A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Aquifers at natural coasts can also be influenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head fluctuations in the aquifers. We present an analytical solution to the two-dimensional depth-averaged groundwater flow equation for a semi-infinite aquifer subject to oscillating head conditions at the boundaries. The solution describes the tidal dynamics of a coastal aquifer that is adjacent to a cross-shore estuary. Both the effects of oceanic and estuarine tides on the aquifer are included in the solution. The analytical prediction of the head fluctuations is verified by comparison with numerical solutions computed using a standard finite-difference method. An essential feature of the present analytical solution is the interaction between the cross- and along-shore tidal waves in the aquifer area near the estuary's entry. As the distance from the estuary or coastline increases, the wave interaction is weakened and the aquifer response is reduced, respectively, to the one-dimensional solution for oceanic tides or the solution of Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour Res 1997;33:1429-35) for two-dimensional non-interacting tidal waves. (C) 2000 Elsevier Science Ltd. All rights reserved.

Numerical modelling of double diffusion driven reactive flow transport in deformable fluid-saturated porous media with particular consideration of temperature-dependent chemical reaction rates

Numerical methods ave used to solve double diffusion driven reactive flow transport problems in deformable fluid-saturated porous media. in particular, thp temperature dependent reaction rate in the non-equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAG and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore-fluid flow, heat transfer and species transport/chemical reactions in deformable fluid-saturated porous media has been developed The coupled problem is divided into two subproblems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, if is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering.

Numerical modelling of single-layer folding: clarification of an issue regarding the possible effect of computer codes and the influence of initial irregularities

The influence of initial perturbation geometry and material propel-ties on final fold geometry has been investigated using finite-difference (FLAC) and finite-element (MARC) numerical models. Previous studies using these two different codes reported very different folding behaviour although the material properties, boundary conditions and initial perturbation geometries were similar. The current results establish that the discrepancy was not due to the different computer codes but due to the different strain rates employed in the two previous studies (i.e. 10(-6) s(-1) in the FLAC models and 10(-14) s(-1) in the MARC models). As a result, different parts of the elasto-viscous rheological field were bring investigated. For the same material properties, strain rate and boundary conditions, the present results using the two different codes are consistent. A transition in Folding behaviour, from a situation where the geometry of initial perturbation determines final fold shape to a situation where material properties control the final geometry, is produced using both models. This transition takes place with increasing strain rate, decreasing elastic moduli or increasing viscosity (reflecting in each case the increasing influence of the elastic component in the Maxwell elastoviscous rheology). The transition described here is mechanically feasible but is associated with very high stresses in the competent layer (on the order of GPa), which is improbable under natural conditions. (C) 2000 Elsevier Science Ltd. All rights reserved.

Effective cell-centred time-domain Maxwell's equations numerical solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed. © 2004 Elsevier Inc. All rights reserved.

Tailoring magnetic field gradient design to magnet cryostat geometry

Eddy currents induced within a magnetic resonance imaging (MRI) cryostat bore during pulsing of gradient coils can be applied constructively together with the gradient currents that generate them, to obtain good quality gradient uniformities within a specified imaging volume over time. This can be achieved by simultaneously optimizing the spatial distribution and temporal pre-emphasis of the gradient coil current, to account for the spatial and temporal variation of the secondary magnetic fields due to the induced eddy currents. This method allows the tailored design of gradient coil/magnet configurations and consequent engineering trade-offs. To compute the transient eddy currents within a realistic cryostat vessel, a low-frequency finite-difference time-domain (FDTD) method using total-field scattered-field (TFSF) scheme has been performed and validated

Towards realistic simulations of lava dome growth using the level set method

The level set method has been implemented in a computational volcanology context. New techniques are presented to solve the advection equation and the reinitialisation equation. These techniques are based upon an algorithm developed in the finite difference context, but are modified to take advantage of the robustness of the finite element method. The resulting algorithm is tested on a well documented Rayleigh–Taylor instability benchmark [19], and on an axisymmetric problem where the analytical solution is known. Finally, the algorithm is applied to a basic study of lava dome growth.

