Top Boundary Conditions Research Articles

Temperature Fluctuations in a Landfill in Response to Periodic Changes in Surface and Tide-Driven Groundwater Temperatures

In Australia, the concentration of population along the coastal regions has resulted in the construction of landfills near the coastal regions. The wastes buried in these unlined landfills are therefore exposed to tidal influence, often resulting in the dispersion of organic and inorganic pollutants to the surrounding environment. In a project cosponsored by the Rockhampton Regional Council, a number of processes at a landfill site situated in the flood plains of the Fitzroy River are being investigated. The processes include those in terms of multiphase flow consisting of gas (methane), solute (measured as salts, via EC and pH) and water in a porous media. In this paper we analyse temperature changes in groundwater and porous media of the landfill which is subject to periodic surface and tide-driven temperatures. The heat equation is solved, subject to two periodic boundary conditions (BC): the top BC is a periodic surface temperature due to the change in air temperature, and bottom BC is a periodic function to account for the changes in groundwater temperature induced by tides. The methods can be used to locate key parameters and variables of concern in the porous media, and to forecast their variability with time, using publicly available air temperature and tide data.

Conceptual Hydrological Modeling of the Soil-bedrock Interface at the Bottom of the Pyroclastic Cover of Cervinara (Italy)

On the basis of the data collected by a monitoring station, a simplified mathematical model of the hydrological behavior of the layered pyroclastic cover of the slope of Cervinara (southern Apennines) has been developed. The model considers a single homogeneous soil layer, for which effective hydraulic characteristic curves have been defined. The top boundary condition accounts for the effects of evapotranspiration. The bottom boundary condition conceptually simulates, by means of a linear reservoir model, the hypothesized effects, on the soil water potential at the soil-bedrock interface, of the fluctuations of the water table of an ephemeral aquifer stored in the underlying fractured limestone. Despite its simplifying assumptions, the model satisfactorily reproduces the observed soil water potential at all the monitored depths. The obtained results indicate that even the highest rainfall intensity can pass through the highly conductive unsaturated soil cover, and leak through the fractured bedrock. Only when the water level in the underlying aquifer is high, as it happens after long lasting periods of rainfall, the establishment of the vertical water potential gradients, needed for the leakage of high infiltration peaks, leads to soil saturation at the bottom of the cover. Such a picture provides a possible interpretation of the triggering mechanism of the landside occurred in 1999 along the slope.

A new, unified, theoretical framework for the formulation of general, nonlinear, single-scale shell theories

A new, general theoretical framework for the generation of single-scale shell theories is presented. The framework is developed for application to the analysis of the general laminated and monolithic shells. The proposed framework is intended to allow the accurate prediction of the effects of material nonlinearity and wave propagation effects through the thickness of a shell.The starting point for the framework is a general, single-scale description of the displacement field expressed in terms of arbitrary expansion functions through the thickness of the shell. The functional forms and orders for the expansion functions in the displacement field representation are arbitrary. The development of the governing equations for the theory is carried out using the general nonlinear equations of continuum mechanics referenced to the initial configuration within the context of general coordinate systems. The equations of motion and the lateral surface boundary conditions for the theory are derived using the method of moments over the domain of the expansion functions. The (arbitrary) top and bottom surface boundary conditions (BCs) are satisfied exactly. The interfacial constraints (continuity of tractions and (dis) continuity of displacements) are also satisfied exactly. Delamination effects are incorporated into the theory through the use of arbitrary functions relating the displacement jumps to appropriate state variables. These functions can be changed without the need for reformulation of the governing equations. The theory is formulated in a sufficiently general fashion that any type of history-dependent material model can be used to describe the history-dependent behavior of the material composing a layer without the need to reformulate the theory.The theoretical framework is unified in the sense that any type of desired single scale shell (smear/equivalent single layer (ESL), discrete layer, or zig-zag) theory can be obtained through suitable specialization of the framework. In the case of a smeared or ESL representation the domain of the displacement representation applies across the entire thickness of the shell. To generate a zig-zag theory within the context of the proposed framework is simply a matter of carrying out the interfacial analysis appropriate to the zig-zag assumptions and substituting the resulting displacement representation into the framework and then proceeding as with a smeared/ESL theory. In the case of a discrete layer analysis the displacement representations applies across each of the individual domains. The domains may correspond to several layers, a lamina, or a sublamina. Thus, the framework represents a comprehensive approach to modeling shells.The predictions of the theory are compared with the results obtained from an exact elastic solution for the static response of a sphere and the exact elastic solution for the dynamic response of monolithic sphere. Both exact solutions are based on the assumptions of spherically symmetric boundary conditions. It is shown that the theory is capable of providing accurate predictions for the pointwise (displacement, strain, and stress) fields distributions in laminated and monolithic shells. Furthermore, it is shown that the behavior of the theory is self-convergent and thus increasing the order of the analysis always converges the predictions to the correct answer.

