Boussinesq equation for flow in an aquifer with time dependent porosity

摘要

A problem of the Boussinesq type for flow of incompressible fluid through a medium with the porosity φ being a given function of time is studied. At first, from the continuity equation the Dupuit relation for the fluid velocity in the considered medium is found. Next the Boussinesq equation is derived for the medium. This equation, if written for quantity H = h/φ and not for the hydraulic head h, has a form of the classical Boussinesq equation, with the coefficient not constant but dependent on time, however. An example of the solution of the modified Boussinesq equation is also given.