An online groundwater model was developed using an explicit formulation of the two-dimensional (x-y) diffusion equation of flow in porous media, applicable to a homogeneous isotropic aquifer, together with the scripting language PHP. The satisfaction of stability and convergence requires that the model's cell Reynolds number D = 1. The model has excellent mass conservation properties, being particularly suited for online learning of groundwater flow modeling and behavior. The model was tested under four scenarios: A, B, C and D. Scenario A assesses aquifer recovery under a permeable boundary, following depletion by pumping. Scenario B assesses aquifer depletion as a consequence of pumping, under a permeable boundary. Scenario C assesses aquifer recovery under an impermeable boundary, following depletion by pumping. Scenario D assesses aquifer depletion as a consequence of pumping, under an impermeable boundary. The permeable hot-start test (scenario A) converged to the steady-equilibrium baseline condition after 15.85 yr. The permeable cold-start test (scenario B) converged to a steady-equilibrium cone of depression after 12.43 yr. The impermeable hot-start test (scenario C) converged to a steady-equilibrium non-baseline condition after 8.34 yr. The impermeable cold-start test (scenario D) properly simulated the linear depletion of the aquifer.
