The "sharpness" of the plume front (that is the degree to which advection dominates the transport) is reflected by the grid Peclet Number:



where:

P_e =Peclet number

l = dimension of grid cell at the critical location

v = average linear velocity in the direction of flow at the critical location

D = dispersion coefficient in that direction at that location

critical location is where the combination os l v and D yield the largest Peclet number

or, if molecular diffusion is trivial, which is probably the case in a situation where you are concerned about the dominance of advection, then you can simplify the Peclet number to:

where:

P_e =Peclet number

delta l = dimension of the x/or/y/or/z grid cell at the critical location

alpha = dispersivity in that direction at that location

critical locations is where the combination of delta l and alpha yield the largest PEclet number= dispersivity in that direction at that location

 

When Advection dominates dispersion, designing a model with a small (<2 but sometimes as high as 10 will yield acceptable results) Peclet number will decrease oscillations, improve accuracy & decrease numerical dispersion.