A numerical method for solving momentum equations in generalized coordinates - Its application to three-dimensional separated flows

A finite difference calculation procedure has been developed for the calculations of the three-dimensional fully elliptic flows over irregular boundaries. A simple control volume analysis is introduced to reformulate the momentum equations in the generalized velocity and coordinate system, without resorting to any extensive tensor calculus. The finite difference equations are obtained by discretizing the conservation equations in this generalized system. For a practical application of the present finite difference calculation scheme, calculations are carried out on the three-dimensional separated flow in a converging-diverging rectangular duct. The calculation results reveal an extremely complex nature of the three-dimensional separated flow.