Results 1  10
of
16
M.: Computational engineering and science methodologies for modeling and simulation of subsurface applications
"... We discuss computational engineering and science (CES) methodologies and tools applicable to a variety of subsurface models and their couplings. First we overview both basic and widely recognized multiphase and multicomponent models. In the CES methodologies area we focus on accurate and robust nume ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
We discuss computational engineering and science (CES) methodologies and tools applicable to a variety of subsurface models and their couplings. First we overview both basic and widely recognized multiphase and multicomponent models. In the CES methodologies area we focus on accurate and robust numerical algorithms and linear and nonlinear solvers with parallel scalability. In the CES tools area, we discuss a few representative programming tools and technologies. We present several simulation examples
Partially saturated flow in a poroelastic medium
 Discrete Contin Dynam Syst––Ser B
"... ..."
(Show Context)
Singlephase Flow in Composite Poroelastic Media
 Math. Methods Appl. Sci
, 2002
"... . The mathematical formulation and analysis of the BarenblattBiot model of elastic deformation and laminar flow in a heterogeneous porous medium is discussed. This describes consolidation processes in a fluidsaturated doublediffusion model of fractured rock. The model includes various degenerate ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
. The mathematical formulation and analysis of the BarenblattBiot model of elastic deformation and laminar flow in a heterogeneous porous medium is discussed. This describes consolidation processes in a fluidsaturated doublediffusion model of fractured rock. The model includes various degenerate cases, such as incompressible constituents or totally fissured components, and it is extended to include boundary conditions arising from partially exposed pores. The quasistatic initialboundary problem is shown to have a unique weak solution, and this solution is strong when the data are smoother. 1. Introduction Any model of fluid flow through a deformable solid matrix must account for the coupling between the mechanical behavior of the matrix and the fluid dynamics. For example, compression of the medium leads to increased pore pressure, if the compression is fast relative to the fluid flow rate. Conversely, an increase in pore pressure induces a dilation of the matrix in response to t...
Partially Saturated Flow in a Composite Poroelastic Medium
 in Poromechanics II, Grenoble, 2002, J.L. Auriault et al (editors), Balkema
"... Preliminary Report.) The model formulation and existence theory is described for di#usion of a barotropic fluid through a partially saturated poroelastic composite medium consisting of two components. This includes the BarenblattBiot doubledi #usion model of elastic deformation and laminar flow ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Preliminary Report.) The model formulation and existence theory is described for di#usion of a barotropic fluid through a partially saturated poroelastic composite medium consisting of two components. This includes the BarenblattBiot doubledi #usion model of elastic deformation and laminar flow in a fissured medium, such as consolidation processes in a system of fissures distributed throughout a matrix of highly porous cells. Nonlinear e#ects of density, saturation, porosity and permeability variations with pressure are included, and the seepage surfaces are determined by variational inequalities on the boundary.
Diffusion in Deforming Porous Media
"... We report on some recent progress in the mathematical theory of nonlinear fluid transport and poromechanics, specifically, the design, analysis and application of mathematical models for the flow of fluids driven by the coupled pressure and stress distributions within a deforming heterogeneous p ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
We report on some recent progress in the mathematical theory of nonlinear fluid transport and poromechanics, specifically, the design, analysis and application of mathematical models for the flow of fluids driven by the coupled pressure and stress distributions within a deforming heterogeneous porous structure. The goal of this work is to develop a set of mathematical models of coupled flow and deformation processes as a basis for fundamental research on the theoretical and numerical modeling and simulation of flow in deforming heterogeneous porous media.
On Convergence of Certain Finite Volume Difference Discretizations for 1D Poroelasticity Interface Problems
, 2006
"... In the article two finite difference schemes for the 1D poroelasticity equations (Biot model) with discontinuous coefficients are derived, analyzed, and numerically tested. A recent discretization [Gaspar et al., Appl Numer Math 44 (2003), 487–506] of these equations with constant coefficients on a ..."
