Contributions to the reliability of numerical simulations in fluid mechanics. Application to the flow simulation of thermodynamically complex gases

At the interface of physics, mathematics, and computer science, Uncertainty Quanti cation (UQ) aims at developing a more rigorous framework and more reliable methods to characterize the impact of uncertainties on the prediction of Quantities Of Interest (QOI). Despite signi cant improvements done in the last years in UQ methods for Fluid Mechanics, there is nonetheless a long way to go before there can be talk of an accurate prediction when considering all the numerous sources of uncertainties of the physical problem (boundary conditions, physical models, geometric tolerances, etc), in particular for shock-dominated problems. This manuscript illustrates my main contributions for improving the reliability of the numerical simulation in Fluid Mechanics: i) the development of e cient and exible schemes for solving at low-cost stochastic partial di erential equations for compressible ows, ii) various works concerning variancebased and high-order analysis, iii) the design of some low-cost techniques for the optimization under uncertainty. The application of interest is the robust design of turbines for Organic Rankine Cycles (ORC). Some contributions to the numerical ow prediction of the thermodynamically complex gases involved in ORC will be presented. This manuscript is divided in two parts. In the rst part, some intrusive algorithms are introduced that feature an innovative formulation allowing the treatment of discontinuities propagating in the coupled physical/stochastic space for shock-dominated compressible ows. Then, variance and higher-order based decompositions are described, that could alleviate problems with large number of uncertainties by performing a dimension reduction with an improved control. Some ANOVAbased analyses are also applied to several ows displaying various types of modeling uncertainties, be it cavitation, thermodynamic or turbulence modeling. Two algorithms for handling stochastic inverse problems are then introduced for improving input uncertainty characterization by directly using experimental data. Finally, robust-optimization algorithms are introduced, that are e cient when dealing with a large number of uncertainties, relying on di erent formulations, i.e. with decoupled/ coupled approaches between the stochastic and the optimization solvers. The second part is devoted to the study of dense gas ow in ORC-cycles, which represent a highly demanding eld of application as far as ow simulation reliability is concerned. The numerical ingredients necessary for this kind of simulation are described. Then, some recent results are illustrated : i) high- delity turbine computations; ii) a feasibility study concerning the appearance and the occurrence of a Rarefaction Shock Wave, using experimental data and di erent operating conditions (in monophasic and two-phase ows); iii) a stochastic study concerning the thermodynamic model uncertainties. This set of research works has produced several papers in international journals and peer-reviewed conferences