Darcian means provide a new mathematical and modeling framework in which ground water modelers may judge the appropriateness of their approximations for intergrid hydraulic conductivity means for vertical and horizontal unsaturated flow. They use and require knowledge of both the porous medium pressureconductivity relation and the model vertical space step size. The latest work demonstrates that many of the simple intergrid conductivity means produce numerous violations of a basic mathematical principle, the minmax principle for elliptic boundary value problems (steadystate flow in the vertical). Drafts and preprints of relevant papers are available in the links below.




Figures 3a and b from Dispersive Errors Induced by a NonDarcian Mean in a Model of Unsaturated Flow, showing how the arithmetic mean produces extremely nonphysical spikes and oscillations in a transient model of a verticallymoving wet pulse, when the arithmetic mean violates the minmax principle for similar conditions of steadystate flow 