  In this paper, we present new parameter-free superconvergent
H(div)-conforming HDG methods for the Brinkman equations on both simplicial and
rectangular meshes. The methods are based on a velocity
gradient-velocity-pressure formulation, which can be considered as a natural
extension of the H(div)-conforming HDG method (defined on simplicial meshes)
for the Stokes flow [Math. Comp. 83(2014), pp. 1571-1598].
  We obtain optimal error estimates in $L^2$-norms for all the variables in
both the Stokes-dominated regime (high viscosity/permeability ratio) and
Darcy-dominated regime (low viscosity/permeability ratio). We also obtain
superconvergent L^2-estimate of one order higher for a suitable projection of
the velocity error, which is typical for (hybrid) mixed methods for elliptic
problems. Moreover, thanks to H(div)-conformity of the velocity, our velocity
error estimates are independent of the pressure regularity.
  Preliminary numerical results on both triangular and rectangular meshes in
two-space dimensions confirm our theoretical predictions.