Numerical investigation of double diffusive natural convection of CO2 in a brine saturated geothermal reservoir

In geologic sequestration or in CO2-based geothermal systems, CO2 is present on top of the brine phase. In this study we performed a numerical analysis of a geothermal reservoir that is impermeable from the sides and is open to CO2 at the top. For this configuration, double diffusive natural convection due to density and temperature differences across the height enhance the mass transfer rate of CO2 into the initially stagnant brine. The analysis is done using mass, momentum, energy conservation laws, and the Darcy laws. The objective is to understand the diffusion of CO2 over long periods of time after sequestration into a subsurface porous media geothermal aquifer. The problem parameters are the solutal Rayleigh number (100≤Ras≤10,000), the buoyancy ratio (2≤N≤100), the cavity aspect ratio (0.5≤A≤2), and a fixed Lewis number (Le=301). Numerical computations do not exhibit natural convection effects for homogeneous initial conditions. Hence a sinusoidal perturbation is added for the initial top boundary condition. It is found that the CO2 plumes move faster when Ras is increased, however they slow down with decreasing N. For every simulation run, the average CO2 concentration (S¯=(∑ini∑jnjci,j/ni×nj)) is computed. Higher concentration rates in laterally wide reservoirs make better candidates than deeper aquifers for CO2 sequestration.

Direct numerical simulations of boundary condition effects on the propagation of density current in wall-bounded and open channels

The propagation of density current under different boundary conditions is investigated using high resolution direct numerical simulations (DNS). A revised Kleiser and Schumann influence-matrix method is used to treat the general Robin type velocity boundary conditions and the related “tau” error corrections in the numerical simulations. Comparison of the simulation results reveals that the boundary conditions change the turbulent flow field and therefore the propagation of the front. This paper mainly focuses on the effects of boundary conditions and initial depth of the dense fluid. The differences in energy dissipation and overall front development in wall-bounded and open channels are examined. Through DNS simulations, it is evident that with the decrease of initial release depth ratio (\(D/H\)), the effect of the top boundary becomes less important. In wall-bounded channels, there are three distinctive layers in the vertical distribution of energy dissipation corresponding to the contributions from bottom wall, interface, and top wall, respectively. In open channels, there are only two layers with the top one missing due to the shear free nature of the boundary. It is found that the energy dissipation distribution in the bottom layer is similar for cases with the same \(D/H\) ratio regardless the top boundary condition. The simulation results also reveal that for low Reynolds number cases, the energy change due to concentration diffusion cannot be neglected in the energy budget. To reflect the real dynamics of density current, the dimensionless Froude number and Reynolds number should be defined using the release depth \(D\) as the length scale.

A new top boundary condition for modeling surface diffusive exchange of a generic volatile tracer: theoretical analysis and application to soil evaporation

