On a monotonicity preserving Eulerian–Lagrangian localized adjoint method for advection–diffusion equations

Eulerian–Lagrangian localized adjoint methods (ELLAMs) provide a general approach to the solution of advection-dominated advection–diffusion equations allowing large time steps while maintaining good accuracy. Moreover, the methods can treat systematically any type of boundary condition and are mass conservative. However, all ELLAMs developed so far suffer from non-physical oscillations and are usually implemented on structured grids. In this paper, we propose a finite volume ELLAM which incorporates a novel correction step rendering the method monotone while maintaining conservation of mass. The method has been implemented on fully unstructured meshes in two space dimensions. Numerical results demonstrate the applicability of the method for problems with highly non-uniform flow fields arising from heterogeneous porous media.     

Adaptive hierarchical grid model of water-borne pollutant dispersion

Water pollution by industrial and agricultural waste is an increasingly major public health issue. It is therefore important for water engineers and managers to be able to predict accurately the local behaviour of water-borne pollutants. This paper describes the novel and efficient coupling of dynamically adaptive hierarchical grids with standard solvers of the advection–diffusion equation. Adaptive quadtree grids are able to focus on regions of interest such as pollutant fronts, while retaining economy in the total number of grid elements through selective grid refinement. Advection is treated using Lagrangian particle tracking. Diffusion is solved separately using two grid-based methods; one is by explicit finite differences, the other a diffusion-velocity approach. Results are given in two dimensions for pure diffusion of an initially Gaussian plume, advection–diffusion of the Gaussian plume in the rotating flow field of a forced vortex, and the transport of species in a rectangular channel with side wall boundary layers. Close agreement is achieved with analytical solutions of the advection–diffusion equation and simulations from a Lagrangian random walk model. An application to Sepetiba Bay, Brazil is included to demonstrate the method with complex flows and topography.     

A new efficient Eulerian–Lagrangian localized adjoint method for solving the advection–dispersion equation on unstructured meshes

A new and high efficient scheme is developed for the Eulerian–Lagrangian Localized Adjoint Method (ELLAM) to solve the Advection–Dispersion transport Equation (ADE) on unstructured triangular meshes. To obtain accurate results, the new method requires a very limited number of integration points (usually 1 per element).     

An ELLAM approximation for advective–dispersive transport with nonlinear sorption

We consider an Eulerian–Lagrangian localized adjoint method (ELLAM) applied to nonlinear model equations governing solute transport and sorption in porous media. Solute transport in the aqueous phase is modeled by standard advection and hydrodynamic dispersion processes, while sorption is modeled with a nonlinear local-equilibrium model. We present our implementation of finite volume ELLAM (FV-ELLAM) and finite element (FE-ELLAM) discretizations to the reactive transport model and evaluate their performance for several test problems containing self-sharpening fronts.     

Surface heat fluxes and thermohaline variability in the Ross Sea and in Terra Nova Bay polynya

