COMPUTATIONAL FLUID DYNAMIC TECHNIQUE VALID AT THE CENTER-LINE FOR NON-AXISYMMETRIC PROBLEMS IN CYLINDRICAL COORDINATES

A technique is described for the numerical solution of non-axisymmetric flow problems posed in cylindrical coordinates when the z-axis is included in the flowfield. The highlight of the technique is the manner in which the singularities at the centerline are handled. Specifically, the governing flowfield equations at r = 0 are put in a special form by applying L'Hospital's Rule. The required radial derivatives are evaluated using a one-sided, second-order accurate, first-difference. This leads to a smooth, convergent calculation of the flow-field at the centerline. This appears to be the first generally applicable numerical method for avoiding coordinate system singularites in the context of a finite-difference scheme, and could have application to many non-axisymmetric flows. The technique is illustrated by specific results for the time-dependent flowfield inside an internal combustion engine. © 1979.