Numerical recirculating flow calculation using a body-fitted coordinate system

A finite-difference algorithm for recirculating flow problem! in a body-fitted coordinate system is presented. A fully staggered grid system is adopted for the velocity components and the scalar variables. The strong conservation law form of the governing equations is written in the general curvilinear coordinates. The SIMPLE calculation procedure originally developed in Cartesian coordinates is extended to the present curvilinear coordinates. Two methods of evaluating the metric derivatives are discussed. Although both methods are formally of the same order of accuracy, it is shown that one performs the physical conservation laws more accurately than the other. The relative merits of three schemes, i.e., hybrid, second-order upwinding, and QUICK, for approximating the convection terms in the momentum equations are compared and the results are quite different from those in Cartesian coordinates in both accuracy and efficiency aspects. The effects of the grid distribution are also studied. Results obtained using the same numerical procedures but with different grid distributions can be very different; the choice of the grid distribution appears to be at least as important as the choice of the difference scheme. It is found that the numerical stability can also be greatly affected by the choice of the finite-difference scheme as well as the grid distribution. Overall, the second-order upwind scheme appears to be superior to the others.