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We give an overview of the research carried out under grant sponsorship and then give details concerning four of the problems we have worked on and for which we have obtained significant results. These are: least-squares finite element methods for incompressible, viscous flows; analysis of a shape control problem for the Navier-Stokes equations; finite dimensional approximation of a class of nonlinear optimal control problems; and feedback control of Karman vortex shedding. We then give lists of papers prepared and personnel supported under grant sponsorship.

We give an overview of the research carried out under grant sponsorship and then give details concerning four of the problems we have worked on and for which we have obtained significant results. These are: least-squares finite element methods for incompressible, viscous flows; analysis of a shape control problem for the Navier-Stokes equations; finite dimensional approximation of a class of nonlinear optimal control problems; and feedback control of Karman vortex shedding. We then give lists of papers prepared and personnel supported under grant sponsorship.

We give an overview of the research carried out under grant sponsorship and then give details concerning four of the problems we have worked on and for which we have obtained significant results. These are: least-squares finite element methods for incompressible, viscous flows; analysis of a shape control problem for the Navier-Stokes equations; finite dimensional approximation of a class of nonlinear optimal control problems; and feedback control of Karman vortex shedding. We then give lists of papers prepared and personnel supported under grant sponsorship.

Probabilistic methods have been implemented with a computational fluid dynamics simulation of fluid flow and heat transfer in a gas turbine engine. The simulation models the temperatures in the T-56 series III 1-2 spacer. Three input quantities are treated as random variables. A random sampling method is used to generate the input values from a probability density function. The implemented Monte Carlo method uses a large number of samples of the input variables to calculate results repeatedly for the output variables (i.e. the predicted temperatures). Statistics of the predicted temperatures, such as the mean and variance, are then calculated. The variation in the predicted temperature at one point in the turbine of the T56 engine is seen to be more sensitive to variability in some parameters than in others.

Probabilistic methods have been implemented with a computational fluid dynamics simulation of fluid flow and heat transfer in a gas turbine engine. The simulation models the temperatures in the T-56 series III 1-2 spacer. Three input quantities are treated as random variables. A random sampling method is used to generate the input values from a probability density function. The implemented Monte Carlo method uses a large number of samples of the input variables to calculate results repeatedly for the output variables (i.e. the predicted temperatures). Statistics of the predicted temperatures, such as the mean and variance, are then calculated. The variation in the predicted temperature at one point in the turbine of the T56 engine is seen to be more sensitive to variability in some parameters than in others.