A SEGREGATED SOLUTION ALGORITHM FOR INCOMPRESSIBLE FLOWS IN GENERAL COORDINATES

To analyse an incompressible Navier-Stokes flow problem in a boundary- fitted curvilinear co-ordinate system is definitely not a trivial task . In the primitive variable formulation, choices between working varia bles and their storage points have to be made judiciously. The present work engages contravariant velocity components and scalar pressure wh ich stagger each other in the mesh to prevent even-odd pressure oscill ations from emerging. Now that smoothness of the pressure field is att ainable, the remaining task is to ensure a discrete divergence-free ve locity field for an incompressible flow simulation. Aside from the flu x discretizations, the indispensable metric tensors, Jacobian and Chri stoffel symbols in the transformed equations should be approximated wi th care. The guiding idea is to get the property of geometric identity pertaining to these grid-sensitive discretizations. In addition, how to maintain the revertible one-to-one equivalence at the discrete leve l between primitive and contravariant velocities is another theme in t he present staggered formulation. A semi-implicit segregated solution algorithm felicitous for a large-scale flow simulation was utilized to solve the entire set of basic equations iteratively. Also of note is that the present segregated solution algorithm has the virtue of requi ring no user-specified relaxation parameters for speeding up the satis faction of incompressibility in an optimal sense. Three benchmark prob lems, including an analytic problem, were investigated to justify the capability of the present formulation in handling problems with comple x geometry. The test cases considered and the results obtained herein make a useful contribution in solving problems subsuming cells with ar bitrary shapes in a boundary-fitted grid system.