The foundation of the model employed in this study is rooted in the pioneering work of [1]. The distinctive aspect of this approach lies in solving both fluid and structure within an Eulerian framework, enabling discretization on a unified mesh. Recognizing that fluid and structure may not always necessitate the same mesh size for certain configurations, a Hier- archical Quadtree-based approach [2] is employed. The discretization stencils are limited to the first layer of neighbors thus enhancing the efficiency of the parallel computations while limiting the numerical order of the finite volume discretizations. To showcase the versatility of the presented numerical model, we examine a biomedical application, the axisymmetric simulation of blood flow in a cardiac pump with simplified geometry. Depending on the pump’s geometry, there may be instances of contact between the elastic membrane and rigid walls. Notably, these contacts are not accounted for in the Navier-Stokes equations, necessitating additional modeling. One viable approach involves introducing a local lubrication force on the membrane sur- face, as demonstrated in [3], to prevent undesired phenomena such as overlaps between the elastic structure and walls. In cases where needed, a collision force can be added to replicate a rebound effect. The fluid structure interface has however to be discretized to be able to locally applied the collision force, and this is not the case in our approach. The ongoing research on collision force within a fully Eulerian framework is centered on modifying the local stress tensor for the elastic material, and at least preliminary results will be presented. REFERENCES [1] G.-H. Cottet and E. Maitre and T. Milcent, Eulerian formulation and level set models for incompressible fluid-structure interaction ESAIM: M2AN, Vol. 42, pp. 471-492, 2008. [2] M. Bergmann and A. Fondaneche and A. Iollo, An Eulerian finite-volume approach of fluid-structure interaction problems on quadtree meshes. Journal of Computational Physics, Vol. 471, 111647, 2022. [3] B Lambert and L. Weynans and M. Bergmann, Local lubrication model for spherical particles within incompressible Navier-Stokes flows. Phys. Rev. E, Vol. 97, 033313, 2018.