International audienceIn this work, modeling of the near-wall region in turbulent flows is addressed. A new wall-layer model is proposed with the goal to perform high-Reynolds number large-eddy simulations of wall bounded flows in the presence of a streamwise pressure gradient. The model applies both in the viscous sublayer and in the inertial region, without any parameter to switch from one region to the other. An analytical expression for the velocity field as a function of the distance from the wall is derived from the simplified thin-boundary equations and by using a turbulent eddy coefficient with a damping function. This damping function relies on a modified van Driest formula to define the mixing-length taking into account the presence of a streamwise pressure gradient. The model is first validated by a priori comparisons with direct numerical simulation data of various flows with and without streamwise pressure gradient and with eventual flow separation. Large-eddy simulations are then performed using the present wall model as wall boundary condition. A plane channel flow and the flow over a periodic arrangement of hills are successively considered. The present model predictions are compared with those obtained using the wall models previously proposed by Spalding, Trans. ASME, J. Appl. Mech 28, 243 (2008) and Manhart et al., Theor. Comput. Fluid Dyn. 22, 243 (2008) . It is shown that the new wall model allows for a good prediction of the mean velocity profile both with and without streamwise pressure gradient. It is shown than, conversely to the previous models, the present model is able to predict flow separation even when a very coarse grid is used

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A numerical investigation of transonic and low-supersonic flows of dense gases of the Bethe–Zel'dovich–Thompson (BZT) type is presented. BZT gases exhibit, in a range of thermodynamic conditions close to the liquid/vapour coexistence curve, negative values of the fundamental derivative of gasdynamics. This can lead, in the transonic and supersonic regime, to non-classical gasdynamic behaviours, such as rarefaction shock waves, mixed shock/fan waves and shock splitting. In the present work, inviscid and viscous flows of a BZT fluid past an airfoil are investigated using accurate thermo-physical models for gases close to saturation conditions and a third-order centred numerical method. The influence of the upstream kinematic and thermodynamic conditions on the flow patterns and the airfoil aerodynamic performance is analysed, and possible advantages deriving from the use of a non-conventional working fluid are pointed out.

In this work a novel adaptive strategy for stochastic problems, inspired to the classical Harten's framework, is presented. The proposed algorithm allows building, in a very general manner, stochastic numerical schemes starting from a whatever type of deterministic schemes and handling a large class of problems, from unsteady to discontinuous solutions. Its formulations permits to recover the same results concerning the interpolation theory of the classical multiresolution approach, but with an extension to uncertainty quantification problems. The interest of the present strategy is demonstrated by performing several numerical problems where different forms of uncertainty distributions are taken into account, such as discontinuous and unsteady custom-defined probability density functions. In addition to algebraic and ordinary differential equations, numerical results for the challenging 1D Kraichnan-Orszag are reported in terms of accuracy and convergence. Finally, a two degree-of-freedom aeroelastic model for a subsonic case is presented. Though quite simple, the model allows recovering some physical key aspect, on the fluid/structure interaction, thanks to the quasi-steady aerodynamic approximation employed. The injection of an uncertainty is chosen in order to obtain a complete parameterization of the mass matrix. All the numerical results are compared with respect to classical Monte Carlo solution and with a non-intrusive Polynomial Chaos method.

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Calculation of tail probabilities is of fundamental importance in several domains, such as for example risk assessment. One major challenge consists in the computation of lowfailure probability and multiple-failure regions, especially when an unbiased estimation of the error is required. Methods developed in literature rely mostly on the construction of an adaptive surrogate, tackling some problems such as the metamodel building criterion and the global computational cost, at the price of a generally biased estimation of the failure probability. In this paper, we propose a novel algorithm permitting to both building an accurate metamodel and to provide a statistically consistent error. In fact, it relies on a novel metamodel building strategy, which aims to refine the limit-state region in all the branches "equally", even in the case of multiple failure regions, with a robust stopping building criterion. Secondly, two "quasi-optimal" importance sampling techniques are used, which permit, by exploiting the accurate knowledge of the metamodel, to provide an unbiased estimation of the failure probability, even if the metamodel is not fully accurate. As a consequence, the proposed method provides a very accurate unbiased estimation even for low failure probability or multiple failure regions. Several numerical examples are carried out, showing the very good performances of the proposed method with respect to the state-of-the-art in terms of accuracy and computational cost. Additionally, another importance sampling technique is proposed in this paper, permitting to drastically reduce the computational cost when estimating some reference values, or when a very weak failure-probability event should be computed directly from the metamodel.

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