We consider a stationary two-phase Stefan problem with convection. The problem is governed by a coupled system involving a nonlinear Darcy law and the energy balance equation with second member in L 1. We prove existence of at least one weak solution of the problem, using the penalty method and the Schauder xed point principle.

In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that treats both Darcy’s law and Stokes equations in a single form of PDE but with strongly discontinuous viscosity coefficient and zerothorder term coefficient. We present three different methods to construct uniformly stable finite element approximations. The first two methods a...

We present modeling of an incompressible viscous flow through a fracture adjacent to a porous medium. A fast stationary flow, predominantly tangential to the porous medium is considered. Slow flow in such setting can be described by the Beavers-Joseph-Saffman slip. For fast flows, a nonlinear filtration law in the porous medium and a nonlinear interface law are expected. In this paper we rigoro...

We study the asymptotic behavior of the solutions of barotropic two-phase twopressure models, with pressure relaxation, drag force and external forces. Using Chapman-Enskog expansions close to the expected equilibrium, a drift-flux model with a Darcy type closure law is obtained. Besides, restricting this closure law to permanent flows (defined as steady flows in some Lagrangian frame), we can ...

A six-channel system was used to determine how differences of Henry’s law constant and vertical water velocity affect the diffusive loss of contaminants from a sandy soil. Two channels (10 cm wide x 110 cm long x 65 cm deep) were each fed with methyl tert-butyl ether, dichloromethane, or trichloroethylene in groundwater. After steady state was attained, vertical concentration gradients were mea...

Recently in Japan, railway ballasts have been flown out several times by heavy or intense rainfalls. However, the mechanism has not yet been investigated in detail, so that the risk and the countermeasures cannot be reasonably proposed. Therefore, in this research, model tests and numerical analyses were conducted to investigate the flow-out mechanism. It was found that the seepage characterist...

This paper formulates and analyzes a weak solution to the coupling of time-dependent Navier-Stokes flow with Darcy flow under certain boundary conditions, one of them being the Beaver-Joseph-Saffman law on the interface. Existence and a priori estimates for the weak solution are shown under additional regularity assumptions. We introduce a fully discrete scheme with the unknowns being the Navie...

Darcy's Law is one of the most essential concepts in hydrogeology. Before moving on to more complex problems, students must first thoroughly understand the basic principles of one-dimensional fluid flow through saturated porous media that are embodied in Darcy’s Law. We believe that the best way for students to learn these principles is through experimentation. In this paper, we introduce an ex...

The Earth’s mantle (or, e.g., a glacier) involves a deformable solid matrix phase within which a second phase, a fluid, may form due to melting processes. The system is modeled as a dual-continuum mixture, with at each point of space the solid matrix being governed by a Stokes flow and the fluid melt, if it exists, being governed by Darcy’s law. This system is mathematically degenerate when the...

In this study, a numerical examination of the significance of rotation and changeable gravitational field on the start of nanofluid convective movement in an anisotropic porous medium layer is shown. A model that accounts for the impact of Brownian diffusion and thermophoresis is used for nanofluid, while Darcy’s law is taken for the porous medium. The porous layer is subjected to uniform rotat...