Explicit Schemes for Dam-Break Simulations

Dam-break problems involve the formation of shocks and rarefaction fans. The performance of 20 explicit numerical schemes used to solve the shallow water wave equations for simulating the dam-break problem is examined. Results from these schemes have been compared with analytical solutions to the dam-break problem with finite water depth and dry bed downstream of the dam. Most of the numerical schemes produce reasonable results for subcritical flows. Their performance for problems where there is a transition between subcritical and supercritical flows is mixed. Although many numerical schemes satisfy the Rankine-Hugoniot condition, some produce solutions which do not satisfy the entropy condition, producing nonphysical solutions. This was the case for the majority of first-order schemes examined. Numerical schemes which consider critical flow in the solution are guaranteed to produce entropy satisfying solutions. Second-order schemes avoid the generation of expansive shocks; however, some form of flux or slope limiter must be used to eliminate oscillations that are associated with these schemes. These limiters increase the complexity and the computational effort required, but they are generally more accurate than their first-order counterparts. The limiters employed by these second-order schemes will produce monotone or total variation diminishing solutions for scalar equations. Some limiters do not exhibit these properties when they are applied to the nonlinear shallow water wave equations. This comparative study shows that there are a variety of shock-capturing numerical schemes that are efficient, accurate, robust, and are suitable for solving the shallow water wave equations when discontinuities are encountered in the problem.     

Unstructured Grid Finite-Volume Algorithm for Shallow-Water Flow and Scalar Transport with Wetting and Drying

A high-resolution, unstructured grid, finite-volume algorithm is developed for unsteady, two-dimensional, shallow-water flow and scalar transport over arbitrary topography with wetting and drying. The algorithm uses a grid of triangular cells to facilitate grid generation and localized refinement when modeling natural waterways. The algorithm uses Roe’s approximate Riemann solver to compute fluxes, a multidimensional limiter for second-order spatial accuracy, and predictor–corrector time stepping for second-order temporal accuracy. The novel aspect of the algorithm is a robust and efficient procedure to consistently track fluid volume and the free surface elevation in partially submerged cells. This leads to perfect conservation of both fluid and dissolved mass, preservation of stationarity, and near elimination of artificial concentration and dilution of scalars at stationary or moving wet/dry interfaces. Multi-dimensional slope limiters, variable reconstruction, and flux evaluation schemes are optimized in the algorithm on the basis of accuracy per computational effort.     

Finite-Difference TVD Scheme for Computation of Dam-Break Problems

A second-order hybrid type of total variation diminishing (TVD) finite-difference scheme is investigated for solving dam-break problems. The scheme is based upon the first-order upwind scheme and the second-order Lax-Wendroff scheme, together with the one-parameter limiter or two-parameter limiter. A comparative study of the scheme with different limiters applied to the Saint Venant equations for 1D dam-break waves in wet bed and dry bed cases shows some differences in numerical performance. An optimum-selected limiter is obtained. The present scheme is extended to the 2D shallow water equations by using an operator-splitting technique, which is validated by comparing the present results with the published results, and good agreement is achieved in the case of a partial dam-break simulation. Predictions of complex dam-break bores, including the reflection and interactions for 1D problems and the diffraction with a rectangular cylinder barrier for a 2D problem, are further implemented. The effects of bed slope, bottom friction, and depth ratio of tailwater∕reservoir are discussed simultaneously.     

Discretization of Integral Equations Describing Flow in Nonprismatic Channels with Uneven Beds

Application of the finite-volume method in one dimension for open channel flow predictions mandates the direct discretization of integral equations for mass conservation and momentum balance. The integral equations include source terms that account for the forces due to changes in bed elevation and channel width, and an exact expression for these source term integrals is presented for the case of a trapezoidal channel cross section whereby the bed elevation, bottom width, and inverse side slope are defined at cell faces and assumed to vary linearly and uniformly within each cell, consistent with a second-order accurate solution. The expressions may be used in the context of any second-order accurate finite-volume scheme with channel properties defined at cell faces, and it is used here in the context of the Monotone Upwind Scheme for Conservation Laws (MUSCL)-Hancock scheme which has been adopted by many researchers. Using these source term expressions, the MUSCL-Hancock scheme is shown to preserve stationarity, accurately converge to the steady state in a frictionless flow test problem, and perform well in field applications without the need for upwinding procedures previously reported in the literature. For most applications, an approximate, point-wise treatment of the bed slope and nonprismatic source terms can be used instead of the exact expression and, in contrast to reports on other finite-volume-based schemes, will not cause unphysical oscillations in the solution.     

