  In this paper, a robustness-enhanced reconstruction for the high-order finite
volume scheme is constructed on the 2-D structured mesh, and both the
high-order gas-kinetic scheme(GKS) and the Lax-Friedrichs(L-F) flux solver are
considered to verify the validity of this algorithm. The strategy of the
successful WENO reconstruction is adopted to select the smooth sub-stencils.
However, there are cases where strong discontinuities exist in all sub-stencils
of the WENO reconstruction, which leads to a decrease in the robustness. To
improve the robustness of the algorithm in discontinuous regions in
two-dimensional space, the hybrid reconstruction based on a combination of
discontinuity feedback factor(DF) \cite{ji2021gradient} and WENO reconstruction
is developed to deal with the possible discontinuities. Numerical results from
smooth to extreme cases have been presented and validate that the new finite
volume scheme is effective for robustness enhancement and maintains high
resolution compared to the WENO scheme.
