High-resolution and low-dissipation weighted essentially non-oscillatory scheme with limit-oriented modified smoothness indicator and min-ratio strategy

For flows dominated by strong discontinuities, particularly in complex scenarios where they coexist with vortices, conventional weighted essentially non-oscillatory (WENO) schemes suffer from excessive numerical dissipation, high-computational complexity, and insufficient adaptability of fixed weights under extreme flow conditions. Addressing these limitations, this paper proposes a high-resolution, low-dissipation WENO scheme (WENO-HL). This scheme incorporates a cosine-modulated adaptive weight function and a global smoothness difference indicator, establishing a dual-strategy mechanism for the dynamic suppression of abnormal stencils. Unlike traditional schemes that rely on fixed empirical parameters, the cosine-modulated weight dynamically allocates each candidate stencil's contribution, thereby avoiding issues of poor adaptability. Additionally, the global smoothness difference indicator accurately identifies and suppresses abnormal stencil interference, alleviating accuracy degradation caused by erroneous smoothness estimation at critical points. Theoretical analysis shows that WENO-HL achieves formal fifth-order accuracy in smooth flow regions. An approximate dispersion relation analysis verifies its superior spectral characteristics, with well-controlled dispersion and dissipation errors that meet high-order standards. Numerical simulations of one-dimensional shock tubes and two-dimensional complex flows show that, compared with the Jiang-Shu-type WENO scheme, the WENO scheme with Z-indicator, and the Z+-type WENO scheme, WENO-HL significantly reduces numerical dissipation and enhances resolution for multi-discontinuity flows. It excels at capturing fine vortex structures in the proximity of strong shocks with higher fidelity and minimal distortion. Using a concise polynomial reconstruction framework, the scheme offers good portability and scalability, providing an efficient, reliable numerical tool for the simultaneous capture of strong discontinuities and fine-scale structures in high-Mach-number flows.