A Robustness-Enhanced Reconstruction Based on Discontinuity Feedback Factor for High-Order Finite Volume Scheme

Abstract

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 and the Lax-Friedrichs flux solver are considered to verify the effectiveness of this algorithm. The strategy of the successful weighted essentially non-oscillatory (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, weakening its 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 (Ji et al. in Int. J. Comput. Fluid Dyn. 35:485–509, 2021) and WENO reconstruction is developed to deal with the possible discontinuities. Numerical results from smooth to extreme cases have been presented, which validates that the new finite volume scheme is effective for robustness enhancement while maintaining high resolution compared with the WENO scheme.