A mesh transparent numerical method for large-eddy simulation of compressible turbulent flows.

A Large Eddy-Simulation code, based on a mesh transparent algorithm, for hybrid unstructured meshes is presented to deal with complex geometries that are often found in engineering flow problems. While tetrahedral elements are very effective in dealing with complex geometry, excessive numerical diffusion often affects results. Thus, prismatic or hexahedral elements are preferable in regions where turbulence structures are important. A second order reconstruction methodology is used since an investigation of a higher order method based upon Lele's compact scheme has shown this to be impractical on general unstructured meshes. The convective fluxes are treated with the Roe scheme that has been modified by introducing a variable scaling to the dissipation matrix to obtain a nearly second order accurate centred scheme in statistically smooth flow, whilst retaining the high resolution TVD behaviour across a shock discontinuity. The code has been parallelised using MPI to ensure portability. The base numerical scheme has been validated for steady flow computations over complex geometries using inviscid and RANS forms of the governing equations. The extension of the numerical scheme to unsteady turbulent flows and the complete LES code have been validated for the interaction of a shock with a laminar mixing layer, a Mach 0.9 turbulent round jet and a fully developed turbulent pipe flow. The mixing layer and round jet computations indicate that, for similar mesh resolution of the shear layer, the present code exhibits results comparable to previously published work using a higher order scheme on a structured mesh. The unstructured meshes have a significantly smaller total number of nodes since tetrahedral elements are used to fill to the far field region. The pipe flow results show that the present code is capable of producing the correct flow features. Finally, the code has been applied to the LES computation of the impingement of a highly under-expanded jet that produces plate shock oscillation. Comparison with other workers' experiments indicates good qualitative agreement for the major features of the flow. However, in this preliminary computation the computed frequency is somewhat lower than that of experimental measurements.