2015, 5(4): 351-357. doi: 10.3934/naco.2015.5.351

Solving the seepage problems with free surface by mathematical programming method

1. 

College of Science, Dalian Nationalities University, Dalian 116600, China, China

Received  January 2015 Revised  October 2015 Published  October 2015

The nonsmooth equations model for seepage problems is proposed based on the basic principles of the seepage dynamic system and the finite element discrete method. The mathematical programming method is therefore applied. The free surface of seepage is plotted through interpolation with pressure intensity on the nodes. The numerical results show the new method is simple and rapid in convergence rate.
Citation: Jinzhi Wang, Yuduo Zhang. Solving the seepage problems with free surface by mathematical programming method. Numerical Algebra, Control and Optimization, 2015, 5 (4) : 351-357. doi: 10.3934/naco.2015.5.351
References:
[1]

K. J. Bathe, Finite element free surface seepage analysis without mesh iteration, Int. J. Numer and Analytical Methods in Geomechanics, 3 (1979), 13-22.

[2]

W. J. Chen and Z. L. Wang, Finite element method of invariable mesh Gauss point for transient seepage problem with free surface, Journal of dalian university of technology, 31 (1991), 537-543.

[3]

C. S. Desai and G. C. Li, A residual flow procedure and application for free surface in porous media, Advances in Water Resources, 6 (1983), 27-35.

[4]

J. S. Pang and L. Q. Qi, Non-smooth equations: motivation and algorithms, SIAM. J. OPTIM., 3 (1993), 443-465. doi: 10.1137/0803021.

[5]

H. Peng et al, Imaginary element for numerical analysis of seepage with free surface, China Rural Water and Hydropower, 3 (1997), 26-27.

[6]

L. Q. Qi, Convergence analysis of some algorithms for solving non-smooth equation, Math Oper Res., 18 (1993), 227-224. doi: 10.1287/moor.18.1.227.

[7]

J. Z. Wang and W. J. Chen, Mixed fixed-Point FE method for seepage problems with free surfaces, Journal of Dalian University of Technology, 47 (2007), 793-797.

[8]

Y. T. Zhang, P. Chen and L. Wang, Initial flow method for seepage analysis with free surface, Chinese journal of Hydraulic, 8 (1988), 18-26.

[9]

H. Zheng et al., A new formulation of Signorini's type for seepage problems with free surface, International Journal for Numerical methods in engineering, online, 2005

show all references

References:
[1]

K. J. Bathe, Finite element free surface seepage analysis without mesh iteration, Int. J. Numer and Analytical Methods in Geomechanics, 3 (1979), 13-22.

[2]

W. J. Chen and Z. L. Wang, Finite element method of invariable mesh Gauss point for transient seepage problem with free surface, Journal of dalian university of technology, 31 (1991), 537-543.

[3]

C. S. Desai and G. C. Li, A residual flow procedure and application for free surface in porous media, Advances in Water Resources, 6 (1983), 27-35.

[4]

J. S. Pang and L. Q. Qi, Non-smooth equations: motivation and algorithms, SIAM. J. OPTIM., 3 (1993), 443-465. doi: 10.1137/0803021.

[5]

H. Peng et al, Imaginary element for numerical analysis of seepage with free surface, China Rural Water and Hydropower, 3 (1997), 26-27.

[6]

L. Q. Qi, Convergence analysis of some algorithms for solving non-smooth equation, Math Oper Res., 18 (1993), 227-224. doi: 10.1287/moor.18.1.227.

[7]

J. Z. Wang and W. J. Chen, Mixed fixed-Point FE method for seepage problems with free surfaces, Journal of Dalian University of Technology, 47 (2007), 793-797.

[8]

Y. T. Zhang, P. Chen and L. Wang, Initial flow method for seepage analysis with free surface, Chinese journal of Hydraulic, 8 (1988), 18-26.

[9]

H. Zheng et al., A new formulation of Signorini's type for seepage problems with free surface, International Journal for Numerical methods in engineering, online, 2005

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