Convergence acceleration of iterative sequences for equilibrium chemistry computations

Computational Geosciences - The modeling of thermodynamic equilibria leads to complex nonlinear chemical systems which are often solved with the Newton-Raphson method. But this resolution can lead...     

Evaluation of factor of safety for vegetated and barren soil slopes with limit equilibrium computations

Limit equilibrium method (LEM) is the most conventional and popular technique in slope stability analysis. Location of the unique failure surface and the determination of corresponding critical factor of safety (critical-FOS) of the soil slope requires a lot of trial and research. With this amount of trial and research results, we evaluate the field of factor of safety (FOS-field), which represents the critical-FOS at a point within the domain of all possible failure surfaces. Such a field can be very important for the precise judgment of the most critical-FOS of the slope and its perturbation. This paper also presents the evaluation of the FOS-field of vegetated slopes, thus providing an analytical way to examine the effect of vegetation on the soil slope stability. We evaluated the stability of vegetated and barren soil slopes under dry and fully saturated conditions. With dry and fully saturated conditions, the behaviour of slopes in most favourable and worst conditions can be simulated. Evaluation of FOS-field for various slope geometries and conditions show that the more unstable the slope becomes, the more difficult it will be to pinpoint the location of the critical failure surface with the unique least FOS. We verified the LEM codes with finite element method (FEM) and spectral element method (SEM) codes considering a sample problem from Smith and Griffiths’ book (Smith and Griffiths 2003).     

Comparison between cell-centered and nodal-based discretization schemes for linear elasticity

In this paper, we study newly developed methods for linear elasticity on polyhedral meshes. Our emphasis is on applications of the methods to geological models. Models of subsurface, and in particular sedimentary rocks, naturally lead to general polyhedral meshes. Numerical methods which can directly handle such representation are highly desirable. Many of the numerical challenges in simulation of subsurface applications come from the lack of robustness and accuracy of numerical methods in the case of highly distorted grids. In this paper, we investigate and compare the Multi-Point Stress Approximation (MPSA) and the Virtual Element Method (VEM) with regard to grid features that are frequently seen in geological models and likely to lead to a lack of accuracy of the methods. In particular, we look at how the methods perform near the incompressible limit. This work shows that both methods are promising for flexible modeling of subsurface mechanics.     

Recent geoid computations for the Hellenic area

New geoid computations for the Hellenic area are carried out using (a) gravity anomalies for the land area available from old and new data bases, and gravity data for the sea area derived from altimetry and a recent digitization of sea gravity maps, and (b) a 1km × 1km digital terrain model. The EGM96 geopotential model is used as the reference field. In order to assess the quality of the computed geoid heights in the continental area comparisons were carried out with GPS/leveling heights and the recently available European Gravimetric Geoid EGG97. In the sea area the geoid heights were compared with sea surface heights of the recent and more accurate TOPEX/POSEIDON (T/P) altimetry mission. At the end of this article the improvement of the data bases is discussed and some plans for further development in the methodological schedule are pointed out.     

Comparison of linear reconstructions for second-order finite volume schemes on polyhedral grids

Improved and enhanced oil recovery methods require sophisticated simulation tools to predict the injected flow pass together with the chemical reactions inside it. One approach is application of higher-order numerical schemes to avoid excessive numerical diffusion that is very typical for transport processes. In this work, we provide a first step towards higher-order schemes applicable on general polyhedral and corner-point grids typically used in reservoir simulation. We compare three possible approaches of linear reconstruction and slope limiting techniques on a variety of different meshes in two and three spatial dimensions and discuss advantages and disadvantages.     

Some numerical experiences on convergence criteria for iterative finite element solvers

Several popular convergence criteria which are frequently used in practical finite element computations are investigated for two kinds of systems: the symmetric positive definite linear system and the symmetric indefinite system involving two distinct variables (displacement and pore fluid pressure). For the first system, the relative residual norm and the relative improvement norm are satisfactory as long as boundary fixities are handled appropriately. For the second system, the relative improvement norm must be adopted with greater care. It was further shown numerically that decoupled relative residual norms can be attractive alternates to the current global stopping criterion.     

