###### Abstract  
On the basis of a previously developed elliptic blending turbulence model (SST-\(k\)-\(\omega\)-\(\varphi\)-\(\alpha\) model), a scale-adaptive simulation (SAS) model is developed by following [PERSON]'s SAS concept. An SAS source term, which is related to the ratio of the modeled turbulence scale to the von Karman length scale, is introduced into the corresponding length-scale determining equation. The major motivation of this study is that the conventional unsteady Reynolds-averaged Navier-Stokes (URANS) models provide only large-scale unsteadiness. The introduction of the SAS term allows the proposed SAS model to dynamically adjust to resolved structures in a URANS framework because this term is sensitive to resolved fluctuations. The predictive capabilities of the proposed SAS model are demonstrated by computing the complex flow configurations in three cases with flow separation from curved surfaces, namely, three-dimensional (3D) diffuser flow, two-dimensional (2D) periodic hills flow, and 2D U-turn duct flow. For comparison, the results predicted by the SST-\(k\)-\(\omega\)-\(\varphi\)-\(\alpha\) model and the [PERSON]'s SAS model (SST-SAS) are provided. The results are also compared with the relevant experimental, direct numerical simulation, and large eddy simulation data. The results show that the SST-\(k\)-\(\omega\)-\(\varphi\)-\(\alpha\) model cannot capture the critical features for all three flows, and that the SST-SAS model is able to predict the results reasonably well. The proposed SAS model is capable of resolving more portions of the turbulence structures, and it yields the best results in all the cases. url  
24 December 2021  
11 February  
owing to the excessively high-resolution requirements for wall boundary layers, LES has a very limited impact on industrial simulation. Hybrid RANS-LES approaches have become increasingly popular in recent years as methods that maintain a balance between accuracy and cost [2]. Hybrid RANS-LES approaches incorporate the advantages of the RANS and LES models. Specifically, the attached wall boundary layers are covered by the RANS model; thus, the excessive resolution requirements of LES can be avoided. Meanwhile, the large, detached regions are handled in the LES mode, i.e., with a partial resolution of the turbulent spectrum. Hybrid RANS-LES approaches have been developed by many researchers. Owing to space limitations, they are not reviewed comprehensively here. Interested readers can refer to the reviews in [3,4]. However, it is worth briefly reviewing one of them, the scale-adaptive simulation (SAS), which is utilized in this study. By revisiting the \(kL\) model of Rotta, the SAS model was developed by [PERSON] and [PERSON] [5]. An additional source term consisting of the von Karman length scale is introduced into the scale-determining equation of the relevant unsteady RANS (URANS) model. When the flow is strongly unstable, this term can reduce the computed length scale, thus yielding a lower eddy viscosity, which in turn allows flow fluctuations to be sustained. The SAS method has several advantages, a few of which are described. First, it is very easy to implement it into an existing URANS model (simply by inserting an additional source term into the scale-determining equation). Second, it does not contain any parameters related to grid size. It is generally known that when the grid resolution is not sufficiently fine, the models related to grid size yield poor results (for instance, the detached eddy simulation (DES) [5] and LES [6] models). Nevertheless, if the grid resolution is not sufficiently fine, the SAS model provides the URANS performance, which is reasonably capable of handling the flow. This feature seems attractive and can be regarded as a safeguard in the simulation of complex industrial flows [3]. Obviously, the performance of the SAS model depends on the RANS model used.