  In this paper, a strongly mass conservative and stabilizer free scheme is
designed and analyzed for the coupled Brinkman-Darcy flow and transport. The
flow equations are discretized by using a strongly mass conservative scheme in
mixed formulation with a suitable incorporation of the interface conditions. In
particular, the interface conditions can be incorporated into the discrete
formulation naturally without introducing additional variables. Moreover, the
proposed scheme behaves uniformly robust for various values of viscosity. A
novel upwinding staggered DG scheme in mixed form is exploited to solve the
transport equation, where the boundary correction terms are added to improve
the stability. A rigorous convergence analysis is carried out for the
approximation of the flow equations. The velocity error is shown to be
independent of the pressure and thus confirms the pressure-robustness.
Stability and a priori error estimates are also obtained for the approximation
of the transport equation; moreover, we are able to achieve a sharp stability
and convergence error estimates thanks to the strong mass conservation
preserved by our scheme. In particular, the stability estimate depends only on
the true velocity on the inflow boundary rather than on the approximated
velocity. Several numerical experiments are presented to verify the theoretical
findings and demonstrate the performances of the method.
