Coupled meshfree and fractal finite element method for unbounded problems

This paper presents a coupling technique for integrating the element-free Galerkin method (EFGM) with the fractal finite element method (FFEM) to analyze unbounded problems in the half-space. FFEM is adopted to model the far field of an unbounded domain and EFGM is used in the near field. In the transition region interface elements are employed. The shape functions of interface elements which comprise both the element-free Galerkin and the finite element shape functions, satisfy the consistency condition thus ensuring convergence of the proposed coupled EFGM–FFEM. The proposed method combines the best features of EFGM and FFEM, in the sense that no structured mesh or special enriched basis functions are necessary. The numerical results show that the proposed method performs extremely well converging rapidly to the analytical solution. Also a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the weight function, the scaling parameter and the number of transformation terms, on the quality of the numerical solutions.     

Depositional processes beneath coastal multi‐year sea ice

The extent of multi‐year sea ice impacts climate processes worldwide, such as ocean–atmosphere carbon dioxide exchange and deep ocean current formation. Reconstructing these processes in the past, and assessing the distribution of ecologically and climatically significant features, such as polynas, requires recognition of sediments deposited under multi‐year sea ice, but little is known about their characteristics. Textural analysis of subaerial and sea floor sediment in Explorers Cove, McMurdo Sound, at the mouth of Taylor Valley, Antarctica, augmented with observations of sedimentary structures and faunal components, elucidates how sediment is transported to the sea floor and allows characterization of the deposits. Comparison of grain‐size characteristics of subaerial (moraine, delta and sea‐ice surface) sediment and sea floor sediment from short cores taken at depths of 7 to 25 m indicates that the likely source of the moderately to poorly sorted sea floor sand is deltaic sediment; small glacial meltwater streams have built deltas since Taylor Valley became ice‐free ca 7000 years ago. Windblown sediment accumulating on the multi‐year sea ice close to the coast typically is coarser grained than sediment on the sea floor; this suggests that the transport of sediment through the ice to the sea floor is not the predominant mode of sediment transfer. However, supra‐sea‐ice sediment does move to the sea floor through local fractures. The rate of sedimentation under multi‐year sea ice is low because of limited stream flow and biogenic sedimentation; the ice cover inhibits primary productivity and dampens waves, precluding physical re‐suspension. The upper centimetres of sea floor sediment are churned by epifaunal scallops and brittle stars that leave no telltale biogenic structures and whose calcite ossicles and shells may be poorly preserved. The resulting deposits under multi‐year sea ice are poorly sorted, massive sand that provides little evidence of the bioturbators that have masked the indicators of the original physical depositional processes.     

Efficient conditional modeling for geotechnical uncertainty evaluation

A first‐order Taylor series method including direct derivative coding (DDC) is presented as a computationally efficient method for producing the probability distribution associated with calculated geotechnical performance. The probability distribution is employed in reliability analyses to calculate the probability of failure, valuable information that is not typically associated with deterministic analyses. The probability distribution also is used to identify important input parameters and to direct sampling efforts. Another approach to generate the probability distribution is the Monte Carlo (MC) method, however, Taylor series results generally are calculated in less time than the MC approach. One key to the implementation of the Taylor series approach is efficient approximation of the sensitivities required by the Taylor series calculation. DDC provides the technique to produce an efficient Taylor series algorithm. Directly coding the sensitivity analysis into the engineering model is accomplished by automatic and hand programming of derivatives. ADIFOR 2.0 was employed to automatically add derivatives to an existing engineering analysis model. For this paper a meshing program and 3D FEM for soil deformation is used to demonstrate the DDC approach. Although DDC requires a large up‐front programming effort, it is not site or data specific. Therefore, once the derivative programming has been performed, the numerical model can be applied to a wide variety of problems without additional user intervention. Copyright © 2001 John Wiley & Sons, Ltd.     

