Control and Optimization Tools for Systems Governed by Nonlinear Partial Differential Equations
Author | : |
Publisher | : |
Total Pages | : 31 |
Release | : 2006 |
Genre | : |
ISBN | : |
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We have developed a number of theoretical and computational tools for optimal design and control of spatially distributed systems. Our main results were focused on complex fluid systems modeled by the Navier-Stokes equations. We considered turbulent flows, thermal fluids, temperature dependent material properties and time dependence among other complexities. Sensitivity analysis, the process of quantifying the dependence of parameters on these flows, was performed for a number of interesting flow problems. We investigated methods for computing sensitivity variables including a novel application of automatic differentiation (AD) technology as well as the implementation of a solver for a general sensitivity equation. This solver includes adaptive mesh refinement for the coupled flow and sensitivity equations. Our research on advanced computational fluid dynamics (CFD) simulation and sensitivity analysis continues, with the development of a parallel 3D finite element based software package to take advantage of modern cluster-based computer architectures.