EFFECTIVE TREATMENT OF THE SINGULAR LINE BOUNDARY-PROBLEM FOR 3-DIMENSIONAL GRIDS

THREE-DIMENSIONAL grids of rotation contain a singular line where the radial grid planes meet. When the flow equations are transformed into generalized coordinates, a mathematical singularity is introduced into the governing equations. Specifically, the grid Jacobian J becomes in finite along the singular line. This can introduce nonphysical perturb ations in the flow solution, particularly if a finite-difference solut ion algorithm is used. A number of recent publications1-5 have discuss ed problems associated with the singular line. This paper presents a m ethod for eliminating the axis singularity. The governing equations ar e reformulated using a redefined grid Jacobian that can be evaluated a t the singular line. This allows a finite-difference algorithm to comp ute a smooth, continuous solution in the region of the singular line.