An improved high-order low dissipation weighted compact nonlinear scheme for compressible flow simulations

Recently, Zhang developed a low-dissipation high-order scheme that employs Fu's targeted essentially non-oscillatory approach. this method incorporates an essentially non-oscillatory-like stencil selection strategy within the framework of the weighted compact nonlinear scheme proposed by Deng. Although this new scheme, termed targeted compact nonlinear scheme (TCNS), can recover ideal weights in smooth regions, it reduces accuracy at the discontinuities by discarding less smooth sub-stencils. Acker et al. showed in a recent study that increasing the weight of less smooth sub-stencils on a relatively coarse grid can further improve the wave resolution. Luo further improved Acker's scheme to fully exploit its potential in spectral characteristics. By following this idea, the less smooth stencil weights were incorporated to overcome problems of classical TCNS and to further improve the scheme's ability to resolve high-frequency waves. Moreover, by introducing an adaptive factor, we further optimized the spectral properties to improve the TCNS. A series of standard cases were used to measure the resolution of the new method for multiscale structures and the ability to suppress nonphysical oscillations at shock waves. The new scheme was applied to three cases involving complex configurations and multiscale flows, demonstrating that its low dissipation characteristics offer advantages in solving real-life problems.