Numerical modelling is a powerful tool for studies of soil gas and radon-222 entry into houses. It is the purpose of this paper to review some main techniques and results. In the past, modelling has focused on Darcy flow of soil gas (driven by indoor-outdoor pressure differences) and combined diffusive and advective transport of radon. Models of different complexity have been used. The simpler ...

Surface water, groundwater and sand can flow into mine goaf through the fractured rock, which often leads to water inrush and quicksand movement. It is important to study the mechanical properties of water and sand in excavations sites under different conditions and the influencing factors of the water and sand seepage system. The viscosity of water-sand mixtures under different particle sizes,...

We propose and analyze two novel decoupled numerical schemes for solving the Cahn-HilliardStokes-Darcy (CHSD) model for two-phase flows in karstic geometry. In the first numerical scheme, we explore a fractional step method (operator splitting) to decouple the phase-field (Cahn-Hilliard equation) from the velocity field (Stokes-Darcy fluid equations). To further decouple the Stokes-Darcy system...

Here u(x, t) is the fluid flux, p(x, t) the pressure, and g(x) is the gravity force, the storeage rate term c(x) is (slight) compressibility and porosity of the fluid and porous medium with sources F (x, t). The density factor has been dropped from each term of (1.1b). The flow resistance a(x) is fluid viscosity times the inverse of permeability of the porous medium. The system (1.1) is supplem...