Godunov格式下高精度二维水流-输运耦合模型

针对复杂流体运动中物质输运方程的数值求解面临地形复杂、数值阻尼过大以及数值振荡等难题,建立了Godunov格式下求解二维水流-输运方程的高精度耦合数学模型,提出了集成输运对流项的HLLC (Harten-Lax-van Leer-Contact)型近似黎曼算子,可同时计算水流通量及输运通量,不仅有效模拟了复杂地形上水流运动,而且解决了输运方程中对流项产生的数值阻尼过大和不稳定振荡等难题。采用水深-水位加权重构技术和Minmod限制器,提高了模型处理复杂混合流态的能力,同时结合Hancock预测-校正方法,使模型具有时空二阶精度。算例结果表明,模型精度高、稳定性好,能有效抑制数值阻尼,适合模拟实际复杂流体运动中物质的输运过程,具有较好的推广应用价值。     

水体交换年龄模型研究

采用剖开算子法,把水体年龄控制方程分成几个连续的初值问题。在任意三角形网格中,分别对不同性质的算子采用各自适合的算法,即采用特征线法求解对流分步,采用半隐式有限元法求解扩散分步和传播分步。利用水体交换模型试验结果和水体年龄对称特性解析解对所建立的年龄模型进行了验证计算,结果表明,建立的水体年龄模型计算结果与试验结果、解析解结果吻合,可较好地预测水体交换年龄。     

基于非充分掺混模式的流域来水组成模型

针对如何减小数值求解对流输运方程耗散误差的问题,引进断面计算浓度的概念来计算河段平均浓度,提出了非充分掺混模式的有限控制体积法离散对流输运方程的新算法,据此构建了模拟流域内的水源组成以及不同水源在流域内的时空变化情况的流域来水组成模型。通过数值试验与具体实例验证,结果表明所提出的非充分掺混模式的新算法可有效地提高流域来水模型的计算精度。     

三维溶质运移问题的分步广义迎风解法

对对流占优的三维溶质运移问题提出了分步广义迎风解法，首先利用Ｎ．Ｎ．Ｙａ－ｎｅｎｋｏ对水动力弥散方程分步求解的思想，将原来的一个定解问题分解为两个定解问题即对流定解问题和扩散定解问题，对对流定解问题采用广义迎风对偶单元均衡法求解，对扩散定解问题采用一般的Ｇａｌｅｒｋｉｎ有限元法求解，不仅避免了用一般有限元法和有限差分法求解对流占优的地下水水质数学模型时常出现数值弥散和过量问题，而且避免了求节点速度这一步，节省运算步骤，对井点的浓度变化给出了更合适的求解方法。     

三维溶质运移问题的分步广义迎风解法

对对流占优的三维溶质运移问题提出了分步广义的迎风解法，首先利用Ｎ，Ｎ，Ｙａｎｅｎｋｏ对水动力弥散方程分步求解的思想，将原来的一个定解问题分解为两个定解问题即对流定解问题和扩散定解问题，对对流定解问题采用广义迎风对偶单元均衡法求解，对扩散定解问题采用一般的Ｇａｌｅｒｋｉｎ有限元法求解，不仅避免了用一般有限元法和有限差分法求解对流占优的地下水水质数学模型时常出现数值弥散和过量问题，而且避免了求节眯速度     

饱和水流溶质运移问题数值解法综述

本文总结了饱和水流中溶质运移方程求解的各种数值方法，分析各种方法的本质特征以及各自的优缺点，并指出了求解对流—弥散方程的各种数值方法的研究进展和值得重视的问题。研究结果表明，自适应欧拉—拉格朗日法(EM)是溶质运移问题中，求解对流—弥散方程是比较有发展潜力的方法之一。以MMOC法为基础在陡峰值高价插值和其它区域低价插值相结合的ELM法，将是未来发展的趋势。而寻求非规则网格上高精度的空间单元插值模式，已开始成为求解对流问题数值方法研究的重点和关键问题。     

求解对流占优地下水水质模型的有限元高精度广义迎风单元均衡格式及应用

根据水质模型的具体特点，对不同的方程采用不同方法，水流问题用有限元法；对流弥散方程先用算子分裂的方法分解为两个方程，即对流方程和弥散方程，前者用高精度广义迎风格式求解，对弥散方程则采用多单元均衡格式法求解，最后合成为高精度广义迎风均衡格式求出溶质浓度。通过对数值实验例子的计算和实验溶质迁移的模拟，可以看出在求解对流弥散定解问题时，广义迎风均衡格式克服了有限元数值波动和浓度出现负值的问题，与有限元相比有较大改进。     

