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Mathematical methods for fluid mechanics cover a broad range of needs and typically require to use, adapt, or develop advanced techniques of solution. Theoretical bases are required to face the solution of special problems (vortices, boundary layers, invariance properties of parametric models, fluid-solid interaction, to cite a few). Numerical methods in fluid mechanics present a continuous need of evolution to face the increasingly complexity of problems to be solved. Therefore techniques for properly handling irregular geometries, and moving elements are needed, as well as the development of multi-scale methods. This is particularly true when industrial processes are investigated. Finally, mathematical methods and models are the unavoidable tool to analyze large experimental and numerical datasets, and to produce the synthesis process required for understanding physical processes.