Evaluation of Advective Schemes for Estuarine Salinity Simulations

Several advective transport schemes are considered in the context of two-dimensional scalar transport. To review the properties of these transport schemes, results are presented for simple advective test cases. Wide variation in accuracy and computational cost is found. The schemes are then applied to simulate salinity fields in South San Francisco Bay using a depth-averaged approach. Our evaluation of the schemes in the salinity simulation leads to some different conclusions than those for the simple test cases. First, testing of a stable, but nonconservative Eulerian-Lagrangian scheme does not produce accurate results, showing the importance of mass conservation. Second, the conservative schemes that are stable in the simulation reproduce salinity data accurately independent of the order of accuracy of each scheme. Third, the leapfrog-central scheme was stable for the model problems but not stable in the unsteady, free surface computations. Thus, for the simulation of salinity in a strongly dispersive setting, the most important properties of a scalar advection scheme are stability and mass conservation.     

Stochastic Analysis of Internal Erosion in Soil Structures—Implications for Risk Assessments

A new modeling framework for internal erosion in heterogeneous stratified soils is developed by combining existing methods used to study sediment transport in canals, filtration phenomena, and stochastic processes. The framework is used to study the erosion process in sediments caused by a flow of water through a covering filter layer that deviates from geometrical filter rules. By the use of spectral analysis and Laplace transforms, mean value solutions to the transport rate and the variance about the mean are derived for a transport constraint at the upstream boundary and a constant initial transport. Increasing the heterogeneity of a defective filter layer in a canal retards the propagation of the expected bed degradation. An implication is that the heterogeneity of the riprap in this respect prolongs the expected degradation process and the expected lifespan of the structure. The increased variance and decreased correlation length of the riprap reduces the confidence of the mean value solution. The stochastic analysis is therefore suitable as part of risk analyses of extreme events such as failure of embankment dams, for which empirical observations are rare.     

Enhanced Dissolution of Trichloroethene: Effect of Carbohydrate Addition and Fermentation Processes

Remediation of source areas is challenging because lingering contaminants are often present as nonaqueous phase liquid (NAPL) and sorbed mass, and therefore difficult to remove via biodegradation or other commonly used remedial methods. Experimental results indicate that enhanced dissolution of a model NAPL, trichloroethene (TCE), can occur through the addition and/or subsequent fermentation of a dilute molasses solution. Enhanced mass transfer occurs by two mechanisms, depending upon whether the molasses solution is fresh or has fermented. The addition of fresh molasses worked to increase TCE solubility (>200%), thereby increasing mass transfer from the NAPL phase. Mixing TCE NAPL with a fermented molasses solution, however, increased TCE mass flux via the formation of a NAPL/aqueous phase emulsion. In addition, fermented liquid may have also decreased the soil partitioning coefficient (Kd) of TCE, indicating that enhanced transfer of sorbed mass to the aqueous phase could also occur in the presence of fermented molasses. These results provide guidance on how remedial systems may be optimized to increase NAPL and sorbed-mass dissolution and are therefore important, particularly when bioremediation is used to polish residual source zones.     

Separation of a midlevel density current from the bottom of a continental slope

The high-salinity water flowing out of the Mediterranean Sea descends to mid depths in the density-stratified ocean, continues as a narrow jet along the Iberian continental slope, and intermittently detaches large-scale eddies (called "Meddies"). This process is important because it maintains the relatively high mean salinity of a major water mass (the "Mediterranean Intermediate Water") in the North Atlantic. Our simplified model of this jet consists of a moving layer with intermediate density rho2 sandwiched between motionless layers of density rho1 < rho2 and rho3 > rho2. The inshore (anticyclonic) portion of the midlevel jet (in the "rho2-water") rests on an inclined bottom (the continental slope), whereas the (cyclonic) offshore portion rests on the density interface of the stagnant deep (rho3) layer. An inviscid, steady, and finite-amplitude longwave theory is used to show that if the cross-stream topographic slope increases gradually in the downstream direction, then the "rho2-jet" is deflected off the bottom slope and onto the upper density interface of the rho3 layer. The computed magnitude of this separation effect is such as to produce an essentially free jet which is removed from the stabilizing influence of the continental topography. It is therefore conjectured that time-dependent effects (baroclinic instability) will produce further amplification, causing an eddy to detach seaward from the branch of the jet remaining on the slope.     

