General strong conservation formulation of Navier-Stokes equations in nonorthogonal curvilinear coordinates

Abstract

The selection of primary dependent variables for the solution of Navier-Stokes equations in the curvilinear body-fitted coordinates is still an unsettled issue. Reported formulations with primitive variables involve contravariant velocity components, Cartesian components, and velocity projections, also known as resolutes. Most of the formulations result in a weak conservation form of the momentum equations which contain grid line curvature- and divergence-related Coriolis and centrifugal terms. This paper presents a general strong conservation formulation of the momentum equations allowing the flexibility in choosing the various forms of the velocity components as the dependent variables. Ambiguous issues relating geometrical topology and forms of governing equations are discussed and clarified. Computational results obtained with both strong and weak forms are presented and compared to known analytical/experimental data. The results confirm the soundness of the formulation. 19 refs.