A large-eddy simulation methodology in generalized curvilinear coordinates

A generalized curvilinear coordinate formulation for the large-eddy simulation (LES) that centers on the fact that two spatial operations are necessary to complete the derivation is proposed. The recommended order of operations is to transform the full resolution system prior to filtering. This sequence rationally directs the filter operation along the curvilinear lines, thereby facilitating explicit evaluation of the Leonard stress and its isolation from the relative errors associated with the finite-difference approximations of the convective derivative. Representing the transformation metrics as filtered quantities in the formulation is justified through their numerical approximation. The generalized LES formulation was tested using direct numerical simulation results of the circular cylinder near wake at Re = 3400. No discernible differences were detected in the spectral energies of the turbulent fluctuations by filtering in either the physical domain or the transformed space. However, the latter filtering scheme was considerably cheaper. In the transformed space, high-order numerical approximations are required for the convective derivatives to inhibit overshadowing of the concurrent contributions by the Leonard stress at all wave-numbers.