Variational bound finite element methods for three-dimensional creeping porous media and sedimentation flows

Pedercini, Matteo; Patera, Anthony T.; Cruz, Manuel

doi:10.1002/(sici)1097-0363(19980130)26:2<145::aid-fld617>3.0.co;2-o

Cited by 3 publications

(2 citation statements)

References 37 publications

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“…The typical situation, which is met for example in the context of composite material [26] or in the S. Bertoluzza modelling of fluid particle flows [25], is the one of a perforated domain, say a cube in R n minus a collection B of (possibly many) balls.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the fully discrete fat boundary method

2010

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International audienceThe Fat Boundary Method is a method of the Fictitious Domain class, which was proposed to solve elliptic problems in complex geometries with non-conforming meshes. It has been designed to recover optimal convergence at any order, despite of the non-conformity of the mesh, and without any change in the discrete Laplace operator on the simple shape domain. We propose here a detailed proof of this high-order convergence, and propose some numerical tests to illustrate the actual behaviour of the method

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Section: Introductionmentioning

confidence: 99%

Analysis of the fully discrete fat boundary method

2010

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“…Narasimhan [5] used an integrated finite difference method for analyzing fluid flow in porous media. Pedercini et al [6] represented variational bound finite element methods for three-dimensional creeping porous media. Shao [7] discussed the numerical implementation by 2-D finite element method and developed new non-reflecting boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

Han

2008

Appl. Math. Mech.-Engl. Ed.

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In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.

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Direct Simulations of 2D Fluid-Particle Flows in Biperiodic Domains

Maury

1999

Journal of Computational Physics

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We propose a method to simulate the motion of 2D rigid particles in a viscous, incompressible fluid. Within the arbitrary Lagrangian Eulerian framework, momentum equations for both the fluid and the particles are discretized, and a coupled variational formulation is established. By introducing an appropriate finite element approximation, a symmetric linear system is obtained. This system is solved by an inexact Uzawa algorithm. The main interest of such simulations lies in the average behaviour of a high number of particles. We therefore introduced a biperiodic formulation of the problem, which makes it possible to represent many-body mixtures at a reasonable computational cost. In order to model realistic situations, an extra term must be added to the pressure. This extra term is shown to be the lagrange multiplier associated with the vertical volume conservation constraint. We developed an appropriate unstructured mesh generator, so that the biperiodicity of the fields can be treated in a strong sense. The question of particle contact is addressed, and a simple technique to overcome numerical problems is proposed. The influence of periodic lengths is investigated through different simulations. The same case is simulated for different sizes of the window, and the behaviour of some space-averaged quantities is studied.

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Variational bound finite element methods for three-dimensional creeping porous media and sedimentation flows

Cited by 3 publications

References 37 publications

Analysis of the fully discrete fat boundary method

Analysis of the fully discrete fat boundary method

A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

Direct Simulations of 2D Fluid-Particle Flows in Biperiodic Domains

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