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We are interested in the study and improvement of the LES component in hybrid RANS-LES formulations. These models are not designed for blunt-body flows with laminar boundary layers, but it is interesting to examine how they behave in that case. A DDES model is compared with a dynamic Variational multi-scale (DVMS) LES model for two subcritical flows past a cylinder. We then propose a hybridation restricting to DVMS in LES regions. The performances of the different options are compared for subcritical flows and for a flow around a tandem cylinder.

Abstract. A frequent configuration in computational fluid mechanics combines an explicit time advancing scheme for accuracy purposes and a computational grid with a very small portion of much smaller elements than in the remaining mesh. Examples of such situations are the traveling of a discontinuity followed by a moving mesh, and the large eddy simulation of high Reynolds number flows around bluff bodies where together very thin boundary layers and vortices of much more important size need to be captured. For such configurations, explicit time advancing schemes with global time stepping are very costly. In order to overcome this problem, the multirate time stepping approach represents an interesting improvement. The objective of such schemes, which allow to use different time steps in the computational domain, is to avoid penalizing the computational cost of the time advancement of unsteady solutions which can become large due to the use of small global time steps imposed by the smallest elements such as those constituting the boundary layers. In the present work, a new multirate scheme based on control volume agglomeration is proposed for the solution of the compressible Navier-Stokes equations possibly equipped with turbulence models. The method relies on a prediction step where large time steps are performed with an evaluation of the fluxes on macro-cells for the smaller elements for stability purpose, and on a correction step in which small time steps are employed only for the smaller elements. The efficiency of the proposed method is evaluated on several benchmarks flows: the problem of a moving contact discontinuity (inviscid flow), the computation with hybrid turbulence model of flows around bluff bodies like a tandem cylinders at Reynolds number 1.66 × 10 5 , a circular cylinder at Reynolds number 8.4 × 10 6 , and a flow around a space probe model at Reynolds number 1 × 10 6 .4703

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Summary A frequent configuration in computational fluid mechanics combines an explicit time advancing scheme for accuracy purposes and a computational grid with a very small portion of much smaller elements than in the remaining mesh. Two examples of such situations are the travel of a discontinuity followed by a moving mesh, and the large eddy simulation of high Reynolds number flows around bluff bodies where together very thin boundary layers and vortices of much more important size need to be captured. For such configurations, multistage explicit time advancing schemes with global time stepping are very accurate but very CPU consuming. In order to reduce this problem, the multirate (MR) time stepping approach represents an interesting improvement. The objective of such schemes, which allow to use different time steps in the computational domain, is to avoid penalizing the computational cost of the time advancement of unsteady solutions that would become large due to the use of small global time steps imposed by the smallest elements such as those constituting the boundary layers. In the present work, a new MR scheme based on control volume agglomeration is proposed for the solution of the compressible Navier‐Stokes equations equipped with turbulence models. The method relies on a prediction step where large time steps are performed with an evaluation of the fluxes on macrocells for the smaller elements for stability purpose and a correction step in which small time steps are employed. The accuracy and efficiency of the proposed method are evaluated on several benchmarks flows: the problem of a moving contact discontinuity (inviscid flow), the computation with a hybrid turbulence model of flows around bluff bodies like a flow around a space probe model at Reynolds number 106, a circular cylinder at Reynolds number 8.4 × 106, and two tandem cylinders at Reynolds number 1.66 × 105 and 1.4 × 105.