Abstract
 Add to MetaCart
(Show Context)
In the article two finite difference schemes for the 1D poroelasticity equations (Biot model) with discontinuous coefficients are derived, analyzed, and numerically tested. A recent discretization [Gaspar et al., Appl Numer Math 44 (2003), 487–506] of these equations with constant coefficients on a staggered grid is used as a basis. Special attention is given to the interfaces and as a result a scheme with harmonic averaging of the coefficients is derived. Convergence rate of O(h 3/2) in a discrete H 1norm for both the pressure and the displacement is established in the case of an arbitrary position of the interface. Further, rate of O(h 2) is proven for the case when the interface coincides with a grid node. Following an approach applied to secondorder elliptic equations in [Ewing et al., SIAM J Sci Comp 23(4) (2001), 1334–1350] we derive a modified and more accurate discretization that gives secondorder convergence of the fluid velocity and the stress of the solid. Finally, numerical experiments of model problems that confirm the theoretical considerations are
PréPublicações do Departamento de Matemática Universidade de Coimbra Preprint Number 09–17 A PRIORI ERROR ESTIMATES FOR THE NUMERICAL SOLUTION OF A COUPLED GEOMECHANICS AND RESERVOIR FLOW MODEL WITH STRESSDEPENDENT
"... Abstract: In this paper we consider the numerical solution of a coupled geomechanics and a stresssensitive porous media reservoir flow model. We combine mixed finite elements for Darcy flow and Galerkin finite elements for elasticity. This work focuses on deriving convergence results for the numer ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract: In this paper we consider the numerical solution of a coupled geomechanics and a stresssensitive porous media reservoir flow model. We combine mixed finite elements for Darcy flow and Galerkin finite elements for elasticity. This work focuses on deriving convergence results for the numerical solution of this nonlinear partial differential system. We establish convergence with respect to the L2norm for the pressure and for the average fluid velocity and with respect to the H1norm for the deformation. Estimates respect to the L2norm for mean stress, which is of special importance since it is used in the computation of permeability for poroelasticity, can be derived using the estimates in the H1norm for the deformation. We start by deriving error estimates in a continuousintime setting. A cutoff operator is introduced in the numerical scheme in order to derive convergence. The spatial grids for the discrete approximations of the pressure and deformation do not need be the same. Theoretical convergence error estimates in a discreteintime setting are also derived in the scope of this investigation. A numerical example supports the convergence results.
unknown title
, 2004
"... www.elsevier.com/locate/na Some existenceuniqueness results for a class of onedimensional nonlinear Biot models ..."
Abstract
 Add to MetaCart
(Show Context)
www.elsevier.com/locate/na Some existenceuniqueness results for a class of onedimensional nonlinear Biot models
www.elsevier.com/locate/na On nonlinear Biot’s consolidation models
"... The propagation of elastic waves in a fluidsaturated porous solid is generally set within the framework of Biot’s mechanics. Its modelling is motivated by many applications such as the study of poroelastic behavior of rocks for engineering reservoir models [4] or the detection of buried objects [18 ..."
Abstract
 Add to MetaCart
(Show Context)
The propagation of elastic waves in a fluidsaturated porous solid is generally set within the framework of Biot’s mechanics. Its modelling is motivated by many applications such as the study of poroelastic behavior of rocks for engineering reservoir models [4] or the detection of buried objects [18]. The general theory of linear poroelasticity was first devel
ANALYSIS OF FINITE ELEMENT METHODS FOR
"... Abstract. This work is concerned with the analysis of a nonstationary HydroMechanical problem. The wellposedness of the continuous, time semidiscretized and fully discretized problems is addressed. An a posteriori error analysis is performed, leading to a family of spacetime error indicators. T ..."
Abstract
 Add to MetaCart
Abstract. This work is concerned with the analysis of a nonstationary HydroMechanical problem. The wellposedness of the continuous, time semidiscretized and fully discretized problems is addressed. An a posteriori error analysis is performed, leading to a family of spacetime error indicators. The reliability of this family, i.e. a global upper bound of the error using the error indicators, is proved. 1