Investigation of the role of cadmium sulfide in the surface passivation of lead sulfide quantum dots

Surface passivation of PbS nanocrystals (NC), resulting in strong photoluminescence, can be achieved by the introduction of CdS precursors. The role of CdS in the surface passivation of PbS NCs is uncertain, as the crystalline structure of CdS and PbS are different, which should impede effective epitaxial overgrowth. Absorption spectroscopy is used to show that the CdS precursors strongly interact with the PbS NC surface. Electron microscopy reveals that the introduction of CdS precursors results in an increased particle size, consistent with overcoating. However, we also find the process to be highly non-uniform. Nevertheless, evidence for epitaxial growth is found, suggesting that effective surface passivation may be possible.

Undergraduate teaching of ideal and real fluid flows: The value of real-world experimental projects

This study describes the pedagogical impact of real-world experimental projects undertaken as part of an advanced undergraduate Fluid Mechanics subject at an Australian university. The projects have been organised to complement traditional lectures and introduce students to the challenges of professional design, physical modelling, data collection and analysis. The physical model studies combine experimental, analytical and numerical work in order to develop students’ abilities to tackle real-world problems. A first study illustrates the differences between ideal and real fluid flow force predictions based upon model tests of buildings in a large size wind tunnel used for research and professional testing. A second study introduces the complexity arising from unsteady non-uniform wave loading on a sheltered pile. The teaching initiative is supported by feedback from undergraduate students. The pedagogy of the course and projects is discussed with reference to experiential, project-based and collaborative learning. The practical work complements traditional lectures and tutorials, and provides opportunities which cannot be learnt in the classroom, real or virtual. Student feedback demonstrates a strong interest for the project phases of the course. This was associated with greater motivation for the course, leading in turn to lower failure rates. In terms of learning outcomes, the primary aim is to enable students to deliver a professional report as the final product, where physical model data are compared to ideal-fluid flow calculations and real-fluid flow analyses. Thus the students are exposed to a professional design approach involving a high level of expertise in fluid mechanics, with sufficient academic guidance to achieve carefully defined learning goals, while retaining sufficient flexibility for students to construct there own learning goals. The overall pedagogy is a blend of problem-based and project-based learning, which reflects academic research and professional practice. The assessment is a mix of peer-assessed oral presentations and written reports that aims to maximise student reflection and development. Student feedback indicated a strong motivation for courses that include a well-designed project component.

Flow and axial dispersion simulation for traveling axisymmetric Taylor vortices

Numerical experiments using a finite difference method were carried out to determine the motion of axisymmetric Taylor vortices for narrow-gap Taylor vortex flow. When a pressure gradient is imposed on the flow the vortices are observed to move with an axial speed of 1.16 +/- 0.005 times the mean axial flow velocity. The method of Brenner was used to calculate the long-time axial spread of material in the flow. For flows where there is no pressure gradient, the axial dispersion scales with the square root of the molecular diffusion, in agreement with the results of Rosen-bluth et al. for high Peclet number dispersion in spatially periodic flows with a roll structure. When a pressure gradient is imposed the dispersion increases by an amount approximately equal to 6.5 x 10(-4) (W) over bar(2)d(2)/D-m, where (W) over bar is the average axial velocity in the annulus, analogous to Taylor dispersion for laminar flow in an empty tube.

