  We present a novel method for fluid structure interaction (FSI) simulations
where an original 2nd-order curved space lattice Boltzmann fluid solver (LBM)
is coupled to a finite element method (FEM) for thin shells. The LBM can work
independently on a standard lattice in curved coordinates without the need for
interpolation, re-meshing or an immersed boundary. The LBM distribution
functions are transformed dynamically under coordinate change. In addition,
force and momentum can be calculated on the nodes exactly in any geometry.
Furthermore, the FEM shell is a complete numerical tool with implementations
such as growth, self-contact and strong external forces. We show resolution
convergent error for standard tests under metric deformation. Mass and volume
conservation, momentum transfer, boundary-slip and pressure maintenance are
verified through specific examples. Additionally, a brief deformation stability
analysis is carried out. Next, we study the interaction of a square fluid flow
channel to a deformable shell. Finally, we simulate a flag at moderate Reynolds
number, air flow channel. The scheme is limited to small deformations of O(10%)
relative to domain size, by improving its stability the method can be naturally
extended to multiple applications without further implementations.
