Very High-order Compact Gas-kinetic Scheme With Discontinuity Feedback Factor

Abstract: This paper presents a robust and efficient very high-order scheme for compressible flow simulation, addressing critical limitations of existing high-order methods. The proposed scheme combines the compact gas-kinetic scheme (CGKS) with an adaptive stencil extension reconstruction with discontinuity feedback factor (ASE-DFF), achieving significant improvements in both robustness and computational efficiency. Traditional weighted essentially non-oscillatory (WENO) schemes suffer from reduced robustness at higher order and require costly smoothness indicators for large stencils. Meanwhile, compact methods based on Discontinuous Galerkin (DG) and Flux Reconstruction (FR) struggle with poor time-marching efficiency. In contrast, the ASE-DFF-CGKS introduces two key innovations: (1) a unified framework enabling arbitrarily high-order compact gas-kinetic scheme without sacrificing large CFL number, and (2) a discontinuity feedback factor that eliminates the need for expensive smoothness indicator calculations while essentially keeping first-order robustness near discontinuities. The scheme's advantages are demonstrated through benchmark simulations. It maintains a CFL number above 0.5 for up to 9th-order case, unlike conventional compact methods that restrict a CFL less than 0.05. Also it delivers high-resolution results for flow involving strong shock and rarefaction wave. This work provides a practically impactful solution for high-fidelity compressible flow simulation, balancing computational efficiency, high-order accuracy and robustness in challenging flow regimes.