The stability of the pristine magnetopause

A MHD theory of combined Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) instabilities for a transition layer with two different scale lengths (Δ and δ for the variation of velocity/magnetic fields and density, respectively) is presented. The study is motivated by reports of magnetopauses with no low latitude boundary layer, in which a sharp density drop over a distance δ?Δ is observed (“pristine” magnetopauses (J. Geophys. Res. 101 (1996) 49). The theory ignores compressibility effects and applies to subsonic regions of the dayside magnetopause. The RT effect is included to account for temporary periods of acceleration of the magnetopause, caused by sudden changes of the solar wind dynamic pressure. For small wavelengths λ, such that δ?λ?Δ, a WKB solution shows that the velocity gradient operates, together with magnetic tensions, to attenuate or even stabilize the Rayleigh-Taylor instability within a certain wavelength range. An exact dispersion relation for flute modes, valid for all λ, in the form of a fourth order polynomial for the complex frequency ω, is obtained from a model with a constant velocity gradient, dV/dy within Δ, and with δ→0. Flute modes are possible because of the existence of bands of very small magnetic shear on the dayside magnetopause (J. Geophys. Res. 103 (1998) 6703). The exact solution allows for a study of the change of the action of the velocity gradient with λ from the long-λ range where dV/dy is KH destabilizing to the short-λ range where dV/dy produces a stabilizing effect. Both, the WKB approximation and the well known tangential discontinuity model (Δ→0) are recovered as limiting cases of the exact solution. Properties of the KH and RT instabilities, for different density ratios on either side of the magnetopause, are described. For flute modes, at very small λ the RT instability grows faster and becomes the dominant effect. However, it is shown that the growth rate remains bounded at a finite value as λ→0, when a theory with a finite δ model is considered. To study configurations with finite, arbitrary, δ/Δ ratios, the MHD perturbation equations are solved numerically, using hyperbolic tangent functions for both the density and velocity transitions across the magnetopause. To examine the influence of different δ/Δ ratios on the growth rates of KH and RT, calculations are performed for different δ/Δ, with and without acceleration, and for two different density ratios. It is found that the general features exhibited by the constant dV/dy model, are confirmed by these numerical solutions. The stability of pristine magnetopauses, and the possibility of observing some theoretical predictions during magnetopause crossings in ongoing missions, are discussed.     

A time‐discontinuous Galerkin method for the dynamical analysis of porous media

We present a time‐discontinuous Galerkin method (DGT) for the dynamic analysis of fully saturated porous media. The numerical method consists of a finite element discretization in space and time. The discrete basis functions are continuous in space and discontinuous in time. The continuity across the time interval is weakly enforced by a flux function. Two applications and several numerical investigations confirm the quality of the proposed space–time finite element scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

一种改善区域地磁场模型边界效应的方法

针对目前建立区域地磁场模型截断阶数受限,地磁图精度偏低等缺陷,研究了运用Taylor多项式拟合法建立区域地磁场模型所存在的边界效应问题.从理论上深入分析了产生边界效应误差的根源,提出了采用边界插值约束的Taylor多项式拟合法,在改善区域地磁模型边界效应的同时,提高了模型拟合的截断阶数,进而绘制出较高精度的区域地磁场图,同时对该技术和现有补充国际地磁参考场值方法进行了比较分析,最后进行了仿真试验.试验证明,该技术具有优于补充国际地磁参考值的方法,能克服现有区域地磁场模型的边界效应问题,提高了区域地磁场模型的拟合精度.     

Buoyancy-driven perturbations in a rapidly rotating,electrically conducting fluid: part I – flow and magnetic field