基于非结构网格有限体积法的二维高精度物质输运模拟

在二维任意多边形无结构网格有限体积水流模型的基础上,通过无插值的通量重构和引入限制因子建立物质输运的高精度无数值震荡数学模型,并从理论上分析了模型的单调和稳定条件.通过旋转流中圆形分布的对流输运算例对模型进行检验,结果表明模型具有守恒、高精度无数值震荡等优点.最后将模型应用到瓯江河口的盐度输运模拟,计算的潮位、流速和盐度过程与原型吻合良好.     

带横隔板圆柱绕流特性数值模拟

为揭示尾迹区添加横隔板对圆柱绕流流场特性影响,把多步格式引入到特征线算子分裂有限元法中,建立了基于多步格式的特征线算子分裂有限元法:在每个时间步内将Navier-Stokes方程分裂成对流项和扩散项,对流项时间离散采用多步格式,在每一子时间步内沿特征线展开并显式求解。方腔流数值模拟结果表明该算法既可降低对整体时间步长的要求又可提高计算精度。对比有无横隔板圆柱绕流流场和圆柱表面压力变化表明,横隔板可以有效地抑制绕流尾迹区涡旋脱落,提高圆柱背流面压力,减少圆柱上下表面的压力差。     

占优问题的通量校正运移解法

描述非饱和土壤中溶质运移的对流弥散方程可分成两部分：对流部分用通量校正运移(FCT)算法求解；弥散部分用常规的隐式差分方法求解.FCT算法包括两个阶段，一个是低阶运移阶段，这一阶段的解，可能会引进过量的数值弥散；另一个是高阶通量校正阶段，通过对反扩散通量进行校正(限定)，可有效地消除数值弥散和数值振荡.而水体积分数用FUCG方法求得，能保持质量守恒.通过数值例子验证了FCT算法的有效性.     

Crack propagation analysis with Galerkin boundary element method

This paper describes the application of symmetric Galerkin boundary element methods (SGBEM) for the analysis of a 2D crack propagation problem. The sub-domain SGBEM for crack problem is derived. The coefficient matrix is completely symmetric. Cohesive crack model is used to simulate crack propagation. The increment control method for crack propagation and the method for unknown crack propagation path have been derived for high-order element. Two-stage interpolation method called the ‘quasi-higher order element method’ (QHOEM) is then proposed to solve the double integrals. In the initial stage, it uses higher order elements to interpolate the field variables, and for the numerical integration involved, it further uses interpolation functions to decompose the higher order elements into lower order elements so that the existing analytical integration can be applied. A finite rectangular plate containing a centre crack growth and four-points bending beam problem have been analysed to check the accuracy of the proposed method. For actual application, a dam buttress with an edge crack has been analysed and the results are found to be in agreement with the other numerical and experimental results. Copyright © 2004 John Wiley & Sons, Ltd.     

非饱和渗流问题的自适应欠松弛变量变换方法

在使用有限元方法求解非饱和土渗流问题时,土-水特征曲线和渗透率函数的强烈非线性经常会造成计算中出现迭代不收敛、计算误差大等问题。基于变量变换的思想,结合时间步长自适应技术提出了一种求解非饱和渗流问题的新方法--欠松弛RFT变换方法（ATUR1）。ATUR1方法通过变量变换,大大降低了Richards方程中未知数在空间和时间上的非线性程度,从而改善这种非线性所带来的计算收敛困难和精度差等问题。欠松弛技术的引入减少了迭代过程中的振荡现象,进一步提高了非线性迭代计算的效率。时间步长自适应技术则有效地控制整个计算过程的误差。数值算例结果说明,ATUR1可以有效地提高计算效率和精度,是一种准确有效的计算方法。     

An efficient finite–discrete element method for quasi‐static nonlinear soil–structure interaction problems

An efficient finite–discrete element method applicable for the analysis of quasi‐static nonlinear soil–structure interaction problems involving large deformations in three‐dimensional space was presented in this paper. The present method differs from previous approaches in that the use of very fine mesh and small time steps was not needed to stabilize the calculation. The domain involving the large displacement was modeled using discrete elements, whereas the rest of the domain was modeled using finite elements. Forces acting on the discrete and finite elements were related by introducing interface elements at the boundary of the two domains. To improve the stability of the developed method, we used explicit time integration with different damping schemes applied to each domain to relax the system and to reach stability condition. With appropriate damping schemes, a relatively coarse finite element mesh can be used, resulting in significant savings in the computation time. The proposed algorithm was validated using three different benchmark problems, and the numerical results were compared with existing analytical and numerical solutions. The algorithm performance in solving practical soil–structure interaction problems was also investigated by simulating a large‐scale soft ground tunneling problem involving soil loss near an existing lining. Copyright © 2011 John Wiley & Sons, Ltd.     