Abstract. We describe a new top boundary condition (TBC) for representing the air–soil diffusive exchange of a generic volatile tracer. This new TBC (1) accounts for the multi-phase flow of a generic tracer; (2) accounts for effects of soil temperature, pH, solubility, sorption, and desorption processes; (3) enables a smooth transition between wet and dry soil conditions; (4) is compatible with the conductance formulation for modeling air–water volatile tracer exchange; and (5) is applicable to site, regional, and global land models. Based on the new TBC, we developed new formulations for bare-soil resistance and corresponding soil evaporation efficiency. The new soil resistance is predicted as the reciprocal of the harmonic sum of two resistances: (1) gaseous and aqueous molecular diffusion and (2) liquid mass flow resulting from the hydraulic pressure gradient between the soil surface and center of the topsoil control volume. We compared the predicted soil evaporation efficiency with those from several field and laboratory soil evaporation measurements and found good agreement with the typically observed two-stage soil evaporation curves. Comparison with the soil evaporation efficiency equation of Lee and Pielke (1992; hereafter LP92) indicates that their equation can overestimate soil evaporation when the atmospheric resistance is low and underestimate soil evaporation when the soil is dry. Using a synthetic inversion experiment, we demonstrated that using inverted soil resistance data from field measurements to derive empirical soil resistance formulations resulted in large uncertainty because (1) the inverted soil resistance data are always severely impacted by measurement error and (2) the derived empirical equation is very sensitive to the number of data points and the assumed functional form of the resistance. We expect the application of our new TBC in land models will provide a consistent representation for the diffusive tracer exchange at the soil–air interface.

Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories

This paper investigates the static analysis of doubly-curved laminated composite shells and panels. A theoretical formulation of 2D Higher-order Shear Deformation Theory (HSDT) is developed. The middle surface of shells and panels is described by means of the differential geometry tool. The adopted HSDT is based on a generalized nine-parameter kinematic hypothesis suitable to represent, in a unified form, most of the displacement fields already presented in literature. A three-dimensional stress recovery procedure based on the equilibrium equations will be shown. Strains and stresses are corrected after the recovery to satisfy the top and bottom boundary conditions of the laminated composite shell or panel. The numerical problems connected with the static analysis of doubly-curved shells and panels are solved using the Generalized Differential Quadrature (GDQ) technique. All displacements, strains and stresses are worked out and plotted through the thickness of the following six types of laminated shell structures: rectangular and annular plates, cylindrical and spherical panels as well as a catenoidal shell and an elliptic paraboloid. Several lamination schemes, loadings and boundary conditions are considered. The GDQ results are compared with those obtained in literature with semi-analytical methods and the ones computed by using the finite element method.

Modeling of groundwater flow at depth in crystalline rock beneath a moving ice-sheet margin, exemplified by the Fennoscandian Shield, Sweden

On-going geological disposal programs for spent nuclear fuel have generated strong demands for investigation and characterization of deep-lying groundwater systems. Because of the long time scales for which radiological safety needs to be demonstrated in safety assessment applications, an analysis of the hydrogeological performance of the geosphere system during glacial climate conditions is needed. Groundwater flow at depth in crystalline rock during the passage of an ice-sheet margin is discussed based on performed groundwater-flow modeling of two bedrock sites, Forsmark and Laxemar, in the Fennoscandian Shield, Sweden. The modeled ice sheet mimics the Weichselian ice sheet during its last major advance and retreat over northern Europe. The paper elaborates and analyzes different choices of top boundary conditions at the ice sheet–subsurface interface (e.g. ice-sheet thickness and ice-margin velocity) and in the proglacial area (presence or lack of permafrost) and relates these choices to available groundwater-flow-model hydraulic output and prevailing conceptual hydrogeochemical models of the salinity evolution at the two sites. It is concluded that the choice of boundary conditions has a strong impact on results and that the studied sites behave differently for identical boundary conditions due to differences in their structural-hydraulic properties.

3D thermal structure of the continental lithosphere beneath China and adjacent regions

Based on the Crust2.0 model and the topography data of Chinese continent and its adjacent regions, a three-dimensional finite element model is constructed in terms of the spherical coordinate system. In our numerical model, the average annual ground temperature from 195 meteorological stations and temperature of upper mantle derived from the seismic velocities are adopted as the top and bottom boundary conditions, respectively. The observed thermal conductivity and heat production from P wave velocity based on empirical formula are employed in our numerical model as well. The comparison between the calculated and observed surface heat flow proved that our results are reliable. The temperature beneath the Precambrian cratons is lower than that of other areas for 100–300°C also. The typical temperature rang at the Moho is estimated to be 800–1000°C beneath the Tibetan plateau and 500–700°C beneath the Precambrian cratons (such as Indian plate, Sichuan basin, South China, North China and Tarim), respectively. The thermal state in the eastern part of Sino-Korean craton at the depth deeper than 60km indicates that it was destructed. The thermal structure in center of Tibetan plateau (especially beneath Qiangtang area) supports the proposed flow of lower crustal or upper mantle material to the east. Generally, the distribution of volcanoes in Chinese continent is consistent with the high temperature areas in the crust or upper mantle. There are many obvious thermal transition zones across the orogenic belts. The thermal transition zone between eastern and western parts in the crust of Chinese continent is consistent with the north–south seismic zone.

