Control and Optimization Tools for Systems Governed by Nonlinear Partial Differential Equations

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 06, 2006
Accession Number
ADA455841

Entities

People

  • Jeff Borggaard

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Human Systems
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Fluid Dynamics
  • Fluid Flow
  • Fluid Mechanics
  • Mathematics
  • Mechanics
  • Navier Stokes Equations
  • Numerical Analysis
  • Partial Differential Equations
  • Simulations
  • Turbulent Flow

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Computational Fluid Dynamics (CFD)