The influence of source terms on stability,accuracy and conservation in two‐dimensional shallow flow simulation using triangular finite volumes

The two‐dimensional shallow water model is a hyperbolic system of equations considered well suited to simulate unsteady phenomena related to some surface wave propagation. The development of numerical schemes to correctly solve that system of equations finds naturally an initial step in two‐dimensional scalar equation, homogeneous or with source terms. We shall first provide a complete formulation of the second‐order finite volume scheme for this equation, paying special attention to the reduction of the method to first order as a particular case. The explicit first and second order in space upwind finite volume schemes are analysed to provide an understanding of the stability constraints, making emphasis in the numerical conservation and in the preservation of the positivity property of the solution when necessary in the presence of source terms. The time step requirements for stability are defined at the cell edges, related with the traditional Courant–Friedrichs–Lewy (CFL) condition. Copyright © 2007 John Wiley & Sons, Ltd.     

Calculation of electroosmotic inflow to hydraulic fractures

A plane flow through a porous medium in the neighborhood of a hydraulic fracture under the action of a potential difference applied between a well (sink) and an external electrode is considered. The problem of calculating the electric field and the induced flow through the porous medium is solved with allowance for the finite electric and hydraulic resistance of the fracture. The problem reduces to a system of singular integral equations for the distribution of the densities of hydraulic and electric sinks along the fracture. This is solved numerically, after which all the parameters of interest can readily be reconstructed. Calculation results illustrating the effect of the fracture resistance on the magnitude and distribution of the electroosmotic flow are given.     

Hydraulic radius and transport in reconstructed model three-dimensional porous media

Methods for reconstructing three-dimensional porous media from two-dimensional cross sections are evaluated in terms of the transport properties of the reconstructed systems. Two-dimensional slices are selected at random from model three-dimensional microstructures, based on penetrable spheres, and processed to create a reconstructed representation of the original system. Permeability, conductivity, and a critial pore diameter are computed for the original and reconstructed microstructures to assess the validity of the reconstruction technique. A surface curvature algorithm is utilized to further modify the reconstructed systems by matching the hydraulic radius of the reconstructed three-dimensional system to that of the two-dimensional slice. While having only minor effects on conductivity, this modification significantly improves the agreement between permeabilities and critical diameters of the original and reconstructed systems for porosities in the range of 25–40%. For lower porosities, critical pore diameter is unaffected by the curvature modification so that little improvement between original and reconstructed permeabilities is obtained by matching hydraulic radii.     

土壤侵蚀的流体力学机制（Ⅱ）－风蚀

土壤的加速侵蚀已成为当前全球性环境灾害之一．对土壤侵蚀及其预防、控制的研究引起了人们的普遍关注．本文通过对国外文献的广泛调研，系统地分析与评价了有关土壤风力侵蚀的研究进展．     

非饱和土壤水分运动参数的分析

本文以土壤水动力学理论为基础，通过室内外试验及野外实测动态资料的分析和计算，确定了非饱和土壤水分运动的参数（土壤水分特征曲线，导水率和扩散度），为新疆乌鲁木齐地区评价地下水资源量提供了可靠的依据．     

The development and influence of gas bubbles in phreatic aquifers under natural flow conditions

In a phreatic aquifer, bubbles may result from the entrapment of air during groundwater recharge and/or bacterial metabolism. The calculated critical depth of about 1 m at which bubbles are most likely to be found in a granular aquifer, coincides with the depth of 0.60 m of an almost stagnant water layer (specific discharge 1 × 10^-6 cm sec^-1) found at the water table region under natural flow conditions. Bubbles clog pores and therefore reduce the hydraulic conductivity without significantly reducing the volumetric water content. Stagnation at the water table region results since prevailing pressures (in the order of 10^-1 atmospheres) are not sufficiently large to move bubbles through porous media in a water environment.     

Effective hydraulic conductivities in unsaturated heterogeneous media by Monte Carlo simulation

When modeling flow and transport through unsaturated heterogeneous geological deposits, it may be neither computationally nor technically feasible to account for the actual heterogeneity in the simulations. One would fall short in terms of technical feasibility because there is simply no way that the entire spatial domain could be characterized (e.g., you cannot measure hydraulic conductivity at every location at a site). With respect to computational feasibility, the non-linear nature of the Richards equation (which is used to model the flow process) makes simulation of most sites extremely computationally intensive. The computational roadblock is being dismantled as computer hardware advances, but our inability to precisely characterize geological heterogeneity is expected to remain with us for a very long time. To address this problem, the analyst typically uses average or effective properties to model flow and transport behavior through heterogeneous media. In this paper, a variety of approaches for developing effective unsaturated flow properties are assessed. Computational results have been obtained which give the hydraulic conductivity ratios (K _parallel/K _nomal) for highly nonisotropic layered materials. These results are compared with analytical models. Good agreement was obtained for all soil saturation levels except for extremely dry conditions.This work was performed at Sandia National Laboratories, which is operated for the U.S. Department of Energy under contract number DE-AC04-76DP00789.     

Uncertainty Propagation in Layered Unsaturated Soils

This study analyzes the wetting front migration in layered unsaturated soils which have uncertain hydraulic properties. A Monte Carlo scheme was used to propagate the uncertainty of hydraulic parameters. RANUF, a computer program, was developed to solve the one-dimensional, pressure-based form of Richards' equation and to implement the Monte Carlo scheme.Uncertainty propagation was investigated for two-layered soils of various alternating fine over coarse or coarse over fine layer configurations and of various nonrandomized and/or randomized layer arrangements. The effects of changing initial and boundary conditions were also investigated. Randomness was introduced via the saturated hydraulic conductivity, K _s, which was assumed to be distributed lognormally with a coefficient of variation of about 10 percent.It was found that in layered soils the mean profiles (i.e., water content and pressure head) remained essentially unchanged regardless of which layer (or layers) was (or were) randomized; however, the variance profiles were affected. Also, higher uniform initial water content tended to inhibit uncertainty, but higher supply rates did not show any characteristic trend for uncertainty behavior.     

Equations of nonisothermal filtration in fast processes in elastic porous media

The problem of the nonisothermal joint motion of an elastic porous body and the fluid filling the pores is considered for the case where the duration of the physical process is fractions of a second. A rigorous derivation of averaged equations (equations not containing fast oscillating coefficients) based on the Nguetseng two-scale convergence method is proposed. For various combinations of physical parameters of the problem, these equations include anisotropic nonisothermal Stokes equations for the velocity of the fluid component and the equations of nonisothermal acoustics for the displacements of the solid component or anisotropic nonisothermal Stokes equations for a single-velocity continuum. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 113–129, July–August, 2008.