现代地球化学的理论思维结构

地球科学和地球化学的进展,不但加深和扩大了对地球的认识和理论成果,同时也总结提炼出了全新的科学思维方法。复杂性理论和系统思维是科学认识论的一次飞跃。现代地球化学建立了较完整的理论和方法体系,给地质科学认知地球提供了依据和支撑。作者论证了系统思维和逻辑演绎法相结合的思维方式,是研究和认识地球复杂巨系统以及推动地球科学理论创新的指导思想,并提出了运用现代地球化学理论构架和方法体系,综合地球科学系统思维与逻辑思维相结合方向的地球化学认知模型,为深入研究地球物质能量系统的行为和解决人类面临的资源、环境和灾害问题提供新的思路。     

Thermal and rheological computations for artificially frozen ground construction

Design considerations for frozen retaining structures are summarized including geology and groundwater conditions; ground deformations due to freezing; the strength and deformation of the frozen earth retaining structures; the thermal assumption and methods of computation; and the refrigeration system. Brief case histories of typical construction projects that illustrate the use of mechanical refrigeration and liquid nitrogen for freezing are presented. Emphasis is placed on the constitutive equation for creep deformation of frozen earth structures and the thermal calculations for predicting times to freeze a structure as well as estimating the energy and power required for different stages of freezing.     

Developing the scientific framework for urban geochemistry

Urban geochemistry is a unique discipline that is distinguished from general geochemistry by the complex infrastructure and intense human activities associated with concentrated population centers. As stated by Thornton (1991) “This subject is concerned with the complex interactions and relationships between chemical elements and their compounds in the urban environment, the influence of past and present human and industrial activities on these, and the impacts or effects of geochemical parameters in urban areas on plant, animal and human health.” Urban areas present special challenges to geochemists attempting to understand geochemical states and fluxes. On the 5–6 of August, 2014, the first meeting of the reorganized Urban Geochemistry Working Group of the International Association of GeoChemistry (IAGC) was held in Columbus, Ohio, United States. Two goals of the meeting were to develop the overall scope, and a general definition of urban geochemistry. Five grand themes were developed: 1) recognizing the urban geochemical signature; 2) recognizing the legacy of altered hydrologic and geochemical cycles in urban environments; 3) measuring the urban geochemical signature; 4) understanding the urban influence on geochemical cycles from the continuous development and erosion of physical infrastructure and episodic perturbations; and 5) relating urban geochemistry to human and environmental health and policy. After synthesizing the discussion of these themes we offer the following perspective on the science of urban geochemistry building on the work of Thornton (1991): Urban geochemistry as a scientific discipline provides valuable information on the chemical composition of environments that support large populations and are critical to human health and well-being. Research into urban geochemistry seeks to 1) elucidate and quantify the sources, transport, transformations, and fate of chemicals in the urban environment, 2) recognize the spatial and temporal (including legacies) variability in these processes, and 3) integrate urban studies into global perspectives on climate change, biogeochemical cycles, and human and ecosystem health. We hope that this discussion will encourage other geochemists to engage in challenges unique to urban systems, as well as provide a framework for the future of urban geochemistry research.     

Scaling improves stability of preconditioned CG‐like solvers for FE consolidation equations

Preconditioned projection (or conjugate gradient like) methods are increasingly used for the accurate and efficient solution to finite element (FE) coupled consolidation equations. Theory indicates that preliminary row/column scaling does not affect the eigenspectrum of the iteration matrix controlling convergence as long as the preconditioner relies on the incomplete factorization of the FE coefficient matrix. However, computational experience with mid‐large size problems shows that the above inexpensive operation can significantly accelerate the solver convergence, and to a minor extent also improve the final accuracy, as a result of a better solver stability to the accumulation and propagation of floating point round‐off errors. This is demonstrated with the aid of the least square logarithm (LSL) scaling algorithm on FE consolidation problems of increasing size up to more than 100 000. It is shown that a major source of numerical instability rests with the sub‐matrix which couples the structural to the fluid part of the underlying mathematical model. It is concluded that for mid‐large size, possibly difficult, FE consolidation problems left/right LSL scaling is to be always recommended when the incomplete factorization is used as a preconditioning technique. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical tools for geoscience computations: Semiautomatic differentiation—SD

