  In this work, we develop a high-order pressure-robust method for the rotation
form of the stationary incompressible Navier-Stokes equations. The original
idea is to change the velocity test functions in the discretization of
trilinear and right hand side terms by using an H(div)-conforming velocity
reconstruction operator. In order to match the rotation form and error
analysis, a novel skew-symmetric discrete trilinear form containing the
reconstruction operator is proposed, in which not only the velocity test
function is changed. The corresponding well-posed discrete weak formulation
stems straight from the classical inf-sup stable mixed conforming high-order
finite elements, and it is proven to achieve the pressure-independent velocity
errors. Optimal convergence rates of H1, L2-error for the velocity and L2-error
for the Bernoulli pressure are completely established. Adequate numerical
experiments are presented to demonstrate the theoretical results and the
remarkable performance of the proposed method.
