标题： 关于各向同性均质多孔介质中流体流动抛物型模型的有效范围 显示英文标题

标题： On the range of validity of parabolic models for fluid flow through isotropic homogeneous porous media

摘要： 格子玻尔兹曼方法是用于流体流动的成熟的介观数值方案，能够恢复宏观量（即速度和压力场）在宏观目标方程作用下的演化。 流体流动的近似目标方程通常是抛物型的，并包含一个（弱）可压缩性项。 已经成功开发了一些针对或利用代表性体积内多孔介质流动的格子玻尔兹曼模型。 然而，除了两个例外情况外，这些方程并未被报告，或者对这些方程的假设和近似没有完全澄清。 在本工作中，讨论、澄清并列出了代表体积内多孔流动抛物型方程的基本假设。 结果表明，通常采用的忽略水力弥散的假设并不能通过明确的论据来证明——事实上，如果不采用该假设，就可以在达西定律的布林克曼修正中提供有效粘度的定性和定量表达。 最后，结果表明，在某些条件下，可以将多孔模型解释为欧拉-欧拉多相模型，其中一相是固体基质。 显示英文摘要

摘要： Lattice-Boltzmann methods are established mesoscopic numerical schemes for fluid flow, that recover the evolution of macroscopic quantities (viz., velocity and pressure fields) evolving under macroscopic target equations. The approximated target equations for fluid flows are typically parabolic and include a (weak) compressibility term. A number of Lattice-Boltzmann models targeting, or making use of, flow through porous media in the representative elementary volume, have been successfully developed. However, apart from two exceptions, the target equations are not reported, or the assumptions for and approximations of these equations are not fully clarified. Within this work, the underlying assumption underpinning parabolic equations for porous flow in the representative elementary volume, are discussed, clarified and listed. It is shown that the commonly-adopted assumption of negligible hydraulic dispersion is not justifiable by clear argument - and in fact, that by not adopting it, one can provide a qualitative and quantitative expression for the effective viscosity in the Brinkman correction of Darcy law. Finally, it is shown that, under certain conditions, it is possible to interpret porous models as Euler-Euler multiphase models wherein one phase is the solid matrix.