A variational principle for the system of P.D.E. of porous metal bearings

A variational approach for the deformation of a saturated porous solid. A second-gradient theory extending Terzaghi's effective stress principle

The principle of virtual power is used to derive the equilibrium field equations of a porous solid saturated with a fluid, including second density-gradient effects; the intention is the elucidation and extension of the effective stress principle of Terzaghi and Fillunger. In the context of a first density-gradient theory for a saturated solid we interpret the porewater pressure as a Lagrange multiplier in the expression for the deformation energy, assuring that the saturation constraint is verified. We prove that this saturation pressure is distributed among the constituents according their r…

基于Onsager变分原理的多孔介质方程移动网格方法

A Moving Mesh Method for Porous Medium Equation by the Onsager Variational Principle

本文基于Onsager变分原理提出移动网格有限元方法求解多孔介质方程，保持能量耗散结构，并开发了完全解耦显式格式，在适当初始网格下具有最优收敛阶，且能自然捕捉等待时间现象。

非均质多孔介质中地下水流和输运的变分多尺度公式的性能

On the performance of the variational multiscale formulation for subsurface flow and transport in heterogeneous porous media

通过数值实验比较了最低阶Raviart-Thomas单元和变分多尺度稳定化单元在高度非均质多孔介质流动与输运问题中的性能，揭示了变分多尺度单元在特定流动条件下存在显著的质量不守恒问题。

Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media

Using thermodynamic and variational principles we examine a basic phase field model for a mixture of two incompressible fluids in strongly perforated domains. With the help of the multiple scale method with drift and our recently introduced splitting strategy for Ginzburg-Landau/Cahn-Hilliard-type equations [Schmuck et al., Proc. R. Soc. A 468:3705-3724, 2012.], we rigorously derive an effective macroscopic phase field formulation under the assumption of periodic flow and a sufficiently large Péclet number. As for classical convection-diffusion problems, we obtain systematically diffusion-disp…