Current developments driven by several communities focus on exploring options to improve DES and WMLES methods.  
There are novel methodological developments in this regard, such as minimal error simulation methods referred to as continuous eddy simulation (CES) [7; 25; 26; 27; 28; 29; 30; 31; 32]. Such CES methods can be used in conjunction with all usually applied turbulence models, including probability density function (PDF) and Reynolds stress equation methods. These methods are based on exact mathematics. They are essentially independent from a variety of simulation settings applied in WMLES and DES methods. Their use continuously enables simulations of partially resolving flow regimes ranging from RANS to LES. Such CES methods receive limited attention so far because their design is different from mainstream approaches. Unsteady RANS equations are known to be capable of involving resolved motion in simulations, but (similar to LES applied on coarse grids) this is no guarantee of a proper simulation performance. The idea that RANS-type equations can stably resolve flow like LES is not generally accepted. CES methods do not explicitly involve information about the grid as given by the filter width \(\Delta\). The latter is usually seen as requirement for proper LES.  
The motivation of this paper is to contribute to the clarification of the latter essential questions. The flow considered, which is the axisymmetric transonic bump flow experimentally studied by [PERSON] and [PERSON] [33], is a complex and high Reynolds number (_Re_) flow. It stands as a well-established test case for assessing turbulence models due to its characteristics involving separation, shock waves, and downstream reattachment, along with various regions of steep gradients. Remarkably, this flow closely resembles the flow over an aircraft, such as the NASA Common Research Model (CRM) under transonic cruise conditions. RANS predictions of this flow reveal significant problems, i.e., the performance of simulation methods depends essentially on the proper inclusion of resolved motion. However, partially resolving simulation methods (such as DES and WMLES) and even WRLES face significant issues regarding such flow simulations. For example, [PERSON] et al. concluded that \"WMLES results are disappointing, even in terms of the shock position, even though the results from two grids, respectively, agree well with each other. This failure of grid refinement to warn of an inaccurate simulation is of great concern\" [34].  
The following are the specific objectives of our investigation:  
1. Performance features: demonstration that CES methods are characterized by a simulation performance that is better than the performance of RANS and usually applied hybrid RANS-LES (in particular DES and WMLES methods) and at least as good as the performance of WRLES.
2. Cost features: demonstration that the computational cost of CES is significantly below the cost of hybrid RANS-LES (DES and WMLES methods) and WRLES.
3. Functionality features: Demonstration that CES is independent of significant functionality requirements of hybrid RANS-LES and WRLES (choice of sufficiently fine grids, appropriate mesh distributions, specific simulation settings for a flow considered, validation data needed to determine simulation settings).  
This paper is organized in the following way. Section 2 introduces the modeling and computational approach. Section 3 describes the resolution features of the CES model considered. Section 4 compares the performance and computational cost of CES with RANS, DES, WMLES, and WRLES methods. The conclusions of this study are presented in Section 5.