岩土体渗流自由面问题的重心插值无网格方法

岩土体的渗透破坏、地下工程的防渗设计等无不与渗流计算有关。针对渗流自由面问题,提出一种重心拉格朗日插值的配点型无网格方法。由于渗流自由面问题的求解区域是不规则区域,该方法通过将不规则求解区域嵌入一个正则矩形区域,在正则区域上采用重心拉格朗日插值近似未知函数,利用配点法离散渗流问题的控制方程,将重心拉格朗日插值的微分矩阵离散成代数方程表达的矩阵形式。将自由面上的边界条件通过重心拉格朗日插值离散,通过置换方程法和附加方程法施加边界条件,利用正则区域上的重心插值配点法,通过迭代确定最终自由面的位置。数值算例表明所提出的无网格方法对于求解渗流自由面问题的正确性和高精度。     

自由度具有物理含义的线性无关高阶数值流形法

数值流形方法（NMM）基于两套覆盖（数学和物理覆盖）和接触环路而建立,能够统一地处理岩土工程中的连续和非连续变形分析问题。与其他基于单位分解理论的数值方法一样,NMM可以自由地提高物理片上局部位移函数（多项式）的阶次,从而在不加密网格的情况下显著地提高计算精度,但有可能会使总体刚度矩阵奇异,产生线性相关问题。针对这种情况,引入了一种新的高次多项式形式的局部位移函数,在此基础上,建立了新的NMM求解体系,并应用于求解一般的弹性力学问题。结果表明：它有效地消除了线性相关问题;较之传统局部位移函数取一次多项式的NMM,达到了更高的精度;节点应力是连续的;定义在物理片上的所有自由度都具有明确的物理含义,其中第3～5个刚好是物理片所对应插值点处的应变分量,因此,直接获得此处的应力状态。该方法可以很容易地推广到其他基于单位分解的数值方法中。     

地下水溶质运移数值模拟中减少误差的新方法

地下水中污染物运移的数值模拟方法一直是学界的研究热点问题.而如何减少与消除对流-弥散方程数值解中浓度陡锋面附近的数值振荡与数值弥散,更是研究的前沿与难点.提出了一种地下水溶质运移数值模拟中减少数值弥散的新方法.该方法的核心思想是在水动力弥散系数上加上一个数值弥散估算值,得到一个修正弥散系数,用其替代方程中有明确物理意义的水动力弥散系数进行计算.并提出了一个参数——数值弥散因子(μ_NDF),可以根据研究需要进行参数分区并适当调节该因子的大小,从而达到控制数值振荡,减小数值弥散的目的.从一维到二维的多个数值算例的模拟计算结果表明,该方法能在消除数值振荡的基础上,较好地减少数值弥散,达到满意的精度.     

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton–Rogers–Lapwood problem in a fluid-saturated porous medium. The Horton–Rogers–Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton–Rogers–Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton–Rogers–Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton–Rogers–Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. © 1997 by John Wiley & Sons, Ltd.     

A new SPH-based approach to simulation of granular flows using viscous damping and stress regularisation

The smoothed particle hydrodynamics (SPH) method was recently extended to simulate granular materials by the authors and demonstrated to be a powerful continuum numerical method to deal with the post-flow behaviour of granular materials. However, most existing SPH simulations of granular flows suffer from significant stress oscillation during the post-failure process, despite the use of an artificial viscosity to damp out stress fluctuation. In this paper, a new SPH approach combining viscous damping with stress/strain regularisation is proposed for simulations of granular flows. It is shown that the proposed SPH algorithm can improve the overall accuracy of the SPH performance by accurately predicting the smooth stress distribution during the post-failure process. It can also effectively remove the stress oscillation issue in the standard SPH model without having to use the standard SPH artificial viscosity that requires unphysical parameters. The predictions by the proposed SPH approach show very good agreement with experimental and numerical results reported in the literature. This suggests that the proposed method could be considered as a promising continuum alternative for simulations of granular flows.