In numerical simulations, achieving high accuracy without significantly increasing computational costs is often challenging. To address this, this paper presents an improved finite volume weighted essentially non-oscillatory (WENO) scheme tailored for applicability in computational fluid dynamics (CFD) and implemented in the flow solver NUAA-Turbo for simulating turbomachinery flows using both RANS and RANS/LES coupling. Firstly, the new WENO scheme is validated against classic numerical test cases to assess its stability and reliability in handling discontinuities, the Double problem, and Raleigh-Taylor (RT) instability issues. Compared to the original format, this enhanced finite volume WENO scheme demonstrates superior stability near discontinuities and resolves flow features with the same grid resolution more effectively. Next, for engineering applications related to turbomachinery, such as compressor and turbine characteristics, computations are performed using RANS, and the results obtained using WENO-ZQ3 and WENO-JS3 are compared. Finally, the new fifth-order WENO scheme is applied to RANS/LES coupled simulations of turbine wakes and film cooling. The results show that the enhanced finite volume WENO scheme offers improved stability and accuracy in engineering applications, allowing for high-precision calculations with fewer grid points to capture more detailed flow physics, thereby reducing computational costs in aerodynamic applications.

To conduct high-precision and high-resolution numerical simulation of complex flow structures in turbomachinery, a high-order finite volume weighted essentially non-oscillatory (WENO) scheme for the large eddy simulation (LES) is improved and embedded into the three-dimensional viscous unsteady CFD solver NUAA-Turbo. Firstly, the spectral characteristics and unsteady convergence of the improved WENO scheme are studied. Compared with the classical WENO scheme, the improved WENO scheme has better dissipation and dispersion characteristics and faster convergence speed. Then, the coefficient CW of the Wall-Adapting Local Eddy-viscosity (WALE) model is calibrated by decaying homogeneous isotropic turbulence (DHIT) test case. Finally, the scheme is applied to conduct high-precision LES calculations of turbulent boundary layer flow, supersonic compression corner flow, and low-pressure turbine cascade separation flow. The numerical simulation results show that this WENO scheme has excellent shock wave capture ability and turbulence resolution and can capture more flow field details with less mesh size, greatly reducing the computational cost and laying a foundation for large-scale engineering application of LES.