The vadose zone is the portion of the subsurface above the water table and its porespace usually contains air and water. Due to the presence of infiltration, erosion, plant growth,microbiota, contaminant transport, aquifer recharge, and discharge to surface water, it is crucial topredict the transport rate of water and other substances within this zone. However, flow in thevadose zone has many complications as the parameters that control it are extremely sensitive to thesaturation of the media, leading to a nonlinear problem. This flow is referred as unsaturated flow and isgoverned by Richards equation. Analytical solutions for this equation exists only for simplified cases, somost practical situations require a numerical solution. Nevertheless, the nonlinear nature of Richardsequation introduces challenges that causes numerical solutions for this problem to be computationallyexpensive and, in some cases, unreliable. High order mimetic finite difference operators are discreteanalogs of the continuous differential operators and have been extensively used in the fields of fluidand solid mechanics. In this work, we present a numerical approach involving high order mimeticoperators along with a Newton root-finding algorithm for the treatment of the nonlinear component.Fully-implicit time discretization scheme is used to deal with the problem’s stiffness.
Homogenization of periodic differential operators of high order
