Exfiltration of waste water in sewer networks represents a potential danger for the soil and the aquifer. Various modelling approaches have been proposed to quantify sewerage exfiltration and its spatial and temporal variation. Common models are based on the law of Darcy, extended by a more or less detailed consideration of the expansion of leaks, the characteristics of the soil and the colmati...

We describe the competitive motion of (N + 1) incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of non-negative measures with prescribed mass endowed with some tensorial Wasserstein distance. We show the convergence of the approximation obtained by a minimization scheme à la [R. Jordan, D. Kinderlehrer & F. Otto, SIAM J. Math. Anal, 2...

The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number...

We introduce a new class of higher order mixed finite volume methods for elliptic problems. We start from the usual way of changing the given equation into a mixed system using the Darcy’s law, u = −K∇p. By integrating the system of equations with some judiciously chosen test spaces on each element, we define new mixed finite volume methods of higher order. We show that these new schemes are eq...

Homogenization techniques are used to derive a double porosity model for single phase flow in a reservoir with a preferred direction of fracture. The equations in the microscopic model are the usual ones derived from Darcy’s law in the fractures and matrix (rock). The permeability coefficients over the matrix domain are scaled, using a parameter ε, based on the fracture direction in the reservo...

The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equations) and in porous media (Darcy equations). In this work, we explore a novel mixed formulation of the Brinkman problem. Introducing the flow’s vorticity as additional unknown, this formulation allows for a uniformly stable and conforming discretization by standard finite elements (Nédélec, Raviart-...

In this paper we present a thorough set of numerical experiments to confirm the robustness of several Discontinuous Galerkin (DG) methods proposed for the approximation of Darcy law. We perform fairly twoand three-dimensional tests involving both low and high order approximations. Convergence tests carried out on Cartesian grids as well as on structured and unstructured triangular grids confirm...

An increase in the flow velocity in flowthrough large porous media and deflection of flow regime from Darcy law causes a nonlinear relationship between hydraulic gradient and pore velocity of media. So many investigations have done previously in such Medias. One of the most important subjects in flowthrough large porous media is relationship between friction coefficient and flow characteristics...

This paper presents studies on applying the novel weak Galerkin finite element method (WGFEM) to a two-phase model for subsurface flow, which couples the Darcy equation for pressure and a transport equation for saturation in a nonlinear manner. The coupled problem is solved in the framework of operator decomposition. Specifically, the Darcy equation is solved by theWGFEM, whereas the saturation...

Hybrid or multiphysics algorithms provide an efficient computational tool for combining microand macroscale descriptions of physical phenomena. Their use becomes imperative when microscale descriptions are too computationally expensive to be conducted in the whole domain, while macroscale descriptions fail in a small portion of the computation domain. We present a hybrid algorithm to model a ge...