3DVAR versus Traditional Dual-Doppler Wind Retrievals of a Simulated Supercell Thunderstorm

Abstract Use of the three-dimensional variational data assimilation (3DVAR) framework in dual-Doppler wind analysis (DDA) offers several advantages over traditional techniques. Perhaps the most important is that the errors that result from explicit integration of the mass continuity equation in traditional methods are avoided. In this study, observing system simulation experiments (OSSEs) are used to compare supercell thunderstorm wind retrievals from a 3DVAR DDA technique and three traditional DDA methods. The 3DVAR technique produces better wind retrievals near the top of the storm than the traditional methods in the experiments. This is largely attributed to the occurrence of severe errors aloft in the traditional retrievals whether the continuity equation integration proceeds upward (due to vertically accumulating errors), downward (due to severe boundary condition errors arising from uncertainty in the horizontal divergence field aloft), or in both directions. Smaller, but statistically significant, improvement occurs near the ground using the 3DVAR method. When lack of upper-level observations prevents application of a top boundary condition in the traditional DDA framework, the 3DVAR approach produces better analyses at all levels. These results strongly suggest the 3DVAR DDA framework is generally preferable to traditional formulations.

Evaluation of models for laterally loaded piles

It is common in the analysis of piles under lateral loads to use a model of a beam on elastic foundation, or a finite element model with the pile represented by a one dimensional beam–column with its axis coinciding with the central line of the finite element mesh. In both cases the lateral stiffness of the pile itself, as a structural element, is a function of the product of its Young’s modulus of elasticity by the moment of inertia of the cross section (EI). For solid piles the moment of inertia is directly related to the radius but this is not the case when dealing with hollow piles where the value of the radius corresponding to a given moment of inertia is not unique. Both of the above models ignore the effect of the value of the radius of the soil cavity occupied by the pile. In this work a more accurate model of the pile with the soil around it represented. A consistent boundary matrix valid for static and dynamic analyses is used to evaluate the accuracy of the results provided by the model of a beam on elastic foundation. In addition, a 1D model of the pile is analyzed with finite elements for the soil. This analysis considers a fixed value of the product EI, but a variable radius in order to illustrate the importance of the radial dimension. Results are obtained for a pile fixed at the bottom, but long enough so that the top boundary conditions do not affect the results and for a shorter floating pile were the shear and moment at the bottom resulting from the underlying soil would not be zero. For the beam on elastic foundation model, the top of the pile was assumed to be fixed.

The Effect of Boundary Conditions on Simulation of Horizontally Homogeneous Atmospheric Boundary Layer

The Influence of six kinds of combinations of different boundary conditions on the maintenance of homogeneity of atmospheric boundary layer in computational wind engineering was investigated. The inlet condition was applied by either prescribing velocity and turbulent quantities or using a periodic boundary. The top boundary condition includes symmetry, prescribing velocity and turbulent quantities, constant static pressure and applying driving shear stress. Numerical results show that the stream-wise velocity and the turbulent dissipation rate are almost immune to boundary conditions, but the turbulent kinetic energy is affected by boundary conditions dramatically. Best maintenance can be obtained by using periodic boundary condition at inlet and outlet and applying driving shear stress on the top of the domain.

NUMERICAL SUNSPOT MODELS: ROBUSTNESS OF PHOTOSPHERIC VELOCITY AND MAGNETIC FIELD STRUCTURE

MHD simulations of sunspots have successfully reproduced many aspects of sunspot fine structure as consequence of magneto convection in inclined magnetic field. We study how global sunspot properties and penumbral fine structure depend on the magnetic top boundary condition as well as on grid spacing. The overall radial extent of the penumbra is subject to the magnetic top boundary condition. All other aspects of sunspot structure and penumbral fine structure are resolved at an acceptable level starting from a grid resolution of 48 [24] km (horizontal [vertical]). We find that the amount of inverse polarity flux and the overall amount of overturning convective motions in the penumbra are robust with regard to both, resolution and boundary conditions. At photospheric levels Evershed flow channels are strongly magnetized. We discuss in detail the relation between velocity and magnetic field structure in the photosphere and point out observational consequences.