The Ross Sea is an important area for the ventilation of the deep layers of the Southern Ocean (e.g. [Jacobs, S.S., Fairbanks, R.G., Horibe, Y., 1985. Origin and evolution of water masses near the Antarctic continental margin: evidence from H218O/H216O ratios in seawater. In: Jacobs, S.S. (Ed.), Oceanology of the Antarctic Continental Shelf. Antarctic Research Series, vol. 43. pp. 59–85; Orsi, A.H., Johnson, G.C., Bullister, J.L., 1999. Circulation, mixing, and the production of Antarctic bottom water. Progress in Oceanography 109, 43–55]). These processes are driven by the atmospheric forcing which, at high latitude, plays a key role in the formation and thickness of sea ice. In order to investigate the effect of the atmospheric forcing variability at different time scales, we analysed the surface heat budget over the Ross Sea continental shelf and in Terra Nova Bay (TNB) polynya, using analyses for the period 1990–2006 provided by European Centre for Medium-range Weather Forecast (ECMWF). This study was also performed using thermohaline data collected within the activities of Climatic Long-term Interaction for the mass-balance in Antarctica project of the Italian National Programme for Antarctic Research for the summer periods from 1994 until 2001.The annual average of the heat budget over the continental shelf of the Ross Sea estimated in the period 1990–2006 shows an interannual variability ranging between −97 and −123 W m⁻². Assuming that the heat loss must be compensated by the sensible heat carried by the Circumpolar Deep Water we estimated its transport (3.1 Sv) and its variability (0.2 Sv). Similarly in the TNB polynya the heat loss reaches its maximum in 2003 (−313 W m⁻²) and its minimum (−58 W m⁻²) in 1996. The related production of sea ice and the High Salinity Shelf Water (HSSW) were also estimated. The HSSW production switched from the lowest values during the first 10 years of the investigated period (1990–2000) to the highest values for the remaining period (2001–2006).The thermohaline characteristics of the water column in TNB show a general decrease in salinity with a superimposed variability. Comparison between the estimated HSSW production and the salinity observed within the TNB water column show similar tendency in the last years after 2002, while during the period 1995–1998 the behaviour is different. Our hypothesis concern a possible role of the CDW inflow in the TNB area and our results could be explained by a different contribution of CDW transport and HSSW production to the salt content within the water column.     

Diurnal sea breeze effects on inner-shelf cross-shore exchange

Cross-shore exchange by strong (cross-shore wind stress, τ_sx>0.05 Pa) diurnal (7–25 h) sea breeze events are investigated using two years of continuous wind, wave, and ocean velocity profiles in 13 m water depth on the inner-shelf in Marina, Monterey bay, California. The diurnal surface wind stress, waves, and currents have spectral peaks at 1, 2, and 3 cpd and the diurnal variability represents about 50% of the total variability. During sea breeze relaxation (−0.05<τ_sx<0.05 Pa), a background wave-driven inner-shelf Eulerian undertow profile exists, which is equal and opposite to the Lagrangian Stokes drift profile, resulting in a net zero Lagrangian transport at depth. In the presence of a sea breeze (τ_sx>0.05 Pa), a uniform offshore profile develops that is different from the background undertow profile allowing cross-shore Lagrangian transport to develop, while including Lagrangian Stokes drift. The diurnal cross-shore current response is similar to subtidal (>25 h) cross-shore current response, as found by Fewings et al. (2008). The seasonality of waves and winds modify the diurnal sea breeze impact. It is suggested that material is not transported cross-shore except during sea breeze events owing to near zero transport during relaxation periods. During sea breeze events, cross-shore exchange of material appears to occur onshore near the surface and offshore near the sea bed. Since sea breeze events last for a few hours, the long-term cross-shore transport is incremental each day.     

A multidimensional streamline-based method to simulate reactive solute transport in heterogeneous porous media

We present a new streamline-based numerical method for simulating reactive solute transport in porous media. The key innovation of the method is that both longitudinal and transverse dispersion are incorporated accurately without numerical dispersion. Dispersion is approximated in a flow-oriented grid using a combination of a one-dimensional finite difference scheme and a meshless approximation. In contrast to previous hybrid alternatives to incorporate dispersion in streamline-based simulations, the proposed scheme does not require a grid and, hence, it does not introduce numerical dispersion. In addition, the proposed scheme eliminates numerical oscillations and negative concentration values even when the dispersion tensor includes the off-diagonal coefficients and the flow field is non-uniform. We demonstrate that for a set of two- and three-dimensional benchmark problems, the new proposed streamline-based formulation compares favorably to two state of the art finite volume and hybrid Eulerian–Lagrangian solvers.     

