Fluid-structure interaction


Our approach is to consider fluid-structure systems in an Eulerian framework as  single variable density/rhelogy fluids.
Level set functions are used to capture the fluid/solid interfaces, and to compute elastic stresses in deformable structures and collisions between solid bodies.

Our work has been to design and validate such models [1,3,7,9], and to perform their mathematical [5] and numerical analysis [8,9].
We have applied this approach in image synthesis [4] and in biophysical systems [6].
Parametric instability of an elastic membrane (movie, more movies)
 Interaction of a rigid solid with  free surfaces or elastic membranes (movie1, movie2, movie3)

[1] G.-H. Cottet,  A particle model for fluid-structure interaction,  C. R. Acad. Sci. Paris, 3,  833-838,  2002.  pdf file

[2] G.-H. Cottet and E. Maitre,  A level-set formulation of immersed boundary methods for fluid-structure interaction problems,   C. R. Acad. Sci. Paris, Ser. I 338,  581-586, 2004. pdf file

[3] G.-H. Cottet and E. Maitre , A level set method for fluid-structure interactions with immersed surfaces,   Mathematical Models and Methods in the Applied Sciences,  16, 415-438, 2006.  pdf file

[4] M. Coquerelle, J. Allard, G.-H. Cottet and M.-P. Cani,  A vortex method for bi-phasic fluids interacting with rigid bodies,  Arxiv preprint math. NA/060759, 2006.

[5] G.-H. Cottet, E. Maitre and T. Milcent, Eulerian formulation and level set models for incompressible fluid-structure interaction, M2AN (42) 2008, 471-492.

[6] E. Maitre, T. Milcent, G.-H. Cottet, A. Raoult and Y. Usson,  Applications of level set methods in computational biophysics,  Math. & Computer Modelling, 2008. pdf file

[7] M. Coquerelle and G.-H. Cottet,  A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies, J. Comp. Phys.,  227, 9121-9137, 2008. pdf file

[8] C. Bost, G.-H. Cottet and E. Maitre, Convergence analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid, SIAM J. Num. Anal., 48(4), 1313-1337, 2010.  pdf file

[9] Cottet and E. Maitre  A semi-implicit level set method for multiphase flows and fluid-structure interaction problems, Journal of Computational Physics (2016), pp. 80-92. pdf file