Gas Pressure Model for Layered Municipal Solid Waste Landfills

AbstractA mathematical model for calculating gas pressure profiles in layered landfill systems is presented. Solutions to scenarios considering a zero-pressure top boundary condition and a zero gas flux or fixed gas pressure bottom boundary condition are presented. Two cases, specified gas pressure and specified inward gas flux, are addressed for scenarios involving horizontal gas collection systems. A series of application examples demonstrate how the proposed model can be used to investigate the influences of (1) variation of gas generation rate with respect to depth and time, (2) soil covers, (3) horizontal collection layers, and (4) geomembrane and geosynthetic clay liner covers on gas pressure distribution in landfills. The proposed model provides a useful tool to landfill engineers in designing landfill gas management systems and in particular when selecting and specifying gas collection system spacing and pumps.

Calibration and validation of an integrated nitrate transport model within a well capture zone

Groundwater contamination by nitrate was investigated in an agricultural area in southern Quebec, Canada, where a municipal well is the local source of drinking water. A network of 38 piezometers was installed within the capture zone of the municipal well to monitor water table levels and nitrate concentrations in the aquifer. Nitrate concentrations were also measured in the municipal well. A Water flow and Nitrate transport Global Model ( WNGM) was developed to simulate the impact of agricultural activities on nitrate concentrations in both the aquifer and municipal well. The WNGM first uses the Agriflux model to simulate vertical water and nitrate fluxes below the root zone for each of the seventy agricultural fields located within the capture zone of the municipal well. The WNGM then uses the HydroGeoSphere model to simulate three-dimensional variably-saturated groundwater flow and nitrate transport in the aquifer using water and nitrate fluxes computed with the Agriflux model as the top boundary conditions. The WNGM model was calibrated by reproducing water levels measured from 2005 to 2007 in the network of piezometers and nitrate concentrations measured in the municipal well from 1997 to 2007. The nitrate concentrations measured in the network of piezometers, however, showed greater variability than in the municipal well and could not be reproduced by the calibrated model. After calibration, the model was validated by successfully reproducing the decrease of nitrate concentrations observed in the municipal well in 2006 and 2007. Although it cannot predict nitrate concentrations in individual piezometers, the calibrated and validated WNGM can be used to assess the impact of changes in agricultural practices on global nitrate concentrations in the aquifer and in the municipal well.

Effect of Top and Bottom Boundary Conditions on Symmetric Instability under Full-Component Coriolis Force

Abstract The linear stability of a zonal flow confined in a domain within horizontal top and bottom boundaries is examined under full consideration of the Coriolis force. The basic zonal flow is assumed to be in thermal wind balance with the density field and to be sheared in both vertical and horizontal directions under statically and inertially stable conditions. By imposing top and bottom boundary conditions in this framework, the number of wave modes increases to four, instead of two in an unbounded domain, as already reported in studies on internal gravity waves. The four modes are classified into two pairs of high- and low-frequency modes: the high modes are superinertial and the low modes are subinertial. The discriminant of symmetric instability is nevertheless determined by the sign of the potential vorticity of the basic zonal flow, as in the case of an unbounded domain. The solutions satisfying the top and bottom boundary conditions are interpreted as the superposition of incident and reflected waves, revealing that the neutral solutions consist of two neutral plane waves with oppositely directed vertical group velocities. This may explain why the properties of wave behavior, such as the instability criteria, remain the same in both the bounded and unbounded domains, although the manifestation of wave activity, such as the order of dispersion relation, is quite different in the two cases. Furthermore, the slope of the constant momentum surface, the slope of the isopycnic surface including the nontraditional effect of the Coriolis force, and the ratio between the frequencies of gravity and inertial waves form an essential set of parameters for symmetric motion. The combination of these dimensionless quantities determines the fundamental nature of symmetric motions, such as stability, regardless of boundary conditions with and without the horizontal component of the planetary vorticity.

