# Application of a Novel High-Order WENO Scheme in LES Simulations
## 1 Introduction
[23] and [PERSON] and [PERSON] [24] constructed a series of high-order WENO-ZQ schemes through the introduction of phantom points, enabling their deployment in both structured and unstructured grid systems. In inviscid flow applications, the solution accuracy, robustness, and computational cost of the WENO-ZQ scheme have been extensively analyzed both qualitatively and quantitatively [21; 22; 24; 25]. This study aims to extend this efficient high-order WENO-ZQ scheme to viscous flow and comprehensively evaluate its performance by integrating it into a structured-grid LES CFD solver. Viscous flow is a complex system, and the WENO scheme is only a small part; thus, the computation time of different schemes on the same grid cells will not significantly differ relative to the entire solver. However, since the WENO-ZQ scheme fundamentally eliminates the real-time calculation of nonlinear weights strongly correlated with grid shape, thereby addressing the issue of computational crashes caused by negative nonlinear weights, it can be qualitatively assumed that this scheme reduces computational costs. When applying the WENO-ZQ scheme in viscous flow, two particularly meaningful questions arise regarding the flow structure that can be captured under the same computational grid resolution and the number of grids needed to capture the same physical phenomenon. In light of this, this study uses the WENO-ZQ and classical WENO-JS schemes to conduct relevant calculations on these two points. Numerous scholars have conducted LES research utilizing high-order WENO schemes, yielding a substantial body of significant findings. For instance, [PERSON] et al. [26] compared the performance of the ENO and WENO-JS schemes in LES for simulating the energy spectrum decay of two-dimensional isotropic compressible turbulence. Their results indicated that the standard ENO scheme exhibited numerical turbulence at high wavenumbers, resulting in insufficient energy dissipation, whereas the WENO scheme demonstrated moderate dissipation characteristics. [PERSON] and [PERSON] [27] conducted LES studies on the collision of dual-jet under three-dimensional supersonic conditions using a fifth-order WENO scheme and a dynamic subgrid-scale turbulence model, revealing that the fifth-order WENO scheme is highly suitable for simulating turbulent flows with bow shocks and can effectively capture unstable shocks within the flow field. [PERSON] and [PERSON] [28] compared three high-precision schemes (the three-order MUSCL, the fifth-order MUSCL, and the ninth-order WENO-JS) in the application of LES for a channel with hill-like curvature. Their findings showed that the WENO scheme achieved the highest resolution and was capable of capturing the finest flow details, though it also incurred the highest computational cost. [PERSON] et al. [29] applied a quasi-fourth-order hybrid central WENO scheme within a finite volume framework to perform LES on transonic turbulent flows over a protuberance, demonstrating the scheme's ability to effectively distinguish between shocks and turbulent fluctuations, thereby exhibiting excellent shock-capturing and turbulence-resolving capabilities. However, the switch function within the hybrid scheme, the smoothness of transitions, and the tunable parameters within the function could impact the computational outcomes [30]. [PERSON] et al. [31] successfully predicted the transition process in flat plate LES using a fifth-order WENO scheme, though the accuracy of wall pressure predictions for a supersonic compression ramp was somewhat limited. It is evident that the current application of high-order WENO schemes in LES is primarily focused on flows with simple geometric configurations. Therefore, this study integrates the high-order, low-dissipation WENO-ZQ scheme into the LES framework to elucidate and evaluate the potential of the WENO-ZQ scheme in LES applications, thereby providing a clearer understanding of its practical applicability and effectiveness in engineering contexts.