  In this paper, we propose a new stabilizer free and pressure robust WG method
for the Stokes equations with super-convergence on polytopal mesh in the
primary velocity-pressure formulation. Convergence rates with one order higher
than the optimal-order for velocity in both energy-norm and the $L^2$-norm and
for pressure in $L^2$-norm are proved in our proposed scheme. The
$H$(div)-preserving operator has been constructed based on the polygonal mesh
for arbitrary polynomial degrees and employed in the body source assembling to
break the locking phenomenon induced by poor mass conservation in the classical
discretization. Moreover, the velocity error in our proposed scheme is proved
to be independent of pressure and thus confirm the pressure-robustness. For
Stokes simulation, our proposed scheme only modifies the body source assembling
but remains the same stiffness matrix. Four numerical experiments are conducted
to validate the convergence results and robustness.
