Wall-Resolved Large-Eddy Simulation of the LS89 Cascade Using an Explicit Local Time-Stepping Method

Today, most turbomachinery CFD simulations rely on computational domains where a large heterogeneity of mesh refinement is present, targeting specific flow regions while relaxing the mesh size in regions of lesser interest. For example, in the context of wall-resolved Large-Eddy Simulations (LES), typical cell size ratios between the main stream grid resolution and the near-wall regions may reach several orders of magnitude.  Although justifying the use of multi-element solvers, such a local refinement / coarsening strategy usually results in a very stringent time step selection especially in the context of compressible flows necessary for turbomachinery applications. For performance, such code algorithms usually rely on explicit time-advancement methods which are very efficiently parallelized. However, this comes with the cost of stability constraints which in the context of multi-element solvers and grid refinement can rapidly be very limiting. The alternative is the use of an implicit time-advancement with the indirect cost of a major coding effort to obtain efficient parallelisation but also with the risk of arbitrarily selecting a time step that may not allow the proper time scale resolution necessary to predict such highly turbulent flows given a grid. Another consequence of grid heterogeneity is that its imposes a single time step for the entire domain of simulation (i.e. the smallest cell CFL condition), which is in most other cells smaller than necessary.  Such a choice again greatly reduces the simulation efficiency since the optimal local CFL of a given scheme is only applicable to a small subset of points of the entire grid. One way to address this issue is to introduce the notion of Local Time-Stepping (LTS). With this formalism, one proposes to divide a given computational domain into sub-domains and associated grids composed of comparable cell sizes. Compressible Navier-Stokes equations are then solved simultaneously for each sub-grid with its dedicated time step meeting the local grid optimal CFL condition. Implemented in the LES explicit solver AVBP, a massively parallel cell-vertex based compressible solver, capable of handling unstructured hybrid meshes, LTS is assessed for configurations where layers of prisms are used in the near-wall region of the blade and tetrahedra are used in the rest of the domain. Both sub-grids are then coupled with an overset grid method, the overlap region between the two grids making use of an interpolation to exchange information. In the following, LTS is first tested and validated for basic test cases: one simple 1D travelling acoustic wave and a vortex propagation test case to confirm the suitability of such a technique, evaluate gains and prove its ability to recover numerical scheme orders.  It is then applied to the LS89 cascade turbomachinery flow. For this last case, the computational domain is divided in two grids: one containing the blade wall and its vicinity; and a second one covering the rest of the domain. Results obtained with wall-resolved LES’s using a single domain and LTS are compared to the experimental data to evaluate the impact on the flow predictions. Overall, for the LS89 configuration that is known as challenging, there is a good agreement between simulations and experiment. More importantly, the results are almost identical when comparing the single domain and the LTS cases despite the significant simulation cost reduction for the latter.