Determination of T1pH relaxation rates in charred and uncharred wood and consequences for NMR quantitation

The performance of three different techniques for determining proton rotating frame relaxation rates (T1pH) in charred and uncharred woods is compared. The variable contact time (VCT) experiment is shown to over-estimate T1pH, particularly for the charred samples, due to the presence of slowly cross-polarizing C-13 nuclei. The variable spin (VSL) or delayed contact experiment is shown to overcome these problems; however, care is needed in the analysis to ensure rapidly relaxing components are not overlooked. T1pH is shown to be non-uniform for both charred and uncharred wood samples; a rapidly relaxing component (T1pH = 0.46-1.07 ms) and a slowly relaxing component (T1pH = 3.58-7.49) is detected in each sample. T1pH for each component generally decreases with heating temperature (degree of charring) and the proportion of rapidly relaxing component increases. Direct T1pH determination (via H-1 detection) shows that all samples contain an even faster relaxing component (0.09-0.24 ms) that is virtually undetectable by the indirect (VCT and VSL) techniques. A new method for correcting for T1pH signal losses in spin counting experiments is developed to deal with the rapidly relaxing component detected in the VSL experiment. Implementation of this correction increased the proportion of potential C-13 CPMAS NMR signal that can be accounted for by up to 50% for the charred samples. An even greater proportion of potential signal can be accounted for if the very rapidly relaxing component detected in the direct T1pH determination is included; however, it must be kept in mind that this experiment also detects H-1 pools which may not be involved in H-1-C-13 cross-polarization. (C) 2002 Elsevier Science (USA).

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.

Modelling of cold-formed purlin-sheeting systems .1. Full model

Purlin-sheeting systems used for roofs and walls commonly take the form of cold-formed channel or zed section purlins, screw-connected to corrugated sheeting. These purlin-sheeting systems have been the subject of numerous theoretical and experimental investigations over the past three decades, but the complexity of the systems has led to great difficulty in developing a sound and general model. This paper presents a non-linear elasto-plastic finite element model, capable of predicting the behaviour of purlin-sheeting systems without the need for either experimental input or over simplifying assumptions. The model incorporates both the sheeting and the purlin, and is able to account for cross-sectional distortion of the purlin, the flexural and membrane restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The validity of the model is shown by its good correlation with experimental results. A simplified version of this model, which is more suitable for use in a design environment, is presented in a companion paper. (C) 1997 Elsevier Science Ltd.

Modelling of cold-formed purlin-sheeting systems .2. Simplified model

A number of theoretical and experimental investigations have been made into the nature of purlin-sheeting systems over the past 30 years. These systems commonly consist of cold-formed zed or channel section purlins, connected to corrugated sheeting. They have proven difficult to model due to the complexity of both the purlin deformation and the restraint provided to the purlin by the sheeting. Part 1 of this paper presented a non-linear elasto plastic finite element model which, by incorporating both the purlin and the sheeting in the analysis, allowed the interaction between the two components of the system to be modelled. This paper presents a simplified version of the first model which has considerably decreased requirements in terms of computer memory, running time and data preparation. The Simplified Model includes only the purlin but allows for the sheeting's shear and rotational restraints by modelling these effects as springs located at the purlin-sheeting connections. Two accompanying programs determine the stiffness of these springs numerically. As in the Full Model, the Simplified Model is able to account for the cross-sectional distortion of the purlin, the shear and rotational restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The model requires no experimental or empirical input and its validity is shown by its goon con elation with experimental results. (C) 1997 Elsevier Science Ltd.

Simulation of mixing in unsteady flow through a periodically obstructed channel

Fluid mixing in steady and unsteady Bow through a channel containing periodic square obstructions has been studied using a finite-difference simulation to determine fluid velocities, followed by the use of passive marker particle advection to look at fluid transport out of the cavities formed between each of the obstructions. The geometry and Bow conditions were chosen from the work by Perkins (1989, M.S. Thesis, Lehigh University; 1992, Ph.D. Thesis, Lehigh University); who investigated heat transfer enhancement due to unsteady flow through such an obstructed channel. Particle advection shows that Bow regimes which are predicted to give good mixing based on snapshots of instantaneous streamline contour plots were not necessarily able to efficiently mix fluid which started in the cavity regions throughout the channel. The use of Poincare sections shows regular regions existing under these conditions which inhibit efficient fluid transport. These regular regions are found to disappear when the unsteady Bow velocity is increased. (C) 1997 Elsevier Science Ltd.

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.