Читать книгу The Mathematics of Fluid Flow Through Porous Media - Myron B. Allen III - Страница 26

As mentioned in Section 2.3, the Navier–Stokes equation (2.15) poses formidable mathematical challenges. Exact solutions are known only in special geometries and only under highly restrictive assumptions, many of which allow us to neglect the nonlinear inertial term . We now examine two such problems in fluid mechanics that bear on the analysis of flows in porous media. Each serves as a highly simplified model of fluid flow in the interstices of a porous medium, and each involves significant reductions in complexity compared with the full Navier–Stokes equation. The Hagen–Poiseuille problem is a simple model of fluid flows in a straight, cylindrical tube, which one can envision as an idealized pore channel. The Stokes problem models slow, viscous flows around a solid sphere, which one can imagine as an idealized solid grain.