Mathematical analysis of a Dupuit-Richards model
Al Nazer, Safaa
Texas State University, Department of Mathematics
This article concerns an alternative model to the 3D-Richards equation to describe the flow of water in shallow aquifers. The model couples the two dominant types of flow existing in the aquifer. The first is described by the classic Richards problem in the upper capillary fringe. The second results from Dupuit's approximation after vertical integration of the conservation laws between the bottom of the aquifer and the saturation interface. The final model consists of a strongly coupled system of parabolic-type partial differential equations that are defined in a time-dependent domain. First, we show how taking the low compressibility of the fluid into account eliminates the nonlinearity in the time derivative of the Richards equation. Then, the general framework of parabolic equations is used in non-cylindrical domains to give a global in time existence result to this problem.
Dupuit-Richards equations, Free boundary problems, Global solution, Weak solution, Fluid flow modeling
Al Nazer, S., Rosier, C., & Tsegmid, M. (2022). Mathematical analysis of a Dupuit-Richards model. <i>Electronic Journal of Differential Equations, 2022</i>(06), pp. 1-22.
Attribution 4.0 International