Gradient-Adaptive-Sigma (GAS) Grid for 3D Mass-Transport Modeling

The accuracy of three-dimensional (3D) mass transport modeling strongly relies on how well the vertical structures of the transport processes are resolved with the model resolution. The widely used vertical “stair-stepped” and topography following sigma (σ)-coordinate systems are fixed in time and space. Hence, these techniques often fail to resolve the details of the time varying, and highly nonlinear, activities in the water column. To better capture the geometrical details of these activities, a new vertical solution-adaptive grid method is introduced in this paper. The method takes into account the gradient variation of a selected variable in the mass transport field as an additional controlling factor in σ-coordinate transformation and so the new transformed grid is called a Gradient-Adaptive-Sigma (GAS) grid. The transformed grid spacing automatically adjusts in time and space according to the local solution gradient of the selected variable and converges in the high gradient regions for better resolution. The solution-adaptive method is implemented in a surface water numerical model to transform Cartesian coordinates into GAS coordinates. The model is established on the basis of an operator splitting scheme coupled with a Eulerian-Lagrangian method. Four numerical experiments describing the sediment transport activities of net entrainment and net deposition, and also pollutant dispersion, are performed with the transformed model. The computed results agree with the laboratory measurements. A comparison between the results computed by the GAS-gridded model and a σ-gridded model show that using the GAS-grid arrangement can improve the solution accuracy by as much as one-fold in regions of high solution gradients.     

气相异辛醇影响溴化锂溶液传质特性研究

通过溴化锂溶液传质性能测试装置,研究了气相异辛醇添加量对溴化锂溶液表面张力的影响,以及在降膜吸收的过程中气相异辛醇的添加量和溶液的流量对传质系数的影响。结果表明：气相异辛醇的添加对溴化锂溶液的表面张力和传质系数均有明显影响,表面张力随异辛醇添加量的增加而减小,传质系数的变化规律与其相反。气相异辛醇分子在溶液表面的吸附作用降低了溶液表面张力梯度,从而引起的Marangoni效应,是对流传质强化比增大的重要原因。     

基于波动理论的露天采场爆破振动高程放大效应分析

为研究露天采场边坡爆破振动高程放大效应规律,基于波动理论,根据采场边坡建立沟槽模型,分析爆破振动波在采场边坡中的反射叠加和绕射作用;在萨道夫斯基公式基础上,推导出爆破振动速度衰减的修正公式,用工程实测数据进行了验证。结果表明:露天采场边坡的高程放大效应,是爆破振动波在边坡内部反射叠加和绕射的结果;修正公式预测精度更高,更加适合露天采场边坡爆破振动速度的预测。     

隐伏多空区下露天边坡坡面角优化数值分析

考虑隐伏多空区和坡面角的变化对边坡稳定性影响,采用FLAC3D对露天边坡的65°、66°和67°三种隐伏多空区下坡面角方案进行了稳定性数值模拟计算,通过坡面角的变化分析边坡的整体最大位移变化规律,应用Mohr圆定量分析了典型应力作用区域的岩体破坏程度。研究结果表明:通过三种不同坡面角方案的比选,坡面角为65°时整体边坡的位移变化最小,典型的应力作用区域均未受到明显的破坏,此研究成果为矿山安全经济设计提供了依据。     

Godunov-Type Solutions for Water Hammer Flows

First- and second-order explicit finite volume (FV) Godunov-type schemes for water hammer problems are formulated, applied, and analyzed. The FV formulation ensures that both schemes conserve mass and momentum and produce physically realizable shock fronts. The exact solution of the Riemann problem provides the fluxes at the cell interfaces. It is through the exact Riemann solution that the physics of water hammer waves is incorporated into the proposed schemes. The implementation of boundary conditions, such as valves, pipe junctions, and reservoirs, within the Godunov approach is similar to that of the method of characteristics (MOC) approach. The schemes are applied to a system consisting of a reservoir, a pipe, and a valve and to a system consisting of a reservoir, two pipes in series, and a valve. The computations are carried out for various Courant numbers and the energy norm is used to evaluate the numerical accuracy of the schemes. Numerical tests and theoretical analysis show that the first-order Godunov scheme is identical to the MOC scheme with space-line interpolation. It is also found that, for a given level of accuracy and using the same computer, the second-order scheme requires much less memory storage and execution time than either the first-order scheme or the MOC scheme with space-line interpolation. Overall, the second-order Godunov scheme is simple to implement, accurate, efficient, conservative, and stable for Courant number less than or equal to one.     

