Investigating pore network models as numerical tools to solve steady saturated groundwater ow

In this paper, a novel procedure is introduced and employed to transform the partial dierential steady saturated ow equation in porous media into a system of linear equations using Pore Network Models (PNMs). At rst, a simple Square Pore Network Model (SPNM) is introduced and then this model is improved by increasing node connectivity (Square-Diagonal PNM; S-DPNM) and modifying the handling of impermeable boundaries by introducing imaginary nodes and pipes (S-DPNMi). Finally, a generalized formulation for the unstructured discretization (Unstructured PNM; UPNM) of the domain is given and the eect of handling impermeable boundaries (UPNMi) on model accuracy is investigated. To explore the capabilities of these models as numerical tools, three examples are solved. Application of these models without modications for impermeable boundaries (SPNM, S-DPNM, and UPNM) yields comparable results to those of traditional Finite Dierence (FD) and Finite Element (FE) methods. Modication in handling impermeable boundary nodes not only yields results that are everywhere more accurate than FD and FE, but also benets by the simplicity of formulations