These can lead to grid crossovers. Its hence best to smoothen the adaptive control functions by simple averaging. Each iteration extends the field of influence of the control by one grid point in all directions. A small value epsilon for normalizing derivatives 0.00001 Multiplication factors for Geometric Control. Else adaptive control functions are calculated in each direction only with respect to the weight function in that direction.
Epsilon serves as a small number to avoid a division by zero.
It also acts as a filter for the flow features resolved. The multipliers magnify the control functions by the specified amount. This way the user can change the effectiveness of each of the factors controlling the grids. Updating the patches every 5-6 iterations is usually good enough, but it depends on application and how much the grid changes with every iteration. The last parameter specifies the number of iterations between solution interpolation.