GENERAL STRONG CONSERVATION FORMULATION OF NAVIER-STOKES EQUATIONS INNONORTHOGONAL CURVILINEAR COORDINATES

The selection of primary dependent variables for the solution of Navie r-Stokes equations in the curvilinear body-fitted coordinates is still an unsettled issue. Reported formulations with primitive variables in volve contra-variant velocity components, Cartesian components, and ve locity projections, also known as resolutes. Most of the formulations result in a weak conservation form of the momentum equations which con tain grid line curvature and divergence-related Coriolis and centrifug al terms. This paper presents a general strong conservation formulatio n of the momentum equations allowing the flexibility in choosing the v arious forms of the velocity components as the dependent variables. Am biguous issues relating geometrical topology and forms of governing eq uations are discussed and clarified. Computational results obtained wi th both strong and weak forms are presented and compared to known anal ytical/experimental data. The results confirm the soundness of the for mulation.