GUICHARD , Cindy

The numerical simulation of two-phase flow in a porous medium may lead, when using coupled finite volume schemes on structured grids, to the apparition of the so-called Grid Orientation Effect (GOE). We propose in this paper a procedure to eliminate this phenomenon, based on the use of new fluxes with a new stencil in the discrete version of...

We focus here on the difficult problem of linear solving, when considering implicit scheme for two-phase flow simulation in porous media. Indeed, this scheme leads to ill-conditioned linear systems, due to the different behaviors of the pressure unknown (which follows a diffusion equation) and the saturation unknown (mainly advected by the...

Some cases of nonlinear coupling between a diffusion equation, related to the computation of a pressure field within a porous medium, and a convection equation, related to the conservation of a species, lead to the apparition of the so-called grid orientation effect. We propose in this paper a new procedure to eliminate this Grid Orientation...

We focus here on the difficult problem of linear solving, when considering implicit scheme for two-phase flow simulation in porous media. Indeed, this scheme leads to ill-conditioned linear systems, due to the different behaviors of the pressure unknown (which follows a diffusion equation) and the saturation unknown (mainly advected by the...

This paper presents a finite volume discretization of two-phase Darcy flows in discrete fracture networks taking into account the mass exchange between the matrix and the fracture. We consider the asymptotic model for which the fractures are represented as interfaces of codimension one immersed in the matrix domain, leading to the so called...

The gradient scheme family, which includes the conforming and mixed finite elements as well as the mimetic mixed hybrid family, is used for the approximation of Richards equation and the two-phase flow problem in heterogeneous porous media. We prove the convergence of the approximate saturation and of the approximate pressures and approximate...

This paper concerns the discretization of multiphase Darcy flows, in the case of heterogeneous anisotropic porous media and general 3D meshes used in practice to represent reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred approach is introduced in this paper. This scheme extends the Vertex Approximate...

We present the use of the Vertex Approximate Gradient scheme for the simulation of multiphase flow in porous media. The porous volume is distributed to the natural grid blocks and to the vertices, hence leading to a new finite volume mesh. Then the unknowns in the control volumes may be eliminated, and a 27-point scheme results on the vertices...

This paper presents the Vertex Approximate Gradient (VAG) discretization of a two-phase Darcy flow in discrete fracture networks (DFN) taking into account the mass exchange between the matrix and the fracture. We consider the asymptotic model for which the fractures are represented as interfaces of codimension one immersed in the matrix domain...

This paper concerns the discretization on general 3D meshes of multiphase compositional Darcy flows in heterogeneous anisotropic porous media. Extending Coats' formulation to an arbitrary number of phases, the model accounts for the coupling of the mass balance of each component with the pore volume conservation and the thermodynamical...

The objective of the ComPASS project is to develop a parallel multiphase Darcy flow simulator adapted to general unstructured polyhedral meshes (in a general sense with possibly non planar faces) and to the parallelization of advanced finite volume discretizations with various choices of the degrees of freedom such as cell centres, vertices, or...

We compare the recently developed Vertex Approximate Gradient (VAG) scheme developed in [R. Eymard et al., ESAIM: Mathematical Modelling and Numerical Analysis, 46(2), 2012] and the multipoint flux approximations (MPFA) O- and L-methods on 3D irregular meshes. It is found that the VAG scheme converges for a wider range of problems than the MPFA...

This article deals with the discretization of hybrid dimensional model of Darcy flow in fractured porous media. These models couple the flow in the fractures represented as the surfaces of codimension one with the flow in the surrounding matrix. The convergence analysis is carried out in the framework of Gradient schemes which accounts for a...

We give here a comparative study of the mathematical analysis of two (classes of) discretisation schemes for the computation of approximate solutions to incompressible two phase flow problem in homogeneous porous media. The first scheme is the well-known finite volume scheme with a two-point flux approximation, classically used in industry. The...

We show in this paper that the gradient schemes (which encompass a large family of discrete schemes) may be used for the approximation of the Stefan problem $\partial_t \bar u - \Delta \zeta (\bar u) = f$. The convergence of the gradient schemes to the continuous solution of the problem is proved thanks to the following steps. First, estimates...

This paper introduces a vertex centred discretization on general 3D meshes of multiphase Darcy flows in heterogeneous anisotropic porous media. The model accounts for the coupling of the mass balance of each component with the pore volume conservation and the thermodynamical equilibrium. The conservative spatial discretization of the Darcy...

This article deals with the discretization of hybrid dimensional model of Darcy flow in fractured porous media. These models couple the flow in the fractures represented as the surfaces of codimension one with the flow in the surrounding matrix. The convergence analysis is carried out in the framework of Gradient schemes which accounts for a...