Section: New Results

Fluid-structure interactions on AMR enabled quadree grids

We develop a versatile fully Eulerian method for the simulation of fluid-structure interactions. In the context of a monolithic approach, the whole system is modeled through a single continuum model. The equations are numerically solved using a finite-volume scheme with a compact stencil on AMR enabled quadtree grids where the dynamic refinement is adapted in time to the fluid-structure system.

The geometry is followed using a level-set formulation. In the Eulerian representation, a smooth Heaviside function is defined according to a level-set function on the cartesian mesh to distinguish between fluid and elastic phases. The temporal deformation of the structure is described according to the backward characteristics which are employed to express the Cauchy stress of a two-parameter hyperelastic Mooney-Rivlin material. This model is particularly adapted to elastomeric materials undergoing large deformations, see figure 12.

Figure 12. Y-component of the velocity for an oscillating elastomeric membrane actuated by a rigid holder at the tip, immersed in glycerin after 3 periods of oscillations. The criterion used for the dynamic AMR mesh is based on the level-set function.