Classical finite-difference methods apply only over regions that are rectangular or decomposed in several rectangular subdomains. We call a finite-difference scheme direct if it can be applied over any region decomposed using a logically-rectangular grid.

Numerical simulations of a linearly stratified diffusive flow past an impulsively started sphere are described. The impulsive start is perpendicular to isopycnal surfaces. The equations are transformed to generalized coordinates and then approximated by a finite difference scheme over a suitable grid which resolves both the diffusive and viscous boundary-layers. The results are compared with experimental evidence.