A large-eddy simulation methodology in generalized curvilinear coordinates

A generalized curvilinear coordinate formulation for the large-eddy simulat ion (LES) that centers on the fact that two spatial operations are necessar y to complete the derivation is proposed. The recommended order of operatio ns is to transform the full resolution system prior to filtering. This sequ ence rationally directs the filter operation along the curvilinear lines, t hereby facilitating explicit evaluation of the Leonard stress and its isola tion from the relative errors associated with the finite-difference approxi mations of the convective derivative. Representing the transformation metri cs as filtered quantities in the formulation is justified through their num erical approximation. The generalized LES formulation was tested using dire ct 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 th e 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 con current contributions by the Leonard stress at all wave-numbers.