Abstract A seepage testing system was designed and a series of experiments on broken rock conducted using different original porosity conditions clay contents. The mass-loss process the change in water flow velocity were investigated. After test, non-Darcy characteristics tested through step-by-step pressure-reduced test. experimental results show that evolution during inrush could be divided i...

The Forchheimer equation is widely used in studying non-Darcy flow. Non-Darcy flow coefficient β the generally thought to be positive, and there are few studies on negative values. In this work, we performed seepage tests sandstone samples with single, T-shaped, Y-shaped fractures under different confining pressures, water angles analyze nonlinear behaviors features of Forchheimer’s coefficient...

We study the dynamics and regularity of level sets in solutions of the semilinear parabolic equation ut −∆ u ∈ a H(u − μ) in Q = Ω × (0, T ], whereΩ ⊂ Rn is a ring-shaped domain, a andμ are given positive constants,H(·) is the Heaviside maximal monotone graph:H(s) = 1 if s > 0,H(0) = [0, 1],H(s) = 0 if s < 0. Such equations arise in climatology (the so-called Budyko energy balance model), as we...

Finite volume methods and finite elements methods are generally opposed as competing approximation techniques. However there are ways to look at them which make these methods closer than what is usually thought, and this leads to the construction of generalized finite volume methods. Here we will restrict ourselves to cell-centered finite volumes. On one hand, cell-centered finite volume method...

A stable finite element scheme that avoids pressure oscillations for a three-field Biot’s model in poroelasticity is considered. The involved variables are the displacements, fluid flux (Darcy velocity), and the pore pressure, and they are discretized by using the lowest possible approximation order: Crouzeix-Raviart finite elements for the displacements, lowest order Raviart-Thomas-Nédélec ele...

Although Darcy-Weisbach (D-W) equation has been accepted as a standard resistance equation in pressurized flow, some researchers and engineers still prefer to utilize Hazen-Williams (H-W) equation for analyzing water distribution networks (WDNs) in practice. The main difference between roughness coefficients of these two resistance equations is that D-W friction factor varies with Reynolds numb...

Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation law and the Darcy ́s law. This equation may be written in three standard forms: the “h-based” form, the “θ-based” form, and the “mixed” form. Numerical aproximations based on different forms of this one-dimensional nonlinear equation can lead to significantly diffe...

A global nonlinear stability analysis is performed for a couple-stress fluid layer heated from below saturating a porous medium with temperature-pressure dependent viscosity for different conducting boundary systems. Here, the global nonlinear stability threshold for convection is exactly the same as the linear instability boundary. This optimal result is important because it shows that lineari...

Domain decomposition methods for solving the coupled Stokes-Darcy system with the Beavers-Joseph interface condition are proposed and analyzed. Robin boundary conditions are used to decouple the Stokes and Darcy parts of the system. Then, parallel and serial domain decomposition methods are constructed based on the two decoupled sub-problems. Convergence of the two methods is demonstrated and t...