An analytical solution for the local suspended sediment concentration profile in tidal sea region

The time-averaged and oscillatory solutions of the one-dimensional vertical (1DV) advection–diffusion equation for the suspended sediment have been derived analytically in a tidal sea region of finite water depth. The basic equation assumes constant eddy diffusivity and settling velocity. No net flux condition is set at the sea surface, while a boundary condition with the erosion rate and depositional velocity is prescribed at the sea bottom. The time-averaged solution has been derived in a straightforward manner, while the advection–diffusion equation governing the oscillatory concentration has been first transformed to a simple diffusion equation and then solved using the Galerkin-eigenfunction method. The former is given in a closed form, while the latter is presented in a series solution.A set of calculations has been performed to examine the change in the vertical structure as well as magnitude of the concentration response function. A possible use of the solution to make an estimate of the erosion rate at the sea bottom based on the concentration information at the sea surface is discussed.     

Runge-Kutta间断有限元格式在一维浅水方程中的应用

针对一维浅水方程组建立了考虑源项离散的Runge-Kutta间断有限元格式,该格式具有通量与源项的和谐性,可以用于求解任意非棱柱体明渠浅水流动问题。所建立的数值模式分别应用于复杂地形下非棱柱体明渠跨临界流浅水流动算例和水跃问题,模拟结果表明,数值解与解析解以及实测值吻合良好,数值格式具有捕捉间断问题中锐利波形的能力。     

A finite element cable model and its applications based on the cubic spline curve

For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.     

求解双相和黏弹性介质波传播方程的间断有限元方法及其波场模拟

间断有限元（Discontinuous Galerkin：DG）方法具有低数值频散、网格剖分灵活、能模拟地震波在复杂介质中传播等优点.因此,本文将一种新的DG方法推广到双相和黏弹性等复杂介质的地震波场模拟,发展了求解Biot弹性波方程和D'Alembert介质波动方程的DG方法.首先通过引入辅助变量将Biot双相介质弹性波方程和D'Alembert介质波动方程转化为关于时间-空间的一阶偏微分方程组,然后对该方程组进行DG空间离散,得到半离散化的常微分方程组.最后,对此常微分方程组,应用加权的Runge-Kutta格式进行时间推进计算.数值结果表明,DG方法可以有效地求解Biot双相介质弹性波方程和D'Alembert介质波动方程,并能很好地压制因离散求解波动方程而产生的数值频散,获得清晰的各种地震波震相.

     

Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach

In this paper, we examine heuristically the reasons for locking in poroelasticity. As a first step, we first reexamine the problem of locking in linear elasticity. From this, we discover how the problem arises in the poroelasticity setting and how the problem might be overcome.     

A space-time discontinuous Galerkin method applied to single-phase flow in porous media

A space-time discontinuous Galerkin finite element method is proposed and applied to a convection-dominant single-phase flow problem in porous media. The numerical scheme is based on a coupled space-time finite element discretization allowing for discontinuous approximations in space and in time. The continuities on the element interfaces are weakly enforced by the flux treatments, so that no extra penalty factor has to be determined. The resulting space-time formulation possesses the advantage of capturing the steep concentration front with sharp gradients efficiently. The stability and reliability of the proposed approach is demonstrated by numerical experiments. The author is grateful to the DFG (German Science Foundation—Deutsche Forschungsgemeinschaft) for the financial support under the grant number Di 430/4-2.     

无单元法在三维断裂力学中的应用

介绍了无单元法在三维断裂力学问题中的应用。无单元法基于滑动最小二乘拟合,只需结点信息就可建立离散模型。采用罚函数法来满足无单元法的本征边界条件。用可视准则来处理裂纹面对高斯点影响域的隔离作用,推导了裂纹两表面的相互作用对整体平衡方程组的贡献方程。利用单点位移公式来计算三维裂纹前缘点的应力强度因子。通过算例验证了应用该法确定三维裂纹前缘应力强度因子的有效性。     

黑龙洞泉域地下水流数值模拟与预测

为了对黑龙洞泉域水资源进行评价, 通过对地质条件、水位观测资料的深入研究, 以水均衡原理、地下水渗流理论为基础, 建立了黑龙洞泉域地下水渗流数值模型.以灰色序列预测模型为辅助手段, 结合历年的降水规律, 对未来现状开采条件下的年均降水量、地下水流场、水位及泉流量进行了不同保证率条件下的预测, 若2010年为丰水年(保证率20%)、平水年(保证率50%)、枯水年(保证率75%), 黑龙洞泉汛期地下水位标高分别为超过130m、达到130m、低于130m, 汛期泉流量分别为超过10m3/s、7m3/s、5m3/s.计算结果有利于指导黑龙洞泉域地下水资源的管理和开发利用.      

Couplex Benchmark Computations Obtained with the Software Toolbox UG

This paper describes the numerical results for the COUPLEX benchmark obtained with the simulation software UG using vertex centered finite volume and higher order discontinuous Galerkin schemes. Multigrid solvers on unstructured grids, local mesh refinement and parallel computation are employed to yield very accurate solutions. Since the full range of results required in the benchmarks is too large to be displayed in this paper we focus on the comparison of discretization schemes, assessment of numerical errors and the presentation of parallel computations.     

基于渗流和管流耦合的管涌数值模拟

堤坝地基的渗透变形过程实际上是“土中水”转变为“水中土”的过程。在渗透变形发生的集中管涌通道区域,采用常规渗流分析理论,单纯增大管涌通道渗透系数的方法是不太合适的。在未发生渗透变形的区域,用常规渗流理论计算;在管涌通道区域,用管流理论,公共边界上两者之间水头相等、流量大小相等且方向相反,能够较好符合渗透变形的发展规律。为了适应计算过程中内部边界条件不断变化的特点,采用无网格法伽辽金法（element free Galerkin method,EFG）对渗流场进行计算。算例计算表明,这种渗流-管流耦合的方法能够模拟管涌通道绕过防渗墙等复杂的发展过程。