## 1 Introduction
[PERSON] and [PERSON] [2; 14; 15; 16] extended the WENO-ZQ scheme by introducing the concept of phantom points and applied it to predict transitional and separated flows with RANS modeling. [PERSON] et al. [4; 17] adopted the idea of WENO-ZQ, replacing two small second-order stencils with three third-order stencils,and developed WENO-AO. [PERSON] et al. [18] proposed a new fifth-order hybrid WENO scheme by integrating methods from [19]. The major advantage of this scheme is its higher efficiency with fewer numerical errors in smooth regions and lower computational costs. [PERSON] et al. [20] proposed a high-order residual distribution conservative finite-difference WENO-ZQ scheme for solving steady-state hyperbolic equations with source terms on uniform meshes. They applied this method to both scalar and system test problems, including Burgers' equation, shallow water equations, nozzle flow problems, Cauchy-Riemann problems, and Euler equations. In addition to the WENO scheme, recent scholars have proposed the high-order TENO (Targeted Essentially Non-Oscillatory) scheme, which boasts high-order accuracy, low numerical dissipation, and sharp shock-capturing capabilities. [PERSON] et al. [21] extended this high-order shock-capturing TENO scheme from being applicable only to Cartesian or curvilinear coordinate grids to being applicable to unstructured grids. By employing a reconstruction strategy with large and small stencils, the TENO scheme achieves excellent numerical stability. [PERSON] et al. [22] used both WENO and TENO schemes in a GPU-accelerated compressible flow solver to solve two-dimensional Riemann problems, yielding good results. Despite the promising results and significant potential for the development of the TENO scheme, the WENO scheme is currently more widely used and has been more extensively developed, making it better suited for broader application in engineering examples. Over the past few years, research on the improved WENO-ZQ scheme has become relatively mature, but there are no reported applications of the finite-volume version of the WENO-ZQ scheme in solving engineering problems. Therefore, this paper derives the applicability of this scheme by implementing flux integration on control volume faces using a single-point quadrature rule, making the scheme more suitable for structured grids. The improved scheme is embedded into the NUAA-Turbo2.0 three-dimensional compressible solver based on structured grids. Using turbulence models such as RANS and hybrid RANS/LES models (SST-SAS), calculations and simulations are conducted for aircraft engine compressors, high-pressure turbines, and turbine film cooling to demonstrate the scheme's applicability in engineering. This also involves physical phenomena such as turbine wake and film cooling efficiency distribution. This paper first briefly explains the one-dimensional finite-volume WENO-ZQ and compares it with WENO-JS. Then, several classic schemes are compared by solving Riemann problems, double Mach reflection problems, and Rayleigh-Taylor (RT) instability problems. Finally, high-fidelity predictions are made by solving engineering applications related to compressor and turbine characteristics, as well as turbine flow field simulations focusing on wake and film cooling issues. The third-order and fifth-order finite-volume versions of the WENO-ZQ scheme are systematically tested on structured grids.