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

这项研究旨在开发解决流体力学中形状优化问题的新算法。尽管有几种流动问题的分析技术可用，但从工程角度来看非常需要的设计技术却很少。在设计方法中，目标是找到提供最佳性能的形状。所提出的工作将解决当系统行为由定常的Navier-Stokes(NS)方程描述时，如何确定系统几何形状以获得最佳流动性能的反问题。这个问题将用约束最优控制的思想来解决。需要求解NS方程和一组附加的伴随偏微分方程组。在拟议的研究中，将编写求解伴随方程的计算代码，并将开发优化算法。用该算法对几个样本问题进行了数值计算，验证了该方法的可行性。分析和数值实现也将扩展到可压缩层流。计算实施将在匹兹堡超级计算中心的克雷YMP上进行。//

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.//