Adaptive Reconstruction Method Using Discontinuity Feedback for High-Order Accuracy Schemes

This paper presents efficient adaptive stencil extension reconstruction methods using a discontinuity feedback factor to address weak robustness and high computational costs in high-order schemes (7th-order and above). The method features two innovations: accuracy order adaptively increases from the lowest level based on local stencil smoothness, unlike WENO and MUSCL limiters that reduce order from highest level; and the Discontinuity Feedback Factor detects sub-cell discontinuity strength while serving as a local smoothness measure. This eliminates expensive smoothness indicators in very high-order schemes and generalizes to arbitrary high orders. Rigorous tests, including a Mach 20000 jet, demonstrate exceptional robustness.