On the quasistatic approximation in the Stokes–Darcy model of groundwater–surface water flows

Abstract

We study the validity of the quasistatic approximation in the fully evolutionary Stokes–Darcy problem for the coupling of groundwater and surface water flows, as well as the dependence of the problem on the specific storage parameter. In the coupled equations that describe the groundwater and surface water flows for an incompressible fluid, the specific storage, $S_0$, represents the volume of water that a fully saturated porous medium will expel (or absorb) per unit volume per unit change in hydraulic head. In confined aquifers, $S_0$ takes values ranging from $10^{-6}$ or smaller to $10^{-2}$. In this work we analyze the validity of the previously studied quasistatic approximation (setting $S_0=0$ in the Stokes–Darcy equations) by proving that the weak solution of the fully evolutionary Stokes–Darcy problem approaches the weak solution of the quasistatic problem as $S_0\to 0$. We also estimate the rate of convergence.