This article provides a condensed overview of some of the major today's features (both classical or recently developed), used in the design and development of algorithms to solve nonlinear continuous optimization problems. We first consider the unconstrained optimization case to introduce the line-search and trust-region approaches as globalization techniques to force an...
Various stochastic programming problems can be formulated as problems of optimization of an expected value function. Quite often the corresponding expectation function cannot be computed exactly and should be approximated, say by Monte Carlo sampling methods. In fact, in many practical applications, Monte Carlo simulation is the only reasonable way of estimating the expectation...
We consider an abstract formulation for optimization problems in some Lp spaces. The variables are restricted by pointwise upper and lower bounds and by finitely many equality and inequality constraints of functional type. Second-order necessary and sufficient optimality conditions are established, where the cone of critical directions is arbitrarily close to the form which is...
Low-Mach-number aeroacoustic theories are applied to predict far-field sound emission from vortex-dominated flows. The latter are simulated using three-dimensional vortex methods. Both particle schemes and filament-based schemes are used. Comparisons of model predictions with theoretical and experimental results on the interaction of two vortex rings are first discussed. Next...
The effects of active flow control, using base mass transpiration as control action, on the stability and dynamics of the cylinder wake at low Reynolds numbers are investigated, using numerical simulation. A spectral element method is used for the simulation. It is found that, in the subcritical Reynolds number regime (Re ‹ 47), slight suction destabilizes the wake, resulting in...
We study optimal boundary control problems for the Navier-Stokes equations in an unbounded domain. The control is of Dirichlet type, i.e., the boundary velocity field. The drag functional is used as an example of control objectives. We identify the trace space for the velocity fields possessing finite energy, we prove the existence of a solution for the Navier-Stokes equations...
The first part of the paper analyses the linear dynamics of a vortex pair thanks to a normal mode analysis. The basic flow is a superposition of two Lamb-Oseen vortices of radius a and distance b. The long-wave Crow instability and the short-wave Widnall instabilities are fully characterized for different aspect ratios a/b of the vortex pair. In particular, as a/b increases, it...
The initial phase of the evolution of trailing vortex sheets is modelled using the continuous sheet method, corresponding to Re=infinity. In the proposed 2D numerical scheme, vorticity is conserved. A qualitative comparison of the numerically simulated results and low-speed data obtained by particle image velocimetry is provided. Among the phenomena discussed are the interactions...
Three-dimensional aspects of vorticity concentration, reorientation, and stretching are investigated in a simplified swirling jet model, consisting of a line vortex along the jet axis surrounded by a jet shear layer with both azimuthal and streamwise vorticity. Inviscid three-dimensional vortex dynamics simulations demonstrate the nonlinear interaction and competition between a...
The particle-in-cell method is coupled with boundary-fitted coordinates in order to realistically model particle flow of electrically charged particles in technical, electromagnetic devices. Numerical algorithms describing the transition between the grid model and the mesh-free model are developed. Applications are presented in which these techniques have been successfully applied.
Direct numerical simulations of a vortex pair embedded in a stable atmospheric boundary layer are presented. The effects of various crosswind conditions are studied. These computations demonstrate the creation of secondary vortices for the range of Reynolds numbers (3770≤Rer≤). The physics of wake vortex interactions with the ground for different values of crosswind are discussed...
The paper deals with the problem of recovering pressure from the given vorticity and velocity fields. Both fields result from the stochastic vortex-blob simulation of the viscous incompressible flow. The vorticity field is a discontinuous function. The method is presented here to find pressure as a solution to the variational problem which forms the weak version of the momentum...
On présente une approche unifiée pour la construction d'éléments finis basée sur une formulation duale-hybride des équations de l'élasticité linéaire. Dans cette formulation le tenseur des contraintes est pris en considération mais sa symétrie est relaxée par un multiplicateur de Lagrange qui n'est autre que le rotationnel du déplacement. Cette construction est reliée à l...
Lorsqu'on observe notre environnement à grande échelle, on voit de la structure. Penser notamment aux grands tourbillons cycloniques ou anticycloniques qui ont un diamètre de l'ordre du millier de kilomètres et qui parcourent l'atmosphère terrestre. Une structure spectaculaire comme la grande tache rouge de Jupiter est un gigantesque tourbillon (environ le diamètre de la terre...
We summarize some of the recent developments in the fields of suboptimal control strategies for time dependent incompressible Navier-Stokes Equations. Reduced order modeling (ROM) and instantaneous control strategies are described. Both approaches are applied to compute controls for the laminar backward facing step flow.
The time optimal control problem for a semilinear parabolic systems is here studied. The singular points of the Minimum Time function are characterized as the initial point of multiple time-optimal trajectories. Moreover, an example is given to show how such singularities may develop.
In this paper we investigate optimal control problems governed by elliptic variational inequalities of the obstacle type. We show how to obtain optimality conditions for a relaxed problem with or without state constraints. Then we present the optimality system related to the original problem with state constraints, using a generalized derivative.
Dans cet article, on analyse le comportement asymptotique des solutions des équations de la chaleur d'ordres impairs et rationnels. On utilisera pour cela la méthode dite du
The development of a baroclinic secondary instability over the primary Kelvin-Helmholtz roll-up of a two-dimensional, variable-density mixing-layer is discussed. A particular attention is paid to the accuracy of the simulations by investigating the conservation of an invariant of the flow. Then, the influence of both the spatial and the temporal resolution on the development of...
A comparison between the equation of motion of the central line of a slender vortex filament deduced from a matched asymptotic expansion(A. Callegari and L. Ting) and the expansion of the equation of motion of the ad-hoc cut-off methods(S. Crow) with the cut-off length as the small asymptotic parameter is performed. It justifies the cut-off methods and gives the link between the...
Mean and turbulent flow characteristics of the wing-tip vortex generated by a 6% scale model of the F/A-18 fighter aircraft equipped with AIM-9 sidewinders were investigated experimentally. This particular configuration was studied as part of the NRC/IAR stores clearance and certification program. However, the present study focuses on the near field structure of the tip vortex...