Nonlinear Flow in Porous Media: Numerical Solution of the Navier-Stokes System with Two Pressures and Application to Paper Making

Flow phenomena in porous media are of great practical interest in applied science and technology. Darcy`s law is commonly used to model and simulate slow flows through porous structures. It states a linear relationship between effective velocity and pressure gradient and was found experimentally in 1856. Moreover, rigorous mathematical justifications based on first principles have been available since three decades. In the case of nonlinear (or fast) flows, empirical laws had to be used until recently due to the lack of mathematical theory.In the present book, a new two-scale homogenization approach developed by A. Mikelic et al. is numerically investigated. Considering the Navier-Stokes equations on the pore-scale, a suitable averaging procedure allows to derive nonlinear filtration laws and error estimates. The derived filtration laws are computed and applied in a macroscopic model of a press nip of a paper machine.The book is aimed at applied mathematicians, physicists, mechanical and process engineers.