Scalar advection schemes for ocean modelling on unstructured triangular grids

Several schemes for scalar advection on unstructured triangular grids are assessed for possible use in ocean modelling applications. Finite element, finite volume and finite volume–element approaches are evaluated. A series of tests, including a numerical order of convergence analysis, idealized rotating cone and cylinder experiments, and transport of a tracer through the Stommel Gyre representation of ocean basin-scale circulation, are carried out. Volume element Eulerian–Lagrangian and third-order Runge-Kutta discontinuous Galerkin schemes are recommended for use in tracer studies. Taylor–Galerkin and second-order Runge–Kutta discontinuous Galerkin are found to be robust and accurate second-order schemes. When positivity is required, a fluctuation redistribution scheme was found to be an easily implemented, accurate, and computationally efficient approach. Responsible editor: Phil Dyke     

Polynomial approximate solutions to the Boussinesq equation

We provide closed-form approximate solutions to models of horizontal infiltration described by the Boussinesq equation in a semi-infinite aquifer that is initially dry. The approximations preserve such important qualitative properties as scaling and wetting fronts. They are applicable to four types of boundary conditions, two on head and two on flux, enumerated in the paper. All the considered problems admit self-similar variables that allow reduction to boundary value problems for a nonlinear ordinary differential equation. This work extends recent results by Lockington et al. [Lockington DA, Parlange J-Y, Parlange MB, Selker J. Similarity solution of the Boussinesq equation. Adv Water Resour 2000;23(7):725–9] and Telyakovskiy et al. [Telyakovskiy AS, Braga GA, Furtado F. Approximate similarity solutions to the Boussinesq equation. Adv Water Resour 2002;25(2):191–4], with new approximations developed for two of the four cases and a new extension of a previously existing method for a third case. Numerical results extending the work of Shampine [Shampine LF. Some singular concentration dependent diffusion problems. ZAMM 1973;53:421–2] provide a basis for assessing the accuracy of the new methods.     

Practical applications of a nonlinear approach to analysis of earthquake-induced liquefaction and deformation of earth structures

Seismic stability, liquefaction, and deformation of earth structures are critical issues in geotechnical earthquake engineering practice. At present, the equivalent linear approach is considered the ‘state of practice’ in common use. More recently, dynamic analyses incorporating nonlinear, effective-stress-based soil models have been used more frequently in engineering applications. This paper describes a bounding surface hypoplasticity model for sand [Wang ZL. Bounding surface hypoplasticity model for granular soils and its applications. PhD Dissertation for the University of California at Davis, U.M.I. Dissertation Information Service, Order No. 9110679; 1990; Wang ZL, Dafalias YF, Shen CK. Bounding surface hypoplasticity model for sand. ASCE, J Eng Mech 1990;116(5):983–1001; Wang ZL, Makdisi FI. Implementing a bounding surface hypoplasticity model for sand into the FLAC program. In: Proceedings of the international symposium on numerical modeling in geomechanics. Minnesota, USA; 1999. p. 483–90] incorporated into a two-dimensional finite difference analysis program [Itasca Consulting Group, Inc. FLAC (Fast Lagrangian Analysis of Continua), Version 4. Minneapolis, MN; 2000] to perform nonlinear, effective-stress analyses of soil structures. The soil properties needed to support such analyses are generally similar to those currently used for equivalent linear and approximate effective-stress analyses. The advantages of using a nonlinear approach are illustrated by comparison with results from the equivalent linear approach for a rockfill dam. The earthquake performance of a waterfront slope and an earth dam were evaluated to demonstrate the model's ability to simulate pore-pressure generation and liquefaction in cohesionless soils.     

Lagrangian simulations of unstable gravity-driven flow of fluids with variable density in randomly heterogeneous porous media

A new Lagrangian particle model based on smoothed particle hydrodynamics (SPH) is developed and used to simulate Darcy scale flow and transport in porous media. The method has excellent conservation properties and treats advection exactly. The Lagrangian method is used in stochastic analysis of miscible density-driven fluid flows. Results show that heterogeneity significantly increases dispersion and slows development of Rayleigh–Taylor instability. The presented numerical examples illustrate the advantages of Lagrangian methods for stochastic transport simulations.     

Water Resources of the Russian Federation in the 20th Century

Water resources of the Russian Federation in 1930–2000 are assessed. It is shown that, as a result of intensification of general atmospheric circulation, water resources increased since 1981 to 2000 by about 6% as compared with those for 1930–1980.     

