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

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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.//