Numerical simulation of liquid redistribution in permeable media involving hysteresis

In this paper, we explore new techniques for numerical simulation of liquid redistribution in permeable media involving hysteresis. We regard the hysteresis as a kind of passive fractional resistance, and integrate it into Partial Differential Equations (PDE). Also numerical methods such as the Finite Volume Method (FVM) are developed. A system of partial differential equations is derived for liquid pressure, including the effects of hysteresis and mixed media. The finite difference schemes based on the conservative law are also provided, which are well suited to the mixed media made up of different material layers. A new algorithm is deliberately designed to evaluate the total liquid volume that satisfies the conservative law exactly.

Furthermore, numerical examples are conducted to imitate the following fascinating phenomena in real physics.

1. (a) The nonuniform equilibrium saturation in redistribution.

2. (b) The noncontinuity of saturation at the interface of mixed media.

3. (c) Conservation of the total liquid volume even when t is large.

The new numerical techniques in this paper are not only easy to carry out with a modest computational effect, but also effective to simulate the real porous flow in the laboratory experiments.