Macroscale seepage equation

Furthermore, if we introduce an integral averaging (- j in the micro-domain S2i, we obtain the following macroscale seepage equation ... 

If a homogenization analysis (HA) is applied to porous media flow, which is described by the Stokes equation, we can immediately obtain Darcy s formula and the seepage equation in a macroscale field while in the microscale field the distributions of velocity and pressure are specified (Sanchez-Palencia 1980). We can also apply HA for a problem with a locally varying viscosity. 

Darcy s law (8.22) into the averaged (8.17), we obtain the following homogenized seepage equation, which gives the macroscale incompressibility condition ... 

In order to solve the multiscale HA seepage problem, we proceed as follows First we solve the microscale equations (8.49) and (8.53), and obtain the characteristic functions vf and p. We next determine the permeabilities Kfj and Kij in the meso-domain and macro-domain using (8.54) and (8.60). Then we can solve the macroscale equation (8.59), and obtain the pressure p. By substituting these into... 

---

See also in sourсe #XX -- [ ]

---