Comparing analytical and numerical solution of nonlinear two and three‐dimensional hydrostatic flows

New test cases for frictionless, three‐dimensional hydrostatic flows have been derived from some known analytical solutions of the two‐dimensional shallow water equations. The flow domain is a paraboloid of revolution and the flow is determined by the initial conditions, the nonlinear advective terms, the Coriolis acceleration and by the hydrostatic pressure. Wetting and drying is also included. Some specific properties of the exact solutions are discussed under different hypothesis and relative importance of the forcing terms. These solutions are proposed for testing the stability, the accuracy and the efficiency of numerical models to be used for simulating environmental hydrostatic flows. The computed solutions obtained with a semi‐implicit finite difference—finite volume algorithm on unstructured grid are compared with the corresponding analytical solutions in both two and three space dimension. Excellent agreement are obtained for the velocity and for the resulting water surface elevation. Comparison of the computed inundation area also shows a good agreement with the analytical solution with degrading accuracy observed when the inundation area becomes relatively large and for long simulation time. Copyright © 2006 John Wiley & Sons, Ltd.     

Founding editor Dr Philip M. Gresho

A numerical technique is presented for the approximation of vertical gradient of the non‐hydrostatic pressure arising in the Reynolds‐averaged Navier–Stokes equations for simulating non‐hydrostatic free‐surface flows. It is based on the Keller‐box method that take into account the effect of non‐hydrostatic pressure with a very small number of vertical grid points. As a result, the proposed technique is capable of simulating relatively short wave propagation, where both frequency dispersion and non‐linear effects play an important role, in an accurate and efficient manner. Numerical examples are provided to illustrate this; accurate wave characteristics are already achieved with only two layers. Copyright © 2003 John Wiley & Sons, Ltd.     

高地应力条件下隧洞开挖动态卸荷的破坏机理初探

分析了高地应力条件下静水压力场中圆形隧洞钻爆开挖时开挖边界上初始应力场动态卸荷效应及破坏机理，并计算了其破坏范围。初始应力动态卸荷时，动应力在隧洞径向表现为卸荷回弹，而在切向出现动应力集中，表现为加载。动态卸荷时间对径向应力的影响较对切向应力大，卸荷时间越短，扰动的幅度越大；初始应力动态卸荷在岩体中所造成的破坏范围较准静态卸荷情况大，卸荷时间越短，破坏范围越大。     

塑性成型弹塑性有限元模拟的静水压力间接计算法

在单元内偏应力导数精度分析的基础上，了偏应力导数佳点逐层积分建立了修正的静水压力间接算法，将该方法应用于金属成型过程的弹塑性有限元模拟中，较好了解决了大步长时应力计算精度低的问题，提高了计算效率，算例表明，在变形总量和应变步长都较大的情况下。用庐方法计算得到的应力和变形载荷仍具有较好的精度。     

Shape and gravitational field of the ellipsoidal satellites

The shape and gravitational field of ellipsoidal satellites are studied by using the tidal theory. For ellipsoidal satellites, the following conclusions were obtained: Firstly, in the early stage of the satellite formation, strong tidal friction allowed the satellites move in a synchronous orbit and evolve into a triaxial ellipsoidal shape. Because the tidal potential from the associated primary and the centrifugal potential from the satellite spin are nearly fixed at the surface, the early satellites are the viscoelastic celestial body, and their surfaces are nearly in the hydrostatic equilibrium state. The deformation is fixed in the surface of the satellite. By using the related parameters of primary and satellite, the tidal height and the theoretical lengths of three primary radii of the ellipsoidal satellite are calculated. Secondly, the current ellipsoidal satellites nearly maintain their ellipsoidal shape from solidification, which happened a few billion years ago. According to the satellite shape, we estimated the orbital period and spinning angular velocity, and then determined the evolution of the orbit. Lastly, assuming an ellipsoidal satellite originated in the hydrostatic equilibrium state, the surface shape could be determined by tidal, rotation, and additional potentials. However, the shape of the satellite’s geoid differs from its surface shape. The relationship between these shapes is discussed and a formula for the gravitational harmonic coefficients is presented.     

