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首页> 外文会议>IUYAM Symposium on Theoretical and Numerical Methods in Continuum Mechanics of Porous Materials, Sep 5-10, 1999, Stuttgart, Germany >Fluid Mechanics in Minkowski Space. Modelling of Fluid Motion in Porous Materials with Anisotropic Pore Space Structure
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Fluid Mechanics in Minkowski Space. Modelling of Fluid Motion in Porous Materials with Anisotropic Pore Space Structure

机译：Minkowski空间中的流体力学。具有各向异性孔空间结构的多孔材料中流体运动的建模

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In the paper a fluid motion in a rigid porous medium of anisotropic pore space structure is described. Considerations are based on the new macroscopic model of saturated porous medium (Cieszko [4], [5]) in which the fluid flow through porous skeleton of anisotropic pore structure is described as a motion of the material continuum in the plane anisotropic metric space - Minkowski space - immersed in Euclidean one that is the model of the physical space. This model takes into account the fundamental fact for kinematics of fluid-saturated porous solid that pore space of permeable skeleton forms the real space for a fluid motion and its structure imposes restriction on that motion. In such approach the metric tensor of the Minkowski space is used to characterise the anisotropic structure of the skeleton pore space. It enabled one to determine the measures of any line, surface and volume elements in Minkowski and Euclidean spaces and to define the geometrical parameters characterising pore structure of porous materials: tortuosity, surface and volume porosity. The mass and linear momentum balance equations for fluid are derived and the equation for wave propagation in barotropic inviscid fluid filling orthotropic space of pores is obtained. It is shown that the velocity of the plane wave in such a medium depends on the direction of wave propagation. It worth to underline that presented description of fluid motion in the Minkowski space is a good starting point for modelling of mechanics of deformable porous solid saturated with fluid where the concept of deforming anisotropic space (Finsler space) as a model of pore space would have to be used.
机译：在本文中，描述了在各向异性孔空间结构的刚性多孔介质中的流体运动。考虑因素基于饱和多孔介质的新宏观模型（Cieszko [4]，[5]），其中流体流经各向异性孔结构的多孔骨架被描述为材料各向异性在平面各向异性度量空间中的运动- Minkowski空间-浸入欧几里得空间中，这是物理空间的模型。该模型考虑了流体饱和多孔固体运动学的基本事实，即渗透性骨架的孔隙空间形成了流体运动的真实空间，并且其结构对该运动施加了限制。在这种方法中，使用Minkowski空间的度量张量来表征骨架孔隙空间的各向异性结构。它使人们能够确定Minkowski和Euclidean空间中任何线，表面和体积元素的尺寸，并定义表征多孔材料孔隙结构的几何参数：曲折度，表面孔隙率和体积孔隙率。推导了流体的质量和线性动量平衡方程，得到了在正压无粘性流体填充孔的正交各向异性空间中的波传播方程。结果表明，平面波在这种介质中的速度取决于波的传播方向。值得强调的是，对Minkowski空间中流体运动的描述是对流体饱和的可变形多孔固体进行力学建模的一个很好的起点，其中将各向异性空间（Finsler空间）变形为孔隙空间模型的概念必须使用。

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