  This work proposes a novel variational approximation of partial differential
equations on moving geometries determined by explicit boundary representations.
The benefits of the proposed formulation are the ability to handle large
displacements of explicitly represented domain boundaries without generating
body-fitted meshes and remeshing techniques. For the space discretization, we
use a background mesh and an unfitted method that relies on integration on cut
cells only. We perform this intersection by using clipping algorithms. To deal
with the mesh movement, we pullback the equations to a reference configuration
(the spatial mesh at the initial time slab times the time interval) that is
constant in time. This way, the geometrical intersection algorithm is only
required in 3D, another key property of the proposed scheme. At the end of the
time slab, we compute the deformed mesh, intersect the deformed boundary with
the background mesh, and consider an exact transfer operator between meshes to
compute jump terms in the time discontinuous Galerkin integration. The transfer
is also computed using geometrical intersection algorithms. We demonstrate the
applicability of the method to fluid problems around rotating (2D and 3D)
geometries described by oriented boundary meshes. We also provide a set of
numerical experiments that show the optimal convergence of the method.
