球层中高阶自由热对流格局及其变化的研究

研究了下边界为应力自由边界, 上边界为刚性边界, 纯粹从底部加热的充满了无穷大普朗特数的Boussinesq流体的同心球层中的非线性自由热对流. 借鉴将极型场和扰动温度场展成勒让德多项式（以下称零级数模型, 即此时m=0）的方法, 将它们展成6阶6级（即l=6; m=0, 1, 2, hellip;, l）的勒让德函数（以下称高级数模型）, 并用Galerkin方法求解非线性方程组, 获得了高级数模型的结果. 与零级数模型仅能获得表征物质垂直运移特征和扰动温度结构的二维南北向（rphi;）剖面相比, 高级数模型还得到了东西向（rphi;）和深度剖面（theta;phi;）, 而且对流运动的许多细特征得以体现, 有利于深化认识球层中自由热对流的特征及其导致的温度结构. 瑞利数的大小对自由热对流的格局和速率产生了重要的影响, 控制着对流层中高温热柱区和低温冷柱区的相对大小. 本文所得到的结果可能主要反映了下地幔物质运动, 其对流格局和速率在不同的位置上存在明显的差异, 可能蕴涵了重要的地球动力学含义.      

Analysis and performance of a predictor‐multicorrector Time Discontinuous Galerkin method in non‐linear elastodynamics

A predictor‐multicorrector implementation of a Time Discontinuous Galerkin method for non‐linear dynamic analysis is described. This implementation is intended to limit the high computational expense typically required by implicit Time Discontinuous Galerkin methods, without degrading their accuracy and stability properties. The algorithm is analysed with reference to conservative Duffing oscillators for which closed‐form solutions are available. Therefore, insight into the accuracy and stability properties of the predictor‐multicorrector algorithm for different approximations of non‐linear internal forces is gained, showing that the properties of the underlying scheme can be substantially retained. Finally, the results of representative numerical simulations relevant to Duffing oscillators and to a stiff spring pendulum discretized with finite elements illustrate the performance of the numerical scheme and confirm the analytical estimates. Copyright © 2002 John Wiley & Sons, Ltd.     

The patterns of high-degree thermal free convection and its features in a spherical shell

Introduction Mantle convection is thought to be the most effective way of heat transportation in the earth and the source of driving lithospheric plates (Elasser, 1971). The velocity field of plate motion can be split into poloidal and toroidal parts, which are corresponding to the vertical (i.e. radial) and horizontal motions, respectively, in global model. The toroidal component is manifested in the existences of transform faults and the poloidal one in the presences of convergence and diver…     

A flux-limiting wetting–drying method for finite-element shallow-water models,with application to the Scheldt Estuary

We present a flux-limiting wetting–drying approach for finite-element discretizations of the shallow-water equations using discontinuous linear elements for the elevation. The key ingredient of the method is the use of limiters for generalized nodal fluxes. This method is implemented into the Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM), and is verified against standard test cases. The method is further applied to the wetting and drying of sand banks in the Scheldt Estuary, which is located in northern Belgium and the southern Netherlands. The results obtained for both the benchmarks and the realistic problem illustrate the accuracy of the method in describing the hydrodynamics in the vicinity of dry areas. In particular, the method strictly conserves mass, and there is no transport through dry areas.     

间断伽辽金法(DGM)求解弹性地基梁问题

间断伽辽金法使用节点位移一类未知数作为测试函数,削弱了内部单元边界上的一阶及n阶导数的连续性,大大降低了构造形函数的难度,特别适合控制方程为高阶微分方程问题的求解。基于间断伽辽金法的基本原理,推导了弹性地基梁四阶微分控制方程的积分“弱”形式,编制了计算程序,进行了数值计算和收敛性分析。计算结果表明：用间断伽辽金法求解弹性地基梁问题是十分有效率的。     

耦合有限单元法扩边的直流电阻率勘探无单元Galerkin法正演

本文分析了目前直流电阻率正演模拟中的无单元Galerkin法（EFGM）和有限单元法（FEM）的优缺点,针对采用第一类边界条件需要足够大的计算域时EFGM计算成本高的问题,在计算域外围区域采用FEM扩边,提出了直流电阻率的无单元Galerkin-有限单元耦合法（EFG-FE）.采用具有Kronecker delta函数性质的径向基点插值法（RPIM）构造EFGM形函数,在外围区域将EFGM与FEM直接耦合,无需其他处理手段,消除了传统EFGM与FEM耦合中存在的界面耦合困难.EFG-FE将模型计算域分割为EFGM区域和FEM区域,模型核心区域采用EFGM计算,发挥EFGM灵活性、适应性强和高精度的优点,使得模型建立简单方便,对任意复杂地电模型适应性强,同时获得高精度模拟结果.在模型计算域外围采用快速扩展的FEM单元网格进行剖分,利用其数值稳定性和高效性,使用少量FEM节点和单元网格将计算域大范围扩大满足第一类边界条件,同时不大幅增加计算成本,进而提高计算效率.最后,通过不同正演方法的模型算例的模拟结果对比,验证了本文提出的EFG-FE有效可行,其模拟结果具有很高的模拟精度,且相比于采用第三类边界条件的EFGM提高了计算效率,具有更好的模拟性能.     

非混溶饱和两相渗流与孔隙介质耦合作用的理论研究——方程解耦与有限元公式

通过对上文（ Ｉ）所推证数学模型方程的进一步处理与简化,得到解耦的流场系统压力方程。以 Ｇａｌｅｒｋｉｎ 弱积分解的形式,给出模型方程数值分析的有限元公式,并进行了初步验证     

大体积混凝土温度裂缝扩展过程模拟

大体积混凝土的温度裂缝是关系到水电工程中混凝土大坝安全的重要问题,它贯穿混凝土坝的施工期直至运行期。重点探讨了应用无网格法求解大体积混凝土温度裂缝扩展过程的模拟方法。无网格法采用节点来离散求解域,特别适用于裂缝开裂过程的模拟。结合混凝土热传导问题推导了伽辽金无网格方法控制方程和基本算法步骤,编制了混凝土温度场计算和温度裂缝扩展过程模拟的无网格法程序,通过具体的算例验证了所编制的伽辽金无网格程序的正确性。数值算例的计算结果表明,无网格法能够有效地模拟混凝土块在温度应力作用下的开裂发展过程,计算结果符合大体积混凝土块在均匀温降和基础强约束条件下的裂缝分布规律。