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The problem concerns the rise of a smoke plume as it is carried along by an air stream having an imposed shear-flow velocity profile at the inlet of a long tunnel

Three-Dimensional steady flow with buoyancy
The Cartesian computational grid has 40 intervals in width x, 40 in height y, and 625 in length, z
Solved-for variables are three velocities, pressure, temperature and smoke concentration
At inlet, the longitudinal velocity profile inceases linearly with height; and a rectangular-sectioned stream of hot smoke enters, the remainder being occupied by atmospheric-temperature air
Buoyancy causes flow in cross-section to exhibit vortices

This case shows how the parabolic option can be employed with advantage for fine-grid calculations on machines of modest size.
Although there are one millionn cells in all, a computer with memory big enough for only 1600 will suffice

Pictures are as follows :

1.The computational grid section across the tunnel

2. An animated sequence of smoke contours
at successive distances along the tunnel

3. Velocity vectors at the tunnel exit