|電子科学研究所 中央キャンパス総合研究棟2号館 5F北側講義室(北12条西7丁目)
|Texas Tech University
|On non-linear flows in porous media and application
In this talk we will be is focused on the analysis of nonlinear flows of compressible fluids in porous media not adequately described by Darcy’s law. We study a class of generalized nonlinear momentum equations which covers all three well-known Forchheimer equations, the so-called two-term, power, and three-term laws. The generalized Forchheimer equation is inverted to a nonlinear Darcy equation with implicit permeability tensor depending on the pressure gradient. This results in a degenerate parabolic equation for the pressure. Two classes of boundary conditions are considered, given pressure and given total flux. In both cases they are allowed to be unbounded in time. The uniqueness, Lyapunov and asymptotic stabilities, and other long-time dynamical features of the corresponding initial boundary value problems are analyzed. The results obtained in this paper have clear hydrodynamic interpretations and can be used for quantitative evaluation of engineering parameters. Some numerical simulations are also included. We will also discuss some aspects of two phase flows in porous media.
|北海道大学電子科学研究所 附属社会創造数学研究センター 人間数理研究分野 長山 雅晴 内線: 3357 firstname.lastname@example.org