Electromechanical-induced antiferroelectricben ferroelectric phase transition in PbLa(Zr,Sn,Ti)O3 ceramic

Antiferroelectric—ferroelectric (AFE—FE) phase transition in ceramic Pb_0.97La_0.02(Zr_0.75Sn_0.136Ti_0.114)O₃ (PLZST) was studied by dielectric spectroscopy as functions of frequency (10²—10⁵ Hz) and pressure (0—500 MPa) under a DC electric field. The hydrostatic pressure-dependent remnant polarization and dielectric constant were measured. The results show that remnant polarization of the metastable rhombohedral ferroelectric PLZST poled ceramic decreases sharply and depoles completely at phase transition under hydrostatic pressure. The dielectric constant undergoes an abrupt jump twice during a load and unload cycle under an electric field. The two abrupt jumps correspond to two phase transitions, FE—AFE and AFE—FE.     

Extraction of Pectin from Satsuma Mandarin Peel: A Comparison of High Hydrostatic Pressure and Conventional Extractions in Different Acids

Satsuma mandarin peel pectin was extracted by high hydrostatic pressure-assisted citric acid (HHPCP) or hydrochloric acid (HHPHP), and the physiochemical, structural, rheological and emulsifying characteristics were compared to those from conventional citric acid (CCP) and hydrochloric acid (CHP). Results showed that HHP and citric acid could both increase the pectin yield, and HHPCP had the highest yield (18.99%). Structural characterization, including NMR and FTIR, demonstrated that HHPHP showed higher Mw than the other pectins. The viscosity of the pectin treated with HHP was higher than that obtained with the conventional method, with HHPHP exhibiting significantly higher viscosity. Interestingly, all the pectin emulsions showed small particle mean diameters (D_4,3 being 0.2–1.3 μm) and extremely good emulsifying stability with centrifugation and 30-day storage assays, all being 100%. Satsuma mandarin peel could become a highly promising pectin source with good emulsifying properties, and HHP-assisted acid could be a more efficient method for pectin extraction.     

Ba2-xLaxTi4O11在静高压下的拉曼振动光谱及软模相变研究

 本文测量了Ba_1.8La_0.2Ti₄O₁₁和Ba_1.6La_0.4Ti₄O₁₁在静高压下的拉曼振动谱，发现了软模的耦合模行为。通过比较Ba₂Ti₄O₁₁的热力学理论计算值和实验数据，确认这种耦合是软模和一个声学模间的耦合，发生的相变是一个由具有B_g对称性的带中心软光学声子驱动的二级铁弹相变。     

4.5 GPa静水压活塞圆筒式高压装置的压力检测分析及压力校正

 本文提供了提高现有活塞圆筒式高压装置流体静压强的一种实验方法。成功地制作了锰铜丝压力计，并利用铋丝相变准确地做了压力校正。各箍的应力检测分析和相对位移测量都表明：无论压腔空载或充液时，在0.000 1~3.08 GPa均不显示出同步箍紧作用；上下缸的压强差偏大带来高压暴露的危险。为把流体静压强提高到3.08 GPa以上，建议改进设计；（1）内箍中箍合二为一，外箍分为上下二层，将增加箍力；（2）调整各箍之间接触圆锥面的面积，将有助于同步箍紧；（3）增大密封套圈的无支承面，将减少上下缸压差，有利于安全运行。     

表面承受常静水载荷下弹性半无限体的表面稳定性分析

本文应用小变形叠加到大变形上的分析方法,考察了表面受常静水载荷作用下可压缩和不可压缩弹性半无限体的表面平面应变失稳问题,得到了各自的临界屈曲条件的一般形式.在此基础上.分别对由Blatz-Ko材料和谐和材料所组成的可压缩弹性半无限体以及由Mooney材料所组成的不可压缩弹性半无限体,详细讨论了表面所受的静水压力对临界屈曲条件的影响.