›› 2018, Vol. 39 ›› Issue (1): 349-355.doi: 10.16285/j.rsm.2017.0691

• Numerical Analysis • Previous Articles     Next Articles

Theoretical interpretation of nodal virtual flux method and its optimized algorithm

ZHOU Bin1, YAN Jun2, LIU Si-hong3, YANG Mao-sheng1   

  1. 1. Zhejiang Design Institute of Water Conservancy and Hydro-electric Power, Hangzhou, Zhejiang 310002, China; 2. Research Institute of Geotechnical Engineering, China Institute of Water Resources and Hydropower Research, Beijing 100038, China; 3. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, Jiangsu 210098, China;4. Country Garden Property Development Limited Company, Foshan, Guangdong 528312, China
  • Received:2017-04-13 Online:2018-01-10 Published:2018-06-06
  • Supported by:

    This work was supported by the National Natural Science Foundation for the Young Scholars of China (51409278, 51609149).

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

CLC Number: 

  • TV 139.1

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