饱和多孔介质渗流的强-弱不连续统一非局部模型

Unified Nonlocal Model Incorporating Strong-Weak Discontinuities for Fluid Transport in Non-Uniform Saturated Porous Media

摘要:

非均匀饱和多孔介质流体传输模拟关键在于需要考虑由孔隙、裂隙以及不同渗透性介质组成的强–弱不连续面，但这与经典连续介质力学局部流体模型所定义的偏微分方程是不相容的，从而导致饱和多孔介质渗流模拟的困难。基于统一变分近场动力学的基本思想，提出了一种向量态函数用于描述饱和多孔介质流体的非局部传输作用，并在此基础上建立饱和多孔介质流体输运的非局部空间积分–时间微分型控制方程。该非局部流体输运模型统一描述了流体在强–弱不连续面的力学行为，避免了传统局部力学模型在不连续界面处的导数无定义性，且从理论上证明，当非局部流体模型中的非局部作用半径趋于零时，非局部模型可退化为局部模型。为了消除非局部模型内在的零能模式问题，基于罚函数方法提出一种全隐式的数值求解格式以保证数值计算的精确性。最后通过算例分析，模拟了三维非均匀不连续多孔介质中流体的传输过程，揭示流体穿越物质界面、孔隙和裂隙的力学行为。为研究饱和多孔介质中流体在不连续界面传输的力学行为提供了一种分析模型。

Abstract:

The critical issue for fluid transport simulation in non-uniform saturated porous media is to capture the mechanical behavior of fluids in the strong-weak discontinuities composed of pores， fractures， and media with different permeabilities， however， this is incompatible with the partial differential equation defined by the local fluid model in classical continuum mechanics， which leads to the difficulty of fluid simulation in saturated porous media. Based on the basic idea of unified variational peridynamics， this paper proposes a new vector state function to describe the nonlocal transport effects of fluid in saturated porous. Using the proposed fluid flux state function， this paper develops a nonlocal governing equation of fluid transport in saturated porous media. The nonlocal fluid transport model uniformly describes the mechanical behavior of fluid at the strong-weak discontinuity， avoiding the singularity of local derivative at the discontinuities. It is theoretically proved that when the radius of nonlocal effects in the nonlocal fluid model approaches to zero， the nonlocal model can be degenerated into the local ones. In order to eliminate the inherent zero energy mode problem of the nonlocal model， a fully implicit numerical scheme combined with the penalty function method is proposed to ensure the accuracy of the numerical solution. Numerical examples show that the proposed model can accurately capture the mechanical behavior of fluid passing through material interfaces， pores， and cracks. This paper provides a new model for studying the mechanical behavior of fluid transport at discontinuities in saturated porous media.