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The main objective of this article is to investigate computational methods for the active control and drag optimization of incompressible viscous flow past cylinders, using the two-dimensional Navier-Stokes equations as the flow model. The computational methodology relies on the following ingredients: space discretization of the Navier-Stokes equations by finite element approximations, time discretization by a second order accurate two step implicit/explicit finite difference scheme, calculation of the cost function gradient by the adjoint equation approach, minimization of the cost function by a quasi-Newton method à la BFGS. The above methods have been applied to predict the optimal forcing-control strategies in reducing drag for flow around a circular cylinder using either an oscillatory rotation or blowing and suction. In the case of oscillatory forcing, a drag reduction of 31% at Reynolds number 200 and 61% at Reynolds number 1000 was demonstrated. Using only three blowing-suction slots, we have been able to completely suppress the formation of the Von-Karman vortex street up to Reynolds number 200 with a significant net drag reduction. We conclude this article by an appendix describing a bisection method which allows very substantial storage memory savings at reasonable extra computational time when applying adjoint equation based methodologies to the solution of control problems modeled by time dependent equations. [ABSTRACT FROM AUTHOR]

In studying glass morphology often models are used that describe it as a strongly viscous Newtonian fluid. In this paper we shall study one of the problems encountered in glass technology. It is dealing with producing packing glass by a so-called pressing process. The pressing problem actually deals with the morphology of a bottle or jar. We first show how to deal with the temperature, by a suitable dimension analysis. In this analysis we see the dominance of the convection over the other modes of heat transfer. However, at the end of the pressing — a stage called The dwell — flow is absent and we have to deal with conduction and radiation in a heat-only problem. A similar analysis is made for the re-heating, where the internal stresses are relaxed before the final, blowing stage of the forming process. We give a number of numerical examples to sustain our results. [ABSTRACT FROM AUTHOR]

When working on the numerical approximation of the solution of the state equations modeling industrial (complex) systems, one meets a number of problems which are rather universal. We present here an introduction to some of these problems and to some of the methods which can be used, some of these methods being already quite old (we give then a short introduction to them). Others are on the contrary in development stage, and we then present them with more details. We begin with stiff problems, i.e. models where one has several orders of magnitude of difference in the size of the coefficients. We introduce in such situations stiff asymptotic expansions. Questions of this type are met very often, for instance in electromagnetism. In Section 3 we consider multi scales problems, where the "multi scales" refer to time scales and to space scales as well. In these cases, associated with multi physics with intrinsic mixing properties of the system under study, one can use expansions based on slow and fast variables, in time and, or in space. The main ideas are presented for rapidly rotating fluids and for flows in porous media, where the expansion leads to Darcy's law. Section 4 deals with the "universal" difficulty of the complexity of the geometry of the system under study. A classical method used to tackle this type of question is the DDM (domain decomposition method). An introduction is presented in Section 4, an introduction to the decomposition of the energy space being presented in Section 5. The Section 4 and 5 are based on the virtual control method, introduced by O. PIRONNEAU and the A. in several conferences in 1998 and in the notes, referred to in Section 4. It contains as a particular case artificial or fictitions domains methods. Many applications and extensions are now under progress, in joint papers by O. PIRONNEAU and the A. The Decomposition of the Energy space has been introduced in a note of R. GLOWINSKI, O. PIRONNEAU and the A. (CRAS, 1999), developments being under development with T.W. PAN Others are in progress with J.P. PERIAUX The method of virtual control applies in a very efficient manner to problems where there is an effective control (a real control !). Extensive developments are then needed. They will be presented elsewhere, a short introduction being given in the second note of O. PIRONNEAU and the A. referred to above. [ABSTRACT FROM AUTHOR]

These Lecture Notes review the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading to a computational cost roughly equal to the cost of two flow solutions. Representative results are presented for viscous optimization of transonic wing-body combinations and inviscid optimization of complex configurations. [ABSTRACT FROM AUTHOR]