论文标题
多孔培养基的动力学方法填充了不可压缩流体的几何变异方法
Geometric variational approach to the dynamics of porous media filled with incompressible fluid
论文作者
论文摘要
我们得出了充满不可压缩流体的多孔培养基动力学的运动方程。我们使用以拉格朗日为代表弹性矩阵动力学和势能的术语的差异方法，以及流体的动能，通过不可压缩性的约束结合。作为该方法的例证，弹性基质和流体的运动方程式均在空间（Eulerian）框架中得出。这种方法是相关的，例如对于生物学问题，例如在水中的海绵中，弹性多孔培养基具有很高的灵活性，并且流体的运动在整个系统的运动中具有“主要”作用。然后，我们分析了描述通过介质传播波的运动的线性化方程。特别是，我们在各向同性介质中得出了S波和P波的传播。我们还分析了波动方程的稳定性标准，并表明它们等于弹性矩阵的物理条件。最后，我们表明，对于我们的模型中的某些参数值，获得了多孔介质中著名的Biot方程。
We derive the equations of motion for the dynamics of a porous media filled with an incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the elastic matrix, and the kinetic energy of the fluid, coupled through the constraint of incompressibility. As an illustration of the method, the equations of motion for both the elastic matrix and the fluid are derived in the spatial (Eulerian) frame. Such an approach is of relevance e.g. for biological problems, such as sponges in water, where the elastic porous media is highly flexible and the motion of the fluid has a 'primary' role in the motion of the whole system. We then analyze the linearized equations of motion describing the propagation of waves through the media. In particular, we derive the propagation of S-waves and P-waves in an isotropic media. We also analyze the stability criteria for the wave equations and show that they are equivalent to the physicality conditions of the elastic matrix. Finally, we show that the celebrated Biot's equations for waves in porous media are obtained for certain values of parameters in our models.
