  In this paper we study a stationary double-diffusive natural convection
problem in porous media given by a Navier-Stokes/Darcy type system, for
describing the velocity and the pressure, coupled to a vector
advection-diffusion equation describing the heat and substance concentration,
of a viscous fluid in a porous media with physical boundary conditions. The
model problem is rewritten in terms of a first-order system, without the
pressure, based on the introduction of the strain tensor and a nonlinear
pseudo-stress tensor in the fluid equations. After a variational approach, the
resulting weak model is then augmented using appropriate redundant penalization
terms for the fluid equations along with a standard primal formulation for the
heat and substance concentration. Then, it is rewritten as an equivalent
fixed-point problem. Well-posedness and uniqueness results for both the
continuous and the discrete schemes are stated, as well as the respective
convergence result under certain regularity assumptions combined with the
Lax-Milgram theorem, and the Banach and Brouwer fixed-point theorems. In
particular, Raviart-Thomas elements of order $k$ are used for approximating the
pseudo-stress tensor, piecewise polynomials of degree $ \leq k$ and $\leq k+1$
are utilized for approximating the strain tensor and the velocity,
respectively, and the heat and substance concentration are approximated by
means of Lagrange finite elements of order $\leq k+1$. Optimal a priori error
estimates are derived and confirmed through some numerical examples that
illustrate the performance of the proposed semi-augmented mixed-primal scheme.