Plate boundary deformation and continuing deflation of the Askja volcano,North Iceland,determined with GPS, 1987–1993

GPS geodetic measurements were conducted around the Askja central volcano located at the divergent plate boundary in north Iceland in 1987, 1990, 1992 and 1993. The accuracy of the 1987 and 1990 measurements is in the range of 10 mm for horizontal components; the accuracy of the 1992 and 1993 measurements is about 4 mm in the horizontal plane. Regional deformation in the Askja region is dominated by extension. Points located outside a 30–45 km wide plate boundary deformation zone indicate a displacement of 2.4±0.5 cm/a in the direction N 99°E±12° of the Eurasian plate relative to the North American plate in the period 1987–1990. Within the plate boundary deformation zone extensional strain accumulates at a rate of 0.8 strain/a. Displacement of control points next to Askja (>7 km from the caldera center) in the periods 1990–1993 and 1992–1993 show deflation and contraction towards the caldera. These results are in accordance with the results obtained by other geodetic methods in the area, which indicate that the deflation at Askja occurs in response to a pressure decrease at about 2.8 km depth, located close to the center of the main Askja caldera. A Mogi point source was fixed at this location and the GPS data used to solve for the source strength. A central subsidence of 11±2.5 cm in the period 1990–1993 is indicated, and 5.5±1.5 cm in the period 1992–1993. The maximum tensional strain rate, according to the point source model, occurs at a horizontal distance of 2.5–6 km from the source, at the same location as the main caldera boundary. Discrepancies between the observed displacements and predicted displacements from the Mogi model near the Askja caldera can be attributed to the regional eastwest extension that occurs at Askja.     

Effect of foundation embedment on seismic behavior of elevated tanks considering fluid–structure-soil interaction

This paper investigates the effects of foundation embedment on the seismic behavior of fluid-elevated tank-foundation–soil system with a structural frame supporting the fluid containing tank. Six different soil types defined in the well-known seismic codes were considered. Both the sloshing effects of the fluid and soil-structure interaction of the elevated tanks located on these six different soils were included in the analyses. Fluid-elevated tank-foundation–soil systems were modeled with the finite element (FE) technique. The fluid-structure interaction was taken into account using Lagrangian fluid FE approximation implemented in the general purpose structural analysis computer program, ANSYS. FE model with viscous boundary was used to include elevated tank-foundation–soil interaction effects. The models were analyzed for the foundations with and without embedment. It was found that the tank roof displacements were affected significantly by the embedment in soft soil, however, this effect was smaller for stiff soil types. Except for soft soil types, embedment did not affect the other response parameters, such as sloshing displacement, of the systems considered in this study.     

A finite-volume ELLAM for three-dimensional solute-transport modeling

A three-dimensional finite-volume ELLAM method has been developed, tested, and successfully implemented as part of the U.S. Geological Survey (USGS) MODFLOW-2000 ground water modeling package. It is included as a solver option for the Ground Water Transport process. The FVELLAM uses space-time finite volumes oriented along the streamlines of the flow field to solve an integral form of the solute-transport equation, thus combining local and global mass conservation with the advantages of Eulerian-Lagrangian characteristic methods. The USGS FVELLAM code simulates solute transport in flowing ground water for a single dissolved solute constituent and represents the processes of advective transport, hydrodynamic dispersion, mixing from fluid sources, retardation, and decay. Implicit time discretization of the dispersive and source/sink terms is combined with a Lagrangian treatment of advection, in which forward tracking moves mass to the new time level, distributing mass among destination cells using approximate indicator functions. This allows the use of large transport time increments (large Courant numbers) with accurate results, even for advection-dominated systems (large Peclet numbers). Four test cases, including comparisons with analytical solutions and benchmarking against other numerical codes, are presented that indicate that the FVELLAM can usually yield excellent results, even if relatively few transport time steps are used, although the quality of the results is problem-dependent.     