Practical laws for natural convection of viscous fluids heated from above in a shallow cavity

Industrial production of glass involves natural convection of viscous fluids heated from above in shallow cavities. This problem is revisited by means of extensive numerical simulations and analytical expansions for a 2D configuration. This approach yields exact and approximate analytical expressions that can be practically used to evaluate the convective intensity and the heat flux in the different regimes. These results also confirm that the control parameter for this problem is the product of the Rayleigh number, based on the height of the enclosure, by the cavity aspect ratio squared whatever the top boundary conditions.

A utilização de soluções exactas baseadas em análise espectral na caracterização do escoamento subterrâneo controlado pela topografia

Spectral analysis enhances the ability to analyze groundwater flow at a steady state by separating the top boundary condition into its periodic forms. Specifically, spectral analysis enables comparisons of the impact of individual spatial scales on the total flow field. New exact spectral solutions are presented for analyzing 3D groundwater flow with an arbitrarily shaped top boundary. These solutions account for depth-decaying, anisotropic and layered permeability while utilizing groundwater flux or the phreatic surface as a top boundary condition. Under certain conditions, groundwater flow is controlled by topography. In areas where the groundwater flow is controlled by the topography, the unknown water table is often approximated by the topography. This approximation induces a systematic error. Here, the optimal resolution of digital elevation models (DEMs) is assessed for use as a top boundary in groundwater flow models. According to the analysis, the water-table undulation is smoother than the topography; therefore, there is an upper limit to the resolution of DEMs that should be used to represent the groundwater surface. The ability to represent DEMs of various spectral solutions was compared and the results indicate that the fit is strongly dependent on the number of harmonics in the spectral solution.

Numerical simulations of the Macondo well blowout reveal strong control of oil flow by reservoir permeability and exsolution of gas

In response to the urgent need for estimates of the oil and gas flow rate from the Macondo well MC252-1 blowout, we assembled a small team and carried out oil and gas flow simulations using the TOUGH2 codes over two weeks in mid-2010. The conceptual model included the oil reservoir and the well with a top boundary condition located at the bottom of the blowout preventer. We developed a fluid properties module (Eoil) applicable to a simple two-phase and two-component oil-gas system. The flow of oil and gas was simulated using T2Well, a coupled reservoir-wellbore flow model, along with iTOUGH2 for sensitivity analysis and uncertainty quantification. The most likely oil flow rate estimated from simulations based on the data available in early June 2010 was about 100,000 bbl/d (barrels per day) with a corresponding gas flow rate of 300 MMscf/d (million standard cubic feet per day) assuming the well was open to the reservoir over 30 m of thickness. A Monte Carlo analysis of reservoir and fluid properties provided an uncertainty distribution with a long tail extending down to 60,000 bbl/d of oil (170 MMscf/d of gas). The flow rate was most strongly sensitive to reservoir permeability. Conceptual model uncertainty was also significant, particularly with regard to the length of the well that was open to the reservoir. For fluid-entry interval length of 1.5 m, the oil flow rate was about 56,000 bbl/d. Sensitivity analyses showed that flow rate was not very sensitive to pressure-drop across the blowout preventer due to the interplay between gas exsolution and oil flow rate.

One-dimensional consolidation under haversine repeated loading with rest period

Presented in this paper is a study of the one-dimensional consolidation process under haversine repeated loading with and without rest period. The analysis was carried out using a hybrid coupled, analytical and numerical implicit finite difference technique. The rate of imposition of excess pore-water pressure was determined analytically, and the remaining part of the governing differential equation was solved numerically. The clay deposit considered was a homogeneous clay layer with permeable top and/or impermeable bottom hydraulic boundary conditions with constant coefficients of permeability and of consolidation. The study reveals that although the loading function is positive for all times, the excess pore-water pressure at the base of the clay deposit with permeable top and impermeable bottom oscillates with time reaching a ‘steady state’ after few cycles of loading depending on whether there is a rest period or not. An increase in the rest period causes a decrease in the number of cycles required to achieve the steady state. The paper shows also that the rest period in the haversine repeated loading decelerates the consolidation process. Similarly, the paper reveals that the effective stress at the bottom of the clay layer with permeable top and impermeable bottom increases with time but showing mild fluctuations that do not change the sign. The maximum positive effective stress achieved depends on the rest period of the haversine repeated loading. A haversine repeated loading without a rest period gives the highest value for the positive effective stress.