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Multiscale compressible turbulent flow is widely present in the aerospace field, and the co-existence of shock wave discontinuities and multi-scale turbulence in the flow field poses significant challenges for high-fidelity numerical simulation. To design high-order nonlinear scheme to improve the accuracy of complex turbulence simulation with stable shock wave capture, a weighted compact nonlinear scheme – targeted essentially non-oscillatory (WCNS-T) scheme is developed based on targeted essentially non-oscillatory scheme within the WCNS framework. Also, an improved variant of WCNS-T with smooth scale separation (denoted as WCNS-ST) is proposed from the perspective of both numerical convergence and accuracy. The numerical properties of different nonlinear weights are discussed in classical numerical problems, including spectral properties analysis, and two-dimensional Riemann problem. Then, the newly developed WCNS-ST scheme based on smooth scale separation was used to combine a unified turbulence model called Self-Adaptive Turbulence Eddy Simulation (SATES), which is applied to simulate subsonic flow past a 30P30N airfoil and supersonic base flow. The good convergence and numerical results are obtained using the newly developed WCNS-ST scheme, whereas WCNS-T shows worse convergence. In addition, adaptive dissipation control is further introduced for the WCNS-ST scheme, and the new variant (denoted as WCNS-STA) still shows good residual convergence and predicts more accurate results due to low numerical dissipation. The above results indicate that the proposed smooth scale separation and its WCNS-STA scheme have a good performance in SATES simulations of multiscale flow problems, making it more potential for complex engineering applications. [ABSTRACT FROM AUTHOR]

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The present work describes an assessment and validation of the newly developed Very-Large Eddy Simulation (VLES) method for the numerical study of complex non-linear response of a lean premixed flame to acoustic velocity fluctuations. The VLES method is a self-adaptive turbulence method which can achieve seamless switching between RANS, LES, and finally approaching DNS. It is extended to the turbulent combustion simulation in the present study. The selected test case is a bluff-body stabilized lean premixed turbulent flame with acoustic forcing. Turbulence modeling is achieved using the VLES method and the premixed turbulent combustion is modeled using the Thickened Flame Model (TFM) combining a reduced two-step chemical reaction mechanism. Harmonically varying velocity fluctuation is imposed on the inlet to introduce the acoustic forcing. Three types of flow including the cold flow, unforced reactive flow, and forced reactive flow are used to validate the simulation method. The mean velocity, dynamic response of the flame to inlet velocity forcing and the quantitative response of the heat release rate are captured by the present calculations with very reasonable accuracy compared with the experimental data. The present VLES predictions are comparable or even better than the present LES results using the combustion model and the same computational grid. This work thus confirms that the VLES methodology is capable of successfully predicting the response of lean premixed turbulent flame to acoustic forcing. [ABSTRACT FROM AUTHOR]