结点虚流量法理论基础阐释及改进算法  

Theoretical interpretation of nodal virtual flux method and its optimized algorithm

作　　者：周斌 严俊[3] 刘斯宏[4] 杨茂盛 

机构地区：[1]浙江省水利水电勘测设计院,浙江杭州310002 [2]碧桂园物业发展有限公司,广东佛山528312 [3]中国水利水电科学研究院岩土工程研究所,北京100038 [4]河海大学水利水电学院,江苏南京210098

出　　处：《岩土力学》2018年第1期349-355,共7页Rock and Soil Mechanics

基　　金：国家自然科学基金青年科学基金(No51409278,No.51609149).

摘　　要：含自由面的无压渗流问题本质上是一类非线性自由边值问题,固定网格的结点虚流量法在全域范围内不断扣除虚域流量贡献,从而使该问题得到求解。它具有网格依赖性小、出逸点收敛快等优点,但其内在理论基础尚未被完全揭示。通过引入互补型约束条件建立了结点虚流量法和Signorini型变分不等式提法的等价性桥梁,在此基础上引入过渡区放大系数(35)h对自由面判别准则进行优化,并以砂槽模型试验为例进行验证。对比结果表明,优化后算法数值稳定性更好,计算结果与试验数据吻合度更高。研究成果为超大规模网格的渗控结构优化设计提供了有效分析手段。Seepage with free surface is essentially one type of nonlinear free boundary problems. In order to solve this problem in global domain, the nodal virtual flux method deducts the virtual flux gradually in each iteration. It has the advantages of weak mesh dependency, fast convergence rate, etc. To reveal its internal theoretical foundation, this paper builds an equivalent bridge between the nodal virtual flux method and variational inequality of Signorini type through a complementarity constraint. The criterion of free surface is optimized by introducing an amplification coefficient Ah for transition region, verified through a sand flume model test. The comparisons show that the improved algorithm has better numerical stability and higher curvature tolerance, and provides an effective approach for optimization design of seepage control structure with large-scale grid.

关 键 词：水工结构工程 结点虚流量法 Signorini型变分不等式 互补型约束 改进算法 

分 类 号：TV139.1[水利工程—水力学及河流动力学] TV31