The dynamics of membranes, shells, and capsules in fluid flow has become an active research area in
computational physics and computational biology. The small thickness of these elastic materials enables
their efficient approximation as a hypersurface, which exhibits an elastic response to in-plane bending and out-of-plane stretching deformations. If such a closed thin shell is filled with (and/or surrounded by) multiple fluids, capillary forces on the contact line between the fluids and the shell may arise and force the shell to deform.
In this work, we present a
novel Arbitrary Lagrangian-Eulerian (ALE) method to simulate such elastic surfaces immersed in Navier-
Stokes fluids, which is combined with a phase field approach to model droplets inside and/or outside the surface. This method combines high accuracy with computational efficiency, since the grid is
matched to the elastic surface and can therefore be resolved with relatively few grid points near the surface. We formulate elastic surface
forces and propose an evolving finite-element discretization. Several wetting test cases demonstrate the versatility of the proposed method. Examples are simulations of single or multiple droplets deforming a vesicle-like shell and approaching different previously defined contact angles.