The Gas Project Non Divergent Adaptive DOP removes divergence from a fluid’s velocity field. Divergence in a velocity represents expansion or contraction of the fluid volume. This divergence is projected out of the velocity field by computing a pressure field throughout the simulated fluid and then applying the gradient of the pressure field to the velocity field. The pressure field is solved on an adaptive (octree) background grid to significantly improve performance over solving with a uniform grid (as done in the Gas Project Non Divergent Variational DOP).

In order to maintain high resolution details in the simulation, a band of fine grid cells are constructed along the boundaries of the fluid. The grid is then progressively coarsened into the interior of the fluid. To minimize the difference between the adaptive and uniform grid pressure solves, the adaptive pressure is up-sampled and smoothed back to the uniform grid before updating the velocity field.

more info: https://www.sidefx.com/docs/houdini18.0/nodes/dop/gasprojectnondivergentadaptive.html

.: Godzilla - nonAdaptive vs adaptive :.