Axisymmetric mass conservative coupling of fluid flow and solute transport

This paper is concerned with the physically consistent simulation of fluid flow and transport in complex geometries axisymmetric geometries. In this situation, cylindrical coordinates allow a dimension reduction of the three-dimensional problem to a two-dimensional one. In the three-dimensional setting, a mass conservative discretization can be achieved, e.g. by coupling divergence-free finite element methods for the flow with a conservative finite volume discretization for the transport. A replication of this approach in the reduced two-dimensional formulation with cylindrical coordinates is not straight-forward. Therefore, modifications are suggested that ensure the desired qualitative properties and allow a priori error estimates in suitable weighted Sobolev norms. Several numerical experiments study convergence rates and confirm the theoretical results.