Low Dissipation Weighted Compact Nonlinear Schemes With an Adaptive Extension Strategy

ABSTRACT This article develops seven‐ and eight‐point low‐dissipation nonlinear schemes within the weighted compact nonlinear scheme (WCNS) framework. The schemes incorporate an ENO‐like (Essentially Non‐Oscillatory) stencil‐selection technique from TENO (Targeted ENO) schemes for midpoint variable interpolation. The smoothness measurement, serving as an explicit discontinuity detector, operates on only three‐point substencils and avoids complex high‐order local or global smoothness indicators. The high‐order interpolation polynomial is constructed through an extension strategy: using a standard five‐point scheme as the base, additional endpoints are incorporated in smooth regions, while the reconstruction reverts to the five‐point scheme near discontinuities to promote nonlinear robustness. The eight‐point scheme extends the seven‐point formulation by introducing controlled downwind blending, further reducing dissipation in the high‐wavenumber range at minimal additional computational cost. Benchmark tests involving strong shocks, fine‐scale wave structures, and broadband turbulence demonstrate robust discontinuity‐capturing behavior and improved high‐wavenumber resolution relative to the WCNS‐7 and WCNS‐T5 baselines considered in this study.