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.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.