This paper presents a differentiation method [referred to here as semiautomatic differentiation (SD)] based on generalization and extension of the Squire and Trapp formula for complex differentiation of real-valued functions. The performance of the generalized formulas for first-order derivatives is tested and compared with manual, automatic (AD), and finite difference (FD) techniques. My results show that, in terms of accuracy, the SD technique is competitive with AD, and in terms of implementation simplicity, it is identical to the FD method with the added advantage of being step-size insensitive and, hence, free from the step-size dilemma that plagues FD. Using central differencing in the complex plane, I extend the SD method to second-order derivatives, thus enabling approximation of the Hessians. Performance of the extension formulas is evaluated and compared with AD and FD methods. The results indicate that the differencing operation reduces the accuracy of the extension formulas by four to five orders of magnitude below that of the original Squire and Trapp formula. Nonetheless, compared to FD schemes, the SD method is six to seven orders of magnitude more accurate in all tests conducted. In addition, the extension formulas exhibit step-size (h) insensitive behavior over the entire h-range of the tests (1–10⁻³⁰), indicating high numerical stability of the schemes. I show by examples that SD provides a complete differentiation system that is computationally stable, efficient, highly accurate, and easy to implement.     

Interactive remote computations for retaining wall design and risk assessment

Remote computation as well as remote design is a hot topic nowadays and becoming popular and also more diversified in use in the recent years. This study applies the retaining wall design as an example to construct a mechanism for complicated computation in civil engineering directly in a network server for risk assessment, so that a user can easily carry out the computation analysis with any available device via internet by using a personal computer or mobile device. To develop a convenient as well as time-saving operating environment for the remote analysis, an effective interactive interface is also developed. In the retaining wall design, this study provides users with the Rankine method, Coulomb method, and theory of plasticity to perform the objective analysis. The automatic checking system of the program will validate the computation results, under this circumstance, users need not worry about whether their input data and calculated results are consistent with practical standards and regulations or not. Various factors of safety, for risk assessment, resulting from the three kinds of computational methods are compared to verify whether there is any significant difference among them while designing a safe retaining wall overall.     

The geochemistry of indium

A double-arc spectrochemical procedure was used to analyse numerous minerals and rocks for indium. The method had sensitivity of the order of 0.02 ppm In with precision of ±20%.     

The geochemistry of strontium

The geochemistry of strontium has been investigated, using an emission spectrographic technique checked by isotope dilution analyses described elsewhere ( et al., in press). Hence the determinations are claimed to have good accuracy as well as precision.

Approximately 700 analyses have been made on silicate rocks and over 300 on carbonate materials (a detailed analysis of the latter appearing in other papers). An attempt was made at a representative sampling of the crust of the earth.

The difference in behaviour of strontium relative to calcium in granitic rocks as compared to basaltic rocks is striking. For granitic rocks there is an increase of strontium content with an increase in calcium not only for samples from a single batholith but also when extended to a universal sampling. On the other hand, though some differentiated basaltic bodies show a covariance of strontium and calcium, it is always with the strontium content increasing as the calcium content decreases. On a worldwide basis, however, this relationship is destroyed because marked regional variations subdue any differentiation effects that might be present locally.

The crustal abundance of strontium in basaltic rocks may be estimated without difficulty by taking a simple average, but a similar procedure for granitic rocks is ruled out because of the dependence of strontium content on rock-type. The table below summarizes the abundances of strontium in the various phases of the earth's crust.