Evaluation of a numerical simulation model for a system coupling atmospheric gas, surface water and unsaturated or saturated porous medium

• An equation for global pressure was newly derived.
• A global pressure equation was integrated into a numerical simulator.
• Global pressure was specified at the boundaries of a porous medium.
• Results of column experiments and simulations were compared.
• Results confirmed the validity of the derived global pressure equation.

Numerical simulations that couple flow in a surface fluid with that in a porous medium are useful for examining problems of pollution that involve interactions among the atmosphere, surface water and groundwater, including, for example, saltwater intrusion along coasts. We previously developed a numerical simulation method for simulating a coupled atmospheric gas, surface water, and groundwater system (called the ASG method) that employs a saturation equation for flow in a porous medium; this equation allows both the void fraction of water in the surface system and water saturation in the porous medium to be solved simultaneously. It remained necessary, however, to evaluate how global pressure, including gas pressure, water pressure, and capillary pressure, should be specified at the boundary between the surface and the porous medium. Therefore, in this study, we derived a new equation for global pressure and integrated it into the ASG method. We then simulated water saturation in a porous medium and the void fraction of water in a surface system by the ASG method and reproduced fairly well the results of two column experiments. Next, we simulated water saturation in a porous medium (sand) with a bank, by using both the ASG method and a modified Picard (MP) method. We found only a slight difference in water saturation between the ASG and MP simulations. This result confirmed that the derived equation for global pressure was valid for a porous medium, and that the global pressure value could thus be used with the saturation equation for porous media. Finally, we used the ASG method to simulate a system coupling atmosphere, surface water, and a porous medium (110 m wide and 50 m high) with a trapezoidal bank. The ASG method was able to simulate the complex flow of fluids in this system and the interaction between the porous medium and the surface water or the atmosphere.