OUR MULTISCALE FINITE ELEMENT MODEL OF GROUNDWATER FLOW TO RADIAL WELL

Abstract

A water supply system with radial wells (RWs) extends usually over tens of kilometers horizontally and tens of meters deep within the soil. Water flows through the soil and then through several lateral screens to the vertical shaft. Lateral screens represent perforated pipes with lengths in meters and diameters measured in centimeters. A common approach in modeling the water flow is to use governing equations based on the Darcy law and transform them to the finite element form. The 3D finite element mesh follows the anisotropy of the space and the elements are dimensionally large. It would be impractical, inefficient, and complex to model lateral screens by 3D elements, and, additionally, to include colmated layers with a thickness of small size (measured in centimeters) around the screens. Therefore, this is dimensionally a multiscale modeling problem. We have resolved this task by modeling the screens by 1D finite elements aligned to the 3D mesh, with the flow according to the Hagen-Poiseuille law. The 1D and 3D element nodes are connected by fictitious (connectivity) 1D elements where a radial flow from the soil to the internal space of the screens is assumed. We have implemented the multiscale model to our code PAK (Kojic et al., version in 2013) and applied it to the calibration of an RW of the Belgrade Groundwater Source.