  In this work we present a novel second order accurate well balanced
Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on moving
nonconforming meshes for the Euler equations of compressible gasdynamics with
gravity in cylindrical coordinates. The main feature of the proposed algorithm
is the capability of preserving many of the physical properties of the system
exactly also on the discrete level: besides being conservative for mass,
momentum and total energy, also any known steady equilibrium between pressure
gradient, centrifugal force and gravity force can be exactly maintained up to
machine precision. Perturbations around such equilibrium solutions are resolved
with high accuracy and with minimal dissipation on moving contact
discontinuities even for very long computational times. This is achieved by the
novel combination of well balanced path-conservative finite volume schemes,
that are expressly designed to deal with source terms written via
nonconservative products, with ALE schemes on moving grids, which exhibit only
very little numerical dissipation on moving contact waves. In particular, we
have formulated a new HLL-type and a novel Osher-type flux that are both able
to guarantee the well balancing in a gas cloud rotating around a central
object. Moreover, to maintain a high level of quality of the moving mesh, we
have adopted a nonconforming treatment of the sliding interfaces that appear
due to the differential rotation. A large set of numerical tests has been
carried out in order to check the accuracy of the method close and far away
from the equilibrium, both, in one and two space dimensions.
