UFO

This project deals with the simulation and optimization of flows when uncertainties in data and models may occur. We only consider non intrusive methods so that existing CFD codes, for example the partners, can simply be used. We focus on how to deal with uncertainties in turbulence models with perfect gases for external aerodynamics and those arising with the thermodynamic models for dense organic flows used in some energy production processes. Since the equations of state of organic gases as well as the optimal turbulence models for a given configuration are not well known, we need, from experimental data, to reconstruct the random variable probability density functions (pdf), then to plug these data into the CFD codes in order to reproduce experiments. The realization of these program needs to master at least three aspects. The number of random variables can be very large with arbitrary pdfs. Hence, we need to have numerical schemes able to handle this, and for systems of PDEs that are highly non linear with possibly chaotic and/or discontinuous solutions. We will pursue the development of an accurate non intrusive method, insensitive to the choice of the pdf, and will seek for robust and accurate algorithms to reconstruct response surfaces. In that case the aim is to better understand the behavior of the PDE and to generate reduced models, which combined with adaptive sparse grid algorithms, will make uncertainty quantification computations as cheap as possible. The second aspect is the applicability of Bayesian approaches to take into account uncertainties in the modelisation and tuning of parameters in fluid mechanics. In a first step, we will provide a critical analysis of existing methods, mainly used in solid mechanics, in order to develop an original one adapted to fluid problems. Starting from the state of the art of classical approaches in turbulence, we will build an adequate framework to define what is a modelisation uncertainty, by taking into account the parametrical aspects of turbulence models as well as their mathematical form. The solution of this critical problem, which is seldom considered, should have a strong impact on applications. This methodological framework will enable to test/evaluate the most appropriate Bayesian approaches to determine a pdf for one given (arbitrary) model. The data basis provided by ONERA will be essential. The last topic is about applications. A common software, written in python, will be developed in order to use and to couple the partners' softwares easily. The knowledge gained in that project will be applied to two realistic situations : external transonic aerodynamics and an internal flow problem arising in energetics. The three tasks will be realized together with a schedule that is described in the proposal: one needs to guaranty that the methods developed in the first task are effective in using the numerical strategies of the second one, and this can only be done by testing them on real applications. Each partner of this project has a good experience of simulation and/or optimization of flows with uncertainties. Four of them are known specialists of CFD, the other one has the experience in large industrial problems in solid mechanics with a large number of uncertainties. He is also known in this community. All the partners share a common will of transfer either in the scientific community, or in training students and engineers, as well as to industry.