Hq. Yang et al., GENERAL STRONG CONSERVATION FORMULATION OF NAVIER-STOKES EQUATIONS INNONORTHOGONAL CURVILINEAR COORDINATES, AIAA journal, 32(5), 1994, pp. 936-941
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.