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Displaying 441 –
460 of
519
We have developed a multiphase flow code that has been applied to study the behavior of non-aqueous phase liquids (NAPL) in the subsurface. We describe model formulation, discretization, and use the model for numerical investigation of sensitivity of the NAPL plume with respect to capillary parameters of the soil. In this paper the soil is assumed to be spatially homogeneous. A 2-D reference problem has been chosen and has been recomputed repeatedly with modified parameters of the Brooks–Corey capillary...
We consider applications, illustration and concrete numerical treatments of some homogenization results on Stokes flow in porous media. In particular, we compute the global permeability tensor corresponding to an unidirectional array of circular fibers for several volume-fractions. A 3-dimensional problem is also considered.
The goal of this paper is to present a different approach to the homogenization of the Dirichlet boundary value problem in porous medium. Unlike the standard energy method or the method of two-scale convergence, this approach is not based on the weak formulation of the problem but on the very weak formulation. To illustrate the method and its advantages we treat the stationary, incompressible Navier-Stokes system with the non-homogeneous Dirichlet boundary condition in periodic porous medium. The...
In this paper we present an overview of some recent results on applications of knot theory in fluid mechanics, as part of a new discipline called `topological fluid mechanics' (TFM). The choice of the topics covered here is deliberately restricted to those areas that involve mainly a combination of ideal fluid mechanics techniques and knot theory concepts, complemented with a brief description of some other concepts that have important applications in fluid systems. We begin with the concept of...
We consider a linear model of interaction between a viscous incompressible
fluid and a thin elastic structure located on a part of the fluid domain
boundary, the other part being rigid. After having given an existence and
uniqueness result for the direct problem, we study the question of
approximate controllability for this system when the control acts as a
normal force applied to the structure. The case of an analytic boundary has
been studied by Lions and Zuazua in [9]
where, in particular,...
We analyze the controllability of the motion of a fluid by means of the
action of a vibrating shell coupled at the boundary of the fluid. The
model considered is linear. We study its approximate controllability,
i.e. whether the fluid may reach a dense set of final configurations at
a given time. We show that this problem can be reduced to a unique
continuation question for the Stokes system. We prove that this unique
continuation property holds generically among analytic domains and
therefore,...
In this paper we analyze the stream function-vorticity-pressure method for the Stokes eigenvalue problem. Further, we obtain full order convergence rate of the eigenvalue approximations for the Stokes eigenvalue problem based on asymptotic error expansions for two nonconforming finite elements, and . Using the technique of eigenvalue error expansion, the technique of integral identities and the extrapolation method, we can improve the accuracy of the eigenvalue approximations.
The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear elliptic problems arising in glaciology. The stationary motion of a glacier is given by a non-newtonian fluid flow model which becomes, in a first two-dimensional approximation, the so-called infinite parallel sided slab model. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1. Numerical results...
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