Incipient Motion of Riverbank Sediments with Outflow Seepage

Based on a force analysis, an expression is derived to describe the critical Shields number for incipient motion of uniform cohesionless sediment particles on a riverbank slope in terms of flow parameters, outflow seepage, and physical and mechanical properties of sediments. Parametric studies were conducted to investigate quantitatively the effects of hydraulic gradient of seepage, slope angle, and flow direction on the critical Shields number. The results show that the critical Shields number decreases with an increase in the hydraulic gradient. Where bank collapse is concerned, the most dangerous direction of hydraulic gradient of outflow seepage is at an angle equal to the effective internal angle of friction of the sediment mass with respect to slope surface. At a certain value of hydraulic gradient, the critical Shields number decreases with increasing slope angle. Open flow becomes more erosive when the current direction changes from horizontally parallel with the riverbank line to turning downward.     

Obituary: Erich Fromm (1900-1980).

Obituary [Erich Fromm; 1900-1980]. Trained as a psychoanalyst, Fromm emerged, on the basis of his own erudition, as a social critic and moral philosopher of considerable reknown. In a very real sense he applied his gifts as a clinician to diagnoses of the ills of society and of social institutions. His well-known books such as Escape From Freedom, The Sane Society, and The Art of Loving attest not only to his original social insights but also to his ability to communicate his ideas simply and directly to a wide audience. Although Fromm was regarded as a popular writer by academics and as a social psychologist by psychoanalysts (a condescending term in their lexicon), his contributions to social science and to therapeutic practice were considerable. Much of contemporary social criticism follows a model that Fromm laid down. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On a Possible Role of Rayleigh Surface Waves in Dynamic Slope Failures

This contribution addresses the effect of a surface wave on the dynamic behavior of a slope. In particular, the interaction of a Rayleigh surface wave, possibly generated by an earthquake or nearby blasting, with a simple wedge-shaped slope is considered. A two-dimensional elastodynamic analysis suggests that the amplitudes and phase shifts of the surface waves reflected and transmitted at the crest strongly depends on the inclination of the slope face, and the superimposition of the reflected and incident waves may induce large stress amplification and thus produce open cracks in the top surface of the slope. The computational semianalytical results are used to investigate the generation mechanism of slope failure caused in the city of Sendai dynamically by the 1978 Miyagi-ken-oki, Japan, earthquake. Finally, the significance of the effect of Rayleigh wave propagation on dynamic slope stability is discussed in comparison with the influence of body waves.     

Dynamic Memory Computation of Impedance Matrix Method

The computational efficiency of the impedance matrix method has been greatly improved for large pipe networks with various dimensions and complexity. Several numerical methods for solving linear system were modified to deal with the complex domain operation and used into impedance evaluation. Two different memory reduction schemes were developed based on one-dimensional storage and implemented with the biconjugate gradient method and the Gaussian elimination scheme, respectively. A new implementation of the impedance matrix method, namely, the dynamic memory allocation scheme, was introduced to efficiently model hydraulic transients in pipeline systems that have large topological structures. Three hypothetical pipe networks, the multiseries system, the multilooped system, and the multiblock system, were used to test the performance of the developed schemes. The impact of randomizing pipeline parameters, i.e., friction factor, length, and wave speed, on computation efficiency was evaluated and compared. The dynamic memory allocation scheme not only reduces costs substantially in CPU execution time and memory space compared to other schemes but also shows significant potential as a real-time unsteady flow predictor for large pipe networks.     

Finite Analytic Model for Flow and Transport in Unsaturated Zone

The finite analytic method is employed to solve the vertical, two-dimensional subsurface flow and transport equations in an unsaturated zone. The finite analytic method treats the nonlinear coefficient terms of the governing equations as constants in the element so that linearized partial differential equations can be obtained and solved in each element. The accuracy and limitations of the numerical method are systematically explored. The flow and transport simulations are examined using a one-dimensional laboratory infiltration test and an analytical solution of a two-dimensional subsurface transport problem, respectively. In the advection-dominant, vertical, one-dimensional infiltration problem, nine spatial weighting schemes are proposed to evaluate the averaged unsaturated hydraulic conductivity in a discretized element. Among them, the geometric mean weighting scheme provides the most accurate results as compared with the infiltration data. In verification of the two-dimensional solute transport problem, the nine-node elements are placed in the interior domain, and different layers of five-node elements are placed at the boundaries to investigate if the numerical experiment setup was proper and the algorithm was accurate. The developed numerical model is then applied to an irregular-domain landfill leaching problem to reveal the features of subsurface transport in unsaturated zone. Numerical aspects to be further explored are suggested.