Eu-type generalized hydrodynamic equations have been derived from the Boltzmann kinetic theory and applied to investigate continuum and/or rarefied gas flows. This short communication first reports detailed and important issues in the use of the mixed discontinuous Galerkin method to solve Eu-type generalized hydrodynamic equations in multidimensions. Three major issues are reported. These include the treatment of solid boundary conditions for the nonlinear constitutive equations, a slope limiter to maintain high accuracy and avoid unphysical oscillations, and the computational efficiency compared with that of the particle method. In addition, we implement the present model to a rigid problem, which includes gas flows around the NACA0018 airfoil, a sharp wedge, a sphere and a three-dimensional Apollo configuration.