokes (NS) equations. This problem will be approached using ideas of constrained optimal control. The NS equations and an additional set of adjoint partial differential equations needs to be solved. In the proposed research, a computational code for the solution of the adjoint equations will be written and an optimization algorithm will be developed. Numerical results will be obtained using this algorithm for several sample problems to demonstrate the feasibility of the approach. The analysis and the numerical implementation will also be extended to compressible laminar flow. Computational implementation will be performed on the Cray YMP of the Pittsburgh Supercomputing Center.//