Adaptive Grid Refinement for High-Order Finite Volume Simulations of Unsteady Compressible and Turbulent Flows

This study investigates dynamic mesh adaptation (DMA) for hybrid RANS/LES (HRLES) simulations of compressible turbulent flows. HRLES models, which blend Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES), are by their nature very sensitive to the computational mesh, because of the very different resolution requirements in the RANS and LES regions. The proposed DMA strategy relies on a high-order k-exact finite volume spatial discretisation [Pont et al. 2017. Multiple-Correction Hybrid k-Exact Schemes for High-Order Compressible RANS-LES Simulations on Fully Unstructured Grids. Journal of Computational Physics 350: 45-83] designed to ensure robust, accurate and conservative solutions for compressible flows with strong discontinuities while limiting the numerical dissipation of vortical structures. A mesh refinement criterion related to the truncation error of the k-exact reconstruction scheme is introduced, and compared with several heuristic refinement criteria from the literature. To limit the computational burden of frequent re-meshing for unsteady flow simulations, the adaptation is performed only at certain time steps, and the error criterion is averaged over the chosen adaptation period. A simple and effective criterion is then introduced to automatically control the adaptation period. The proposed DMA strategy is evaluated against a series of test cases of increasing complexity, ranging from inviscid vortex advection to turbulent transonic flow past an axisymmetric backward-facing step, representative of the base flow behind a space launcher.