  As model problem we consider the prototype for flow and transport of a
concentration in porous media in an interior domain and couple it with a
diffusion process in the corresponding unbounded exterior domain. To solve the
problem we develop a new non-symmetric coupling between the vertex-centered
finite volume and boundary element method. This discretization provides
naturally conservation of local fluxes and with an upwind option also stability
in the convection dominated case. We aim to provide a first rigorous analysis
of the system for different model parameters; stability, convergence, and
a~priori estimates. This includes the use of an implicit stabilization, known
from the finite element and boundary element method coupling. Some numerical
experiments conclude the work and confirm the theoretical results.
