  This paper develops a class of robust weak Galerkin methods for the
stationary incompressible convective Brinkman-Forchheimer equations. The
methods adopt piecewise polynomials of degrees $m\ (m\geq1)$ and $m-1$
respectively for the approximations of velocity and pressure variables inside
the elements and piecewise polynomials of degrees $k \ ( k=m-1,m)$ and $m$
respectively for their numerical traces on the interfaces of elements, and are
shown to yield globally divergence-free velocity approximation. Existence and
uniqueness results for the discrete schemes, as well as optimal a priori error
estimates, are established. A convergent linearized iterative algorithm is also
presented. Numerical experiments are provided to verify the performance of the
proposed methods
