We propose in this paper an anisotropic, adaptive, finite element algorithm for steady, linear advection-diffusion-reaction problems with strong anisotropic features. The error analysis is based on the dual weighted residual methodology, allowing us to perform "goal-oriented" adaptation of a certain functional J(u) of the solution and derive an "optimal" metric tensor for local mesh adaptation with linear and quadratic finite elements. As a novelty, and to evaluate the weights of the error estimator on unstructured meshes composed of anisotropic triangles, we make use of a patchwise, higher-order interpolation recovery readily extendable to finite elements of arbitrary order. We carry out a number of numerical experiments in two dimensions so as to prove the capabilities of the goal-oriented adaptive method. We compute the convergence rate and the effectivity index for a series of output functionals of the solution. The results show the good performance of the algorithm with linear as well as quadratic finite elements.Key words. adaptive finite element algorithm, unstructured triangular anisotropic meshes, DWR method, linear and quadratic finite elements, patch-wise higher-order interpolation recovery 1. Introduction. Nowadays, the number of scientific and technological problems requiring an efficient numerical approach is arguably higher than ever before. Whether in the field of fluid mechanics, biology, rheology, or computer-generated imagery, the solution to those challenging applications involving multiple scales usually comes from a well-rounded, adaptive scheme. Our goal with this paper is to make a contribution in such a direction by providing a means to design "economical" meshes suitable for an accurate numerical discretization of linear, advection-diffusion-reaction problems, based on an a posteriori error estimate analysis.Great effort has been devoted to research in adaptive algorithms since the seminal work by Babuska and Rheinboldt in 1978 (see [7] and [8]), where they first introduced the concept of an a posteriori error estimate to design local refinement procedures. Given that meshes with equilateral shapes behave best in problems exhibiting isotropic solutions, studies in local refinement have focused mainly on isotropic mesh adaptation [3]. The former notwithstanding, a wide range of applications display "directional features" (boundary and internal layers, singularities, shock waves, jets, vortices, fracture propagation, etc.) which isotropic meshes fail to handle efficiently: the number of elements provided by standard, isotropic adaptation would be lowered by an "anisotropic" adaptive procedure making use of an optimal triangulation where not only the size of the elements, but also their shape and orientation would

Pool fires are known to undergo a bifurcation to a globally unstable puffing state driven by baroclinic and buoyant vorticity production. Although the supercritical puffing regime away from the bifurcation has been studied extensively in the literature, no detailed account has been given of the critical conditions for its onset, that being the purpose of the present paper. For the relevant canonical case of round liquid pools without swirl, aside from the inherent thermochemical and transport parameters associated with the fuel, pool-fire puffing is governed by a single dimensionless number, the Rayleigh number, which scales with the cube of the pool diameter. Consequently, for a fixed fuel and under fixed ambient conditions, there is a critical fuel pool diameter, associated with a critical value of the Rayleigh number, above which the flame starts puffing. A global linear stability analysis that accounts for the axisymmetry of the prevailing instability mode is developed here to describe the bifurcation. The mathematical formulation employs the limit of infinitely fast reaction, with account taken of the nonunity Lewis number and vaporization characteristics of typical liquid fuels. Predictions of critical puffing conditions, including critical diameters and puffing frequencies, are provided for methanol and for heptane pool fires, and the results are compared with results of new small-scale experiments under controlled laboratory conditions, reported here, yielding reasonably good agreement.

This paper presents the Expectation Maximization algorithm (EM) applied to operational modal analysis of structures. The EM algorithm is a general-purpose method for maximum likelihood estimation (MLE) that in this work is used to estimate state space models. As it is well known, the MLE enjoys some optimal properties from a statistical point of view, which make it very attractive in practice. However, the EM algorithm has two main drawbacks: its slow convergence and the dependence of the solution on the initial values used. This paper proposes two different strategies to choose initial values for the EM algorithm when used for operational modal analysis: to begin with the parameters estimated by Stochastic Subspace Identification method (SSI) and to start using random points.The effectiveness of the proposed identification method has been evaluated through numerical simulation and measured vibration data in the context of a benchmark problem. Modal parameters (natural frequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using SSI and the EM algorithm. On the whole, the results show that the application of the EM algorithm starting from the solution given by SSI is very useful to identify the vibration modes of a structure, discarding the spurious modes that appear in high order models and discovering other hidden modes. Similar results are obtained using random starting values, although this strategy allows us to analyze the solution of several starting points what overcome the dependence on the initial values used.

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The present study employs a linear global stability analysis to investigate buoyancyinduced flickering of axisymmetric laminar jet diffusion flames as a hydrodynamic global mode. The instability-driving interactions of the buoyancy force with the density differences induced by the chemical heat release are described in the infinitely fast reaction limit for unity Lewis numbers of the reactants. The analysis determines the critical conditions at the onset of the linear global instability as well as the Strouhal number of the associated oscillations in terms of the governing parameters of the problem. Marginal instability boundaries are delineated in the Froude-number/Reynolds-number plane for different fuel-jet dilutions. The results of the global stability analysis are compared with direct numerical simulations of time-dependent axisymmetric jet flames and also with results of a local spatio-temporal stability analysis.

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a b s t r a c tThis study addresses deflagration initiation of lean and stoichiometric hydrogeneair mixtures by the sudden discharge of a hot jet of their adiabatic combustion products. The objective is to compute the minimum jet radius required for ignition, a relevant quantity of interest for safety and technological applications. For sufficiently small discharge velocities, the numerical solution of the problem requires integration of the axisymmetric NaviereStokes equations for chemically reacting ideal-gas mixtures, supplemented by standard descriptions of the molecular transport terms and a suitably reduced chemicalkinetic mechanism for the chemistry description. The computations provide the variation of the critical radius for hot-jet ignition with both the jet velocity and the equivalence ratio of the mixture, giving values that vary between a few tens microns to a few hundred microns in the range of conditions explored. For a given equivalence ratio, the critical radius is found to increase with increasing injection velocities, although the increase is only moderately large. On the other hand, for a given injection velocity, the smallest critical radius is found at stoichiometric conditions. .