On Applicability of Local Inertia Model for Integrated Surface-Subsurface Flow Systems

Interaction between surface water and groundwater is observed in all-natural water bodies such as lakes and ponds and coastal areas. This complex interaction of fluid and the porous media can be resolved in three-dimensional models with significant accuracy, however, with humongous computational overhead. Very few unified surface and groundwater flow models exist in the literature, where a single set of equations can describe such flows. The current study considers a single set of conservation laws for flow in/outside of porous media obtained from the volume-averaging and then subsequent depth-averaging of the three-dimensional conservation laws. Further simplifications based on the assumption that inertial effects in these flows are very small leads to the development of the current local inertia model (LIM). LIM conceptualization of the flow significantly reduces the computational overhead compared to diffusive wave models, signaling potential extension to the real-time scenarios. The resulting model is solved using an augmented approximate Riemann solver [Harten, Lax, and Leer (HLL) method]. The potential applicability of the model is tested against different representative scenarios (such as vertical and inclined interfaces).