Masters (Modeling, Analysis and Simulation of fluids with heTERogeneitieS) is a NEAT (Nancy Emerging Associate Team) between Sphinx and a Chilean team.

The principal investigators are Takéo Takahashi (France) and Jorge San Martín (Chile)

###### Chilean team members

The Chilean team is a part of the Center for Mathematical Modeling (CMM) in the University of Chile.

- Carlos Conca, University of Chile, Full professor
- Raúl Gormaz, University of Chile, Engineer
- Benjamín Obando, University of Chile, PhD Student
- Jorge San Martín, University of Chile, Full professor

###### French team members

- Julien Lequeurre, University of Lorraine, Assistant Professor
- Alexandre Munnier, University of Lorraine, Assistant Professor
- Jean-François Scheid, University of Lorraine, Assistant Professor
- Takéo Takahashi, Inria Nancy-Grand Est, Researcher

###### Scientific Objectives

- Modeling and mathematical analysis of fluid-rigid body system. We are working on new boundary conditions for the Navier-Stokes system. Our aim is to describe the collisions between rigid bodies moving into a viscous incompressible fluid. Another objective is to consider the motion of structures in a viscoplastic fluid such as a Bingham fluid. Such a model can be used to describe the behavior of very viscous mixtures such as tailings in copper production. The corresponding model has not been studied in the literature. One of the difficulties of both problems is that the corresponding models involve variational inequalities.
- Inverse problems. An important inverse problem in fluid-structure interaction consists in recovering the position and the shape of a structure immersed into a fluid through measurements in the fluid. We aim to develop new tools to reconstruct such quantities even as the structure is moving.
- Numerical analysis and simulations. We aim to improve our Lagrange-Galerkin method for the simulation of a fish swimming in an incompressible Navier-Stokes fluid. The idea is to introduce of a new characteristics function related to the nonlinear inertial term coming from the displacement and the deformation of the structure in the fluid.