Effects of open boundary location on the far-field hydrodynamics of a Severn Barrage

2007 ◽

Vol 464 (2090) ◽

pp. 491-511 ◽

Cited By ~ 9

Author(s):

Vladimir Gerasik ◽

Marek Stastna

Keyword(s):

Complex Analysis ◽

Near Field ◽

Plane Boundary ◽

Open Boundary ◽

Far Field ◽

S Wave ◽

Asymptotic Results ◽

Dimensional Boundary ◽

Wave Trains ◽

Biot’S Equations

A two-dimensional boundary-value problem for a porous half-space with an open boundary, described by the widely recognized Biot's equations of poroelasticity, is considered. Using complex analysis techniques, a general solution is represented as a superposition of contributions from the four different types of motion corresponding to P1, P2, S and Rayleigh waves. Far-field asymptotic solutions for the bulk modes, as well as near-field numerical results, are investigated. Most notably, this analysis reveals the following: (i) a line traction generates three wave trains corresponding to the bulk modes, so that P1, P2 and S modes emerge from corresponding wave trains at a certain distance from the source, (ii) bulk modes propagating along the plane boundary are subjected to geometric attenuation, which is found quantitatively to be x −3/2 , similar to the classical results in perfect elasticity theory, (iii) the Rayleigh wave is found to be predominant at the surface in both the near (due to the negation of the P1 and S wave trains) and the far field (due to geometric attenuation of the bulk modes), and (iv) the recovery of the transition to the classical perfect elasticity asymptotic results validates the asymptotics established herein.

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Finite Element Analysis of Dam-Reservoir Interaction Using High-Order Doubly Asymptotic Open Boundary

Mathematical Problems in Engineering ◽

10.1155/2011/210624 ◽

2011 ◽

Vol 2011 ◽

pp. 1-23 ◽

Cited By ~ 5

Author(s):

Yichao Gao ◽

Feng Jin ◽

Xiang Wang ◽

Jinting Wang

Keyword(s):

Finite Element ◽

Near Field ◽

Time Integration ◽

High Order ◽

Open Boundary ◽

Far Field ◽

Dam Reservoir ◽

Element Analysis ◽

Finite Element Equation ◽

Reservoir System

The dam-reservoir system is divided into the near field modeled by the finite element method, and the far field modeled by the excellent high-order doubly asymptotic open boundary (DAOB). Direct and partitioned coupled methods are developed for the analysis of dam-reservoir system. In the direct coupled method, a symmetric monolithic governing equation is formulated by incorporating the DAOB with the finite element equation and solved using the standard time-integration methods. In contrast, the near-field finite element equation and the far-field DAOB condition are separately solved in the partitioned coupled methodm, and coupling is achieved by applying the interaction force on the truncated boundary. To improve its numerical stability and accuracy, an iteration strategy is employed to obtain the solution of each step. Both coupled methods are implemented on the open-source finite element code OpenSees. Numerical examples are employed to demonstrate the performance of these two proposed methods.

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Effects of Gravity and Inlet Location on a Two-Phase Countercurrent Imbibition in Porous Media

International Journal of Chemical Engineering ◽

10.1155/2012/210128 ◽

2012 ◽

Vol 2012 ◽

pp. 1-7 ◽

Cited By ~ 4

Author(s):

M. F. El-Amin ◽

Amgad Salama ◽

Shuyu Sun

Keyword(s):

Numerical Simulation ◽

Porous Media ◽

Numerical Investigation ◽

Rectangular Domain ◽

Open Boundary ◽

Two Phase ◽

Boundary Location ◽

Countercurrent Imbibition

We introduce a numerical investigation of the effect of gravity on the problem of two-phase countercurrent imbibition in porous media. We consider three cases of inlet location, namely, from, side, top, and bottom. A 2D rectangular domain is considered for numerical simulation. The results indicate that gravity has a significant effect depending on open-boundary location.

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Possible applications of fraunhofer holography in high resolution electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108258 ◽

1978 ◽

Vol 36 (1) ◽

pp. 222-223 ◽

Cited By ~ 1

Author(s):

N. Bonnet ◽

M. Troyon ◽

P. Gallion

Keyword(s):

Electron Microscopy ◽

High Resolution ◽

Transfer Function ◽

Radiation Damage ◽

High Resolution Electron Microscopy ◽

Far Field ◽

Field Region ◽

Crystalline Materials ◽

Resolution Electron ◽

The Ideal

Two main problems in high resolution electron microscopy are first, the existence of gaps in the transfer function, and then the difficulty to find complex amplitude of the diffracted wawe from registered intensity. The solution of this second problem is in most cases only intended by the realization of several micrographs in different conditions (defocusing distance, illuminating angle, complementary objective apertures…) which can lead to severe problems of contamination or radiation damage for certain specimens.Fraunhofer holography can in principle solve both problems stated above (1,2). The microscope objective is strongly defocused (far-field region) so that the two diffracted beams do not interfere. The ideal transfer function after reconstruction is then unity and the twin image do not overlap on the reconstructed one.We show some applications of the method and results of preliminary tests.Possible application to the study of cavitiesSmall voids (or gas-filled bubbles) created by irradiation in crystalline materials can be observed near the Scherzer focus, but it is then difficult to extract other informations than the approximated size.

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