A robustness-enhanced reconstruction based on discontinuity feedback factor for high-order finite volume scheme

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.