A connection between the Lagrangian stochastic–convective and cumulant expansion approaches for describing solute transport in heterogeneous porous media

The equation describing the ensemble-average solute concentration in a heterogeneous porous media can be developed from the Lagrangian (stochastic–convective) approach and from a method that uses a renormalized cumulant expansion. These two approaches are compared for the case of steady flow, and it is shown that they are related. The cumulant expansion approach can be interpreted as a series expansion of the convolution path integral that defines the ensemble-average concentration in the Lagrangian approach. The two methods can be used independently to develop the classical form for the convection–dispersion equation, and are shown to lead to identical transport equations under certain simplifying assumptions. In the development of such transport equations, the cumulant expansion does not require a priori the assumption of any particular distribution for the Lagrangian displacements or velocity field, and does not require one to approximate trajectories with their ensemble-average. In order to obtain a second-order equation, the cumulant expansion method does require truncation of a series, but this truncation is done rationally by the development of a constraint in terms of parameters of the transport field. This constraint is less demanding than requiring that the distribution for the Lagrangian displacements be strictly Gaussian, and it indicates under what velocity field conditions a second-order transport equation is a reasonable approximation.     

Evaluation of confidence intervals for a steady-state leaky aquifer model

The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. & Cooley, R.L., Water Resources Research, 1987, 23(7), 1237–1250] was used to calculate nonlinear Scheffé-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km² of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.     

Frictional Behavior of Steel-PTFE Interfaces for Seismic Isolation

The widespread use of sliding bearings for the seismic isolation of structures requires detailed knowledge of their behavior and improved modeling capability under seismic conditions. The paper summarizes the results of a large experimental investigation on steel–PTFE interfaces, aimed at evaluating the effects of sliding velocity, contact pressure, air temperature and state of lubrication on the mechanical behavior of steel-PTFE sliding bearings. Based on the experimental outcomes, two different mathematical models have been calibrated, which are capable of accounting for the investigated parameters in the evaluation of the sliding friction coefficient. The first model is basically an extension of the model proposed by Constantinou et al. (1990)Journal of Earthquake Engineering, 116(2), 455–472, while the second model is derived from the one proposed by Changet al. (1990)Journal of Engineering Mechanics, 116, 2749–2763. Expressions of the model parameters as a function of bearing pressure and air temperature are presented for lubricated and non-lubricated sliding surfaces. Predicted and experimental results are finally compared.     

Shear wave velocity structure of the upper mantle under the NW Indian Ocean

Shear wave velocity structure of the NW Indian ocean is analysed by using fundamental mode Rayleigh wave dispersion data of 67 events occurred during 1990–98 at the central Indian Ridge and Carlsberg Ridge and recorded at Hyderabad Geoscope station (HYB). These events provide a dense coverage of the NW Indian ocean and Chagos-Laccadive Ridge (CLR) in the back-azimuthal range of 192–253° with respect to HYB. The dispersion curves, corrected for continental and young ocean paths, indicate large variations in the shear wave velocity structure of the region. The group velocities along the CLR path support a typical aseismic ridge-type structure. However, the central region bounded between the Central Indian Ridge and India in the back-azimuth of 206–234° indicates a decrease in the group velocity by 0.1 km/s. Inversion of these data sets indicates presence of aseismic-ridge type lithospheric structure for CLR, a thin lithosphere and high velocity block in the depth range of 125–200 km for the central region, and a continental-type lithospheric structure for the northern-most part of the Indian ocean. It is inferred that the dynamic state of the upper mantle in this region has been significantly perturbed during the recent geological past.     

Water Quality Assessment Based on Chemical and Biological Characteristics: An Example of Classification of Characteristics for the Cheremushnyi Creek–Yenisey River Water System

A six-class scale for a complex classifier of water quality is applied to the Cheremushnyi Creek–Yenisey River water system. The classifier incorporates a chemical index of water pollution and biological characteristics with autotrophic and heterotrophic periphyton groups and macrozoobenthos used as biological indicators. The oligochaeta index and Woodiwiss biotic index are shown to have low indicator capacity. Bioassay studies were based on recording acute and chronic toxic effects for three test species at different trophic levels. The level of biologically safe dilution is proposed as a quantitative index of toxicity. Saprobity and toxicity (saprotoxobity) characteristics are given for individual species. Water of the Cheremushnyi Creek–Yenisey River water system is referred to the IV–VI quality class.