The steady velocity, perturbation pressure and perturbation magnetic field, driven by an isolated buoyant parcel of Gaussian shape in a rapidly rotating, unconfined, incompressible electrically conducting fluid in the presence of an imposed uniform magnetic field, are obtained by means of the Fourier transform in the limit of small Ekman number. Lorentz and inertial forces are neglected. The solution requires at most evaluation of a single integral and is found in closed form in some spatial regions. The solution has structure on two disparate scales: on the scale of the buoyant parcel and on the scale of the Taylor column, which is elongated in the direction of the rotation axis. The detailed structures of the flow and pressure depend linearly on the relative orientation of gravity and rotation, with the solution for arbitrary orientation being a linear combination of two limiting cases in which these vectors are colinear (polar case) and perpendicular (equatorial case). The perturbation magnetic field depends additionally on the relative orientation of the imposed magnetic field, and three limiting cases of interest are presented in which gravity and rotation are colinear (polar–toroidal case), gravity and imposed field are colinear (equatorial–radial case) and all three are mutually perpendicular (equatorial–toroidal case). Visualization and analysis of the velocity and perturbation magnetic field vectors are facilitated by dividing these vector fields into geostrophic and ageostrophic protions. In all cases, the geostrophic and ageostrophic portions have different structure on the Taylor-column scale. The buoyancy force is balanced by a pressure force in the polar case and by a flux of momentum in the equatorial case. The pressure force and momentum flux do not decay in strength with increasing axial distance. Far from the parcel, the axial mass flux varies as the inverse one-third power of distance from the parcel. The velocity has a single geostrophic vortex in the polar case and two vortices in the equatorial case. The perturbation magnetic field has two, four and one geostrophic vortices in the polar–toroidal, equatorial–radial and equatorial–toroidal cases, respectively. To facilitate comparison of the present results with numerical simulations carried out in a finite domain, a set of boundary conditions are developed, with may be applied at a finite distance from the parcel.     

Seasonal variability of the complementary relationship in the Asian monsoon region

The complementary relationship (CR) between potential evaporation (LE_p) and actual evaporation (LE) is widely used to explain the evaporation paradox and to estimate LE, in which wet environment evaporation (LE_w) is usually calculated using the Priestley–Taylor equation. However, in many studies on the CR, it has been found that the Priestley–Taylor parameter α is not a constant. Through seasonal variation of α for estimating LE_w in the CR, this paper analyses its seasonal variability. Based on flux observation data at two flux experiment sites (Kogma in Thailand and Weishan in China) in the Asian monsoon region, seasonal variability of the CR is detected, i.e. the α value is larger in winter than in summer. This seasonal variability might be caused by seasonal variability in the transport of water vapor and sensible heat between oceans and continent. The monsoon increases air humidity and lowers air temperature in summer, which leads to a decrease in α; it increases atmospheric air temperature and vapor content in winter, increasing α. Nevertheless, during May–September, α has a range of 1.06–1.16 at the Kogma site and 1.00–1.36 at the Weishan site, which is approximate to the typical range 1.1–1.4. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling of contaminant transport through landfill liners using EFGM

Modelling of contaminant transport through landfill liners and natural soil deposits is an important area of research activity in geoenvironmental engineering. Conventional mesh‐based numerical methods depend on mesh/grid size and element connectivity and possess some difficulties when dealing with advection‐dominant transport problems. In the present investigation, an attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the two‐dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using element‐free Galerkin method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The EFGM employs moving least‐square approximants to approximate the function and uses the Lagrange multiplier method for imposing essential boundary conditions. The results of the EFGM are validated using experimental results. Analytical and finite element solutions are also used to compare the results of the EFGM. In order to test the practical applicability and performance of the EFGM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the EFGM and the field investigation data. Copyright © 2009 John Wiley & Sons, Ltd.     

Topographic eddies in temporally varying oceanic flows

Abstract

In this paper we examine the behaviour of oceanic unsteady flow impinging on isolated topography by means of numerical simulation. The ocean model is quasigeostrophic and forced by an oscillatory mean flow. The fluid domain is of the channel type and open-boundary numerical conditions are used to represent downstream and upstream flow.

In certain cases, vortex shedding, either cyclonic or anticyclonic, is observed in the lee of obstacles. Such shedding can be explained as the consequence of both an enhanced process of vorticity dissipation over the topography which locally affects the balance of potential vorticity on the advective timescale, and a periodic dominance of advective effects which sweep the fluid particles trapped on the seamount. For refined resolution and smallest viscosity the model will predict flows in which the shed eddies are coherent structures with closed streamlines.

The model suggests a mechanism by which topographically generated eddies may be swept away from a seamount in the ocean.