• The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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## Section: Overall Objectives

### Overall Objectives

CARDAMOM$\phantom{\rule{0.277778em}{0ex}}$is a joint team of Inria Bordeaux - Sud-Ouest, University of Bordeaux and Bordeaux Inst. Nat. Polytechnique) and IMB (Institut de Mathématiques de Bordeaux – CNRS UMR 5251, University of Bordeaux). CARDAMOM $\phantom{\rule{0.277778em}{0ex}}$has been created on January 1st, 2015 (https://team.inria.fr/cardamom/). The CARDAMOM $\phantom{\rule{0.277778em}{0ex}}$project aims at providing a robust modelling strategy for engineering applications involving complex flows with moving fronts. The term front here denotes either an actual material boundary (e.g. multiple phases), a physical discontinuity (e.g. shock waves), or a transition layer between regions with completely different dominant flow behaviour (e.g. breaking waves). These fronts introduce a multi-scale behaviour. The resolution of all the scales is however not feasible in certification and optimization cycles, and not necessary in many engineering applications, while in others it is enough to model the average effect of small scales on large ones (closure models). We plan to develop application-tailored models obtained by a tight combination of asymptotic PDE (Partial Differential Equations) modelling, adaptive high order PDE discretizations, and a quantitative certification step assessing the sensitivity of outputs to both model components (equations, numerical methods, etc) and random variations of the data. The goal is to improve parametric analysis and design cycles, by increasing both accuracy and confidence in the results thanks to improved physical and numerical modelling, and to a quantitative assessment of output uncertainties. This requires a research program mixing of PDE analysis, high order discretizations, Uncertainty Quantification (UQ), robust optimization, and some specific engineering know how. Part of these scientific activities started in the BACCHUS $\phantom{\rule{0.277778em}{0ex}}$and MC2 $\phantom{\rule{0.277778em}{0ex}}$teams. CARDAMOM $\phantom{\rule{0.277778em}{0ex}}$harmonizes and gives new directions to this know how.