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

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.