Fast iterative solution of large undrained soil‐structure interaction problems

In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd.     

三维斜压模式对冬季南海环流的数值计算

用一个三维、自由表面、原始方程模式对南海环流进行了计算.计算结果表明:黑潮在巴士海峡以西呈一反气旋弯曲流动路径,有一相对高温高盐的水舌从巴士海峡伸入南海,表明有部分黑潮水侵入南海.冬季南海的一些观测事实在模式结果里得到了很好的反映,像冬季逆风向东北方向流动的“南海暖流”和一些中尺度涡旋.同时还分析了巴士海峡沿120.75°E断面的流速和盐度的垂直结构,并同观测结果进行了比较.根据模式结果,我们还进一步讨论了“南海暖流”的形成和驱动机制.     

南海罗斯贝变形半径的地理及季节变化

根据南海 1°× 1°网格的标准层季节平均温、盐度资料 ,在未引入Boussinesq近似条件下 ,采用改进的Thompson Haskell算法求解线性化斜压海洋水平大尺度波的垂直结构方程 (重力内波方程 ) ,从而得到了南海各网格点的第一斜压重力波相速度和相应的罗斯贝变形半径 ,并探讨其地理分布和季节变化特征 ,以期有助于南海环流和中尺度涡旋以及有关海洋侧边界效应的研究。     

珠江河口西南风强迫下潮流场的数值模拟

采用Backhaus三维斜压模型模拟了均匀西南风场对珠江口近岸海域的影响，并与无风情况作了对比；通过对珠江河口盐度场及风生环流的分析比较，结果表明，模型较为真实地再现了夏季珠江河口的水动力学特性。     

Baroclinic Buoyancy-Inertia Joint Stability Parameter

At present, the barotropic buoyant stability parameter has been derived from a vertical virtual displacement of a water parcel. The barotropic inertial stability parameter in the eccentrically cyclogeostrophic, basic current field was derived in 2003 from a horizontal cross-stream virtual displacement of a parcel. By expressing acceleration of a parcel due to a virtual displacement, which is arbitrarily sloping within a vertical section across the basic current, in terms of natural coordinates, we derived the vertical component of baroclinic buoyant stability parameter B ₂ ², the horizontal component of baroclinic inertial stability parameter I ₂ ², the baroclinic joint stability parameter J ², its buoyant component B ² and its inertial component I ². B ² is far greater than I ₂ ², and when neglecting relative vorticity except for vertical shear, a downward convex curve of J ² plotted against the slope of a virtual displacement follows a trend of B ² curve. If a parcel displaces along a horizontal surface or an isopycnal surface, however, B ² vanishes, and J ² becomes equal to I ². Actual parcel is apt to displace not only along the bottom slope, but also along the sea surface and an isopycnal interfacial surface, which is approximately equivalent to an isentropic surface, preferred by lateral mixing and exchange of momentum. Such actual displacement makes B ² vanishing, and grants I ² an important role. The present analysis of I ² examining effects due to curvature and horizontal and vertical shear vorticities are useful in deepening our understanding of baroclinic instability in actual oceanic streams.     

BP神经网络在局部似大地水准面精化的应用

针对高程拟合中的模型误差问题,采用BP神经网络方法进行拟合,可以减小模型误差,提高似大地水准面的精化精度。在焦作市局部似大地水准面精化算例中,BP神经网络高程拟合取得了良好的效果。     

新疆地区夏季平流层低层风场特征分析及数值模拟

利用2017年6—8月的FNL再分析资料分析了新疆地区夏季平流层低层风场的时空演变特征，开展了平流层低层风场的高分辨率数值模拟和检验。结果表明：新疆地区夏季平流层纬向风随时间的变化存在经向差异，同时准零风层开始和结束的时间也存在经向差异，准零风层开始时间南部地区早于北部地区，而准零风层结束时间则相反。整个夏季新疆地区上空的准零风层处于70～40 hPa之间，其高度随时间呈先降低而后升高的变化趋势。准零风层数值模拟结果表明，模拟的准零风层参数与探空资料分析结果相比二者存在一致的变化趋势，准零风层起始高度的平均绝对误差为467 m，该高度对应的风速均方根误差为1.75 m/s。     

Phillips模式的斜压不稳定的非线性饱和问题:能量情形

A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model-the case of energy-is studied within the context of Arnold's second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd's; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances φ'i at any time.     

正常椭球内部场的内蕴几何与密度分布

将重力场内蕴几何结构的研究引入到正常椭球内部场的研究中，深入探讨了内蕴几何量及其与内部物理量之间的关系，并据此建立了弱平衡条件下的基本微分方程，进而给出确定椭球内部内蕴几何量与场源密度分布的方法。研究表明，平衡形状理论中的Ｗａｖｒｅ公式和Ｃｌａｉｒａｕｔ方程可由内蕴几何与内部物理量之间的关系导出，它们是在平衡假设下取椭球近似的结果。     

“96.8”特大暴雨的中尺度对流云团特征

１９９６年８月３－５日河北省的西南部地区出现了特大暴雨过程。此次特大暴雨，主要是８６０８号台风登陆后减弱为低气压西北上，副热带高压加强西进，低层从东北部有弱冷空气扩散南下，在暴雨区域形成湿斜压锋区，触发不稳定能量释放，致使台我低压北方形成３个中尺度对流云团所致。