Efficient reconstruction method with common weighting strategy and spectral optimization based on scale sensor

High-order schemes are essential for high-fidelity aerodynamic simulations. To enhance computational efficiency while maintaining the adaptability of high-order schemes across various flow regions, this study proposes a simplified discontinuity-detection method based on the scale sensor. It operates prior to the reconstruction algorithm. In smooth regions, common weights are applied for all governing equations, whereas in multi-scale regions, the scheme adaptively switches between schemes with varying dispersion properties. By integrating these novel techniques with a computationally efficient smoothness indicator within the TENO framework, the schemes called FTENO and its optimized version are constructed. Comparative analyses of several typical benchmark cases demonstrate the superior comprehensive performance in efficiency and multi-scale resolution of the proposed schemes.