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

Abstract: 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 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.

Key words: hydraulic structure engineering, node virtual flow method, variational inequality of Signorini